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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 2
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 47-69 
    ISSN: 0271-2091
    Keywords: Partial differential equations ; Non-linear equations ; Coupled system ; Numerical methods ; Finite elements ; Adaptive grid ; Flow in porous media ; Groundwater contamination ; Multiphase flow ; Immiscible flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents numerical examples for the moving grid finite element algorithm derived in Part Ito solve the non-linear coupled set of PDEs governing immiscible multiphase flow in porous media in one dimension. Examples include single- and double-front simulations for two- and three-phase flow regimes and incorporating a mass sink. The modelling approach is shown to achieve significant savings in computation time and memory allocation when compared with fixed grid solutions of equivalent accuracy. This work includes sensitivity analyses for the parameters which are incorporated in the grid adaptation method, including the curvature weights, artificial viscosity and artificial repulsive force. It is found that the curvature weights are exponential functions of the negative ratio of the square root of the domain length to the number of discrete nodes. These weighting parameters are also shown to depend upon the shape of the front. On the basis of the examined simulations, it is recommended that artificial viscosity be neglected in the solution of the coupled non-linear set of PDEs governing multiphase flow in porous media. Similarly, use of a repulsive force is found to be unnecessary in simulations involving the migration of two liquid phases. For multiphase flows incorporating a gas phase it is recommended to use a non-zero value for the repulslive force to avoid development of an ill-conditioned nodal distribution matrix. An equation to evaluate the repulsive force under these circumstances is suggested.
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  • 3
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 4
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 95-108 
    ISSN: 0271-2091
    Keywords: Parallel processing ; Panel methods ; Conjugate gradients ; Computational fluid dynamics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A parallel algorithm for the solution of potential flow problems using the panel method of Hess and Smith and conjugate and bi-conjugate gradient techniques is presented. Analysis of the parallelism for the matrix. solvers shows the algorithms to have scalable properties as the problem size grows indefinitely large. Speed-up and efficiency values are presented along with experimental and theoretical values for the optimum number of processors for maximum speed-up. It is envisaged that the parallel techniques presented here have applications using other boundary integral methods for solving engineering problems of a more complex nature.
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  • 5
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 267-288 
    ISSN: 0271-2091
    Keywords: Compressible flow ; Hypersonic ; Perfect gas ; Time-dependent ; Convection method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A simple convection algorithm for simulation of time-dependent supersonic and hypersonic flows of a perfect but viscous gas is described. The algorithm is based on conservation and convection of mass, momentum and energy in a grid of rectangular cells. Examples are given for starting flow in a shock tube and oblique shocks generated by a wedge at Mach numbers up to 30·4. Good comparisons are achieved with well-known perfect gas flows.
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  • 6
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 147-165 
    ISSN: 0271-2091
    Keywords: Domain decomposition ; Computational fluid dynamics ; Preconditioned Krylov iteration ; Newton's method ; Locally uniform mesh refinement ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The divide-and-conquer paradigm of iterative domain decomposition or substructuring has become a practical tool in computational fluid dynamics applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. We illustrate these features on the classic model problem of flow over a backstep using Newton's method as the non-linear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately and can be combined synergistically. We include sample performance results from an Intel iPSC/860 hypercube implementation.
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  • 7
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 197-215 
    ISSN: 0271-2091
    Keywords: Thermocapillary flow ; Buoyancy ; Free surface ; Finite difference ; Picard iteration ; ADI ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Navier-Stokes-Boussinesq equations governing the transport of momentum, mass and heat in a non-isothermal liquid bridge with a temperature-dependent surface tension are solved using a vorticity-stream-function formulation together with a non-orthogonal co-ordinate transformation. The equations are discretized using a pseudo-unsteady semi-implicit finite difference scheme and are solved by the ADI method. A Picard-type iteration is adopted which consists of inner and outer iterative processes. The outer iteration is used to update the shape of the free surface. Two schemes have been used for the outer iteration; both use the force balance normal to the free surface as the distinguished boundary condition. The first scheme involves successive approximation by the direct solution of the distinguished boundary condition. The second scheme uses the artificial force imbalance between the fluid pressure, viscous and capillary forces at the free surface which arises when the boundary condition for force balance normal to the surface is not satisfied. This artificial imbalance is then used to change the surface shape until the distinguished boundary condition is satisfied. These schemes have been used to examine a variety of model liquid bridge situations including purely thermocapillary-driven flow situations and mixed thermocapillary- and bouyancy-driven flow.
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  • 8
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 217-239 
    ISSN: 0271-2091
    Keywords: Swirling flow ; Swirling angle ; Combustion flow ; κ-∊ model ; Algebraic ; Reynolds stress ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Hot flow of a sudden-expansion dump combustor with swirling is analysed by employing an infinite chemical reaction rate. Turbulence properties are closed using one type of algebraic Reynolds stress model and two types of κ-∊ model. One of the κ-∊ models includes a swirling effect modification to the ε-equation. Computations have been performed by the SIMPLE-C algorithm with a power-law scheme. The calculated results of the momentum fields and turbulence quantities for swirling flow are compared with the available experimental data. It is shown that the standard κ-∊ model gives poor prediction of the mean velocity, particularly the tangential velocity. For the hot flow analysis of a sudden-expansion dump combustor with swirling flow it is suggested that it is necessary to use the modified κ-∊ model or algebraic Reynolds stress model.
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  • 9
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 299-325 
    ISSN: 0271-2091
    Keywords: Compressible gas bearing ; Choked flow ; Finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A theoretical analysis is presented to solve numerically the steady state Navier-Stokes equations, continuity equation and energy equation for a compressible ideal gas flow between two closely spaced, in general nonparallel, infinitely wide plates (siider bearing). The analysis includes the gas inertia effect and covers both non-choked and choked flows. The results of the present analysis compare very well with both analytical and experimental results of compressible flow in a slider bearing comprised of two parallel and stationary plates. It was found that for choked flow the gas inertia effect is important, while the consideration of the energy equation does not affect the accuracy of the calculated flow substantially. Finally, the stiffness of a slider bearing is presented for different geometrical characteristics of the bearing.
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  • 10
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 327-341 
    ISSN: 0271-2091
    Keywords: Vortex shedding ; Unsteady ; Stability analysis ; Continuation methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: It is common knowledge that flow around bluff bodies exhibits oscillatory behaviour. The aim of the present study is to compute the steady two-dimensional flow around a square cylinder at different Reynolds numbers and to determine the onset of unsteadiness through a linear stability analysis of the steady flow. Stability of the steady flow to small two-dimensional perturbations is analysed by computing the evolution of these perturbations. An analysis of various time-stepping techniques is carried out to select the most appropriate technique for predicting the growth of the perturbations and hence the stability of the flow. The critical Reynolds number is determined from the growth rate of the perturbations. Computations are then made for periodic unsteady flow at a Reynolds number above the critical value. The predicted Strouhal number agrees well with experimental data. Heat transfer from the cylinder is also studied for the unsteady laminar flow.
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  • 11
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 505-527 
    ISSN: 0271-2091
    Keywords: Cell vertex ; Accuracy on parallelepipeds ; Triangulated control volumes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The cell vertex method is generalized to three dimensions. It is proved that there exists a one-parameter family of eight-point three-dimensional methods with second-order truncation error on parallelepipeds. Using different triangulations of control volume faces, various finite volume methods are derived. Some of these are identified as members of the aforementioned one-parameter family and may be regarded as second-order upwind schemes. A Fourier analysis is used to investigate the spectral properties of these discretizations.Numerical experiments illustrate that second-order global accuracy is achieved on parallelepiped grids, as suggested by the theory. Randomly perturbed, stretched, sheared meshes are used to test these methods to destruction. It is found that upwinding improves both the accuracy on distorted meshes and the spectrum of the discretization.
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  • 12
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 627-629 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 13
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 609-625 
    ISSN: 0271-2091
    Keywords: 3D extrusion ; Moving boundaries ; Kinematic condition ; Remeshing ; Finite elements ; Free surfaces ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a numerical technique for solving three-dimensional free surface problems in extrusion applications. The method is fully implicit in the sense that a Newton-Raphson scheme is applied on all variables, and geometrically general. In particular, the die section shape may be complex and contains multiple corners: very few restrictions apply on the mesh generation because the method does not require the nodes to be located on straight lines (spines). A clear distinction is introduced between the directions associated with the kinematic condition and the remeshing rules. As a difference with respect to earlier publications, these concepts are handled separately. Only Stokes problems are solved in this paper and we have not introduced surface tension. Therefore corners in the die section propagate discontinuities in the extrudate shape, an a method for relocating corners without losing the quadratic convergence of the scheme is presented. Data structures used for the implementation are briefly discussed.We present results on the extrusion of various profiles, including a rectangular die (a benchmark problem) and various complex sections containing multiple corners.
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  • 14
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 681-705 
    ISSN: 0271-2091
    Keywords: Unsteady Navier-Stokes equations ; Finite element method ; Viscous flow ; Free boundary flow ; Multiphase flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element method for the transient incompressible Navier-Stokes equations with the ability to handle multiple free boundaries is presented. Problems of liquid-liquid type are treated by solving two coupled Navier-Stokes problems for two separate phases. The possibility to solve problems of liquid-gas, liquid-liquid-gas or liquid-liquid-liquid type is demonstrated too. Surface tension effects are included at deformable interfaces.The method is of Lagrangian type with mesh redefinition. A predictor-corrector scheme is used to compute the position of the deformable interface with automatic control of its accuracy and smoothness. The method is provided with an automatic choice of the time integration step and an optional spline filtration of the truncation error at the free surface. In order to show the accuracy of the method, tests and comparisons are presented. Numerical examples include motion of bubbles and multiple drops.
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  • 15
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 753-755 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 16
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 775-791 
    ISSN: 0271-2091
    Keywords: Adaptive grid ; Truncation error ; Recirculating flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this study a method of equidistribution of a weight function for grid adaption is modified to produce a smoother grid which yields a more accurate solution. In the original scheme the weight function was estimated on each grid independently and a large variation in the values of the, weight function could generate a highly skewed and non-uniform grid which produced large errors. In this study the weight function is smoothed by coupling neighbouring weight functions. Abrupt changes in the weight function are alleviated and a smoother grid distribution is obtained. With relatively minor modifications of the original weight function it is demonstrated in this study that the solution can be improved. The test cases presented are the one-dimensional convection-diffusion equation, a laminar polar cavity flow, a laminar backwardfacing step flow and a turbulent reacting sudden expansion pipe flow. Numerical efficiencies ranging from factors of five to 10 are achieved over uniform grid methods.
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  • 17
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 843-859 
    ISSN: 0271-2091
    Keywords: Finite element ; Least squares ; Navier-Stokcs equations ; First-order system ; Velocity-pressure-vorticity ; Equal-order interpolations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A least-squares finite element method based on the velocity-pressure-vorticity formulation was proposed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to the saddle point problem of the classic mixed method and can thus accommodate equal-order interpolations. The method has no parameter to tune. The associated algebraic system is symmetric and positive definite. In order to show the validity of the method for high-Reynolds-number problems, this paper provides numerical results for cavity flow at Reynolds number up to 10 000 and backward-facing step flow at Reynolds number up to 900.
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  • 18
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 883-905 
    ISSN: 0271-2091
    Keywords: Von Mises transformation ; Curved boundaries ; Numerical solution ; Two-phase fluid flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical method to handle the flow of a two-phase fluid over curved boundaries is proposed. The method is based on the double von Mises transformation which is derived in this work and is expected to be applicable to a variety of flow situations while utilizing the finite difference technique. In order to illustrate the numerical implementation of the method, dusty fluid flow through a porous channel possessing curved boundaries and the flow through a semi-infinite porous layer overlying a curved lower boundary are considered. The flow is assumed to be governed by model equations based on Brinkman's equation and reflecting boundary conditions are employed in the study based on a uniform dust particle distribution. Results indicate that an increase in the permeability results in decreasing the tangential velocity component in regions close to the curved boundary, and increasing the dust parameters decreases this component. The effects of the grid size and the extent of the computational domain are discussed. The results also shed some light on the applicability of the dusty fluid flow model and suggest that the model is best employed when the permeability is high, a conclusion that is consistent with the validity of Brinkman's equation.
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  • 19
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 919-934 
    ISSN: 0271-2091
    Keywords: Secondary clarifier ; Numerical model ; Density currents ; Turbulence ; Circular tank ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical model for predicting the velocity field and suspended solids distribution in a secondary circular clarifier with density difference is evaluated. The density effects are characterized by the inlet densimetric Froude number. This study focuses on the role of the reaction baffle position in the performance of the clarifiers. For a large-radius baffle and low densimetric Froude number an important phenomenon known as the density waterfall occurs in the inlet zone of the clarifiers. This was predicted by the numerical model and confirmed by the physical model tests. This model consists of a series of conservation equations for fluid mass and momentum and sediment concentration. The turbulent stresses are calculated by use of the eddy viscosity concept and the κ-∊. turbulence model. The study showed that the density waterfall results in high entrainment and high recirculation. A comparison of the solids concentration distribution for a tank with a small skirt radius to that with a large skirt radius shows that small skirt radius reduces the density waterfall effect and significantly improves the clarifier performance at low densimetric Froude numbers.
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  • 20
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 935-960 
    ISSN: 0271-2091
    Keywords: Riemann solver ; Hypersonic flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper we study an extension of Osher's Riemann solver to mixtures of perfect gases whose equation of state is of the form encountered in hypersonic applications. As classically, one needs to compute the Riemann invariants of the system to evaluate Osher's numerical flux. For the case of interest here it is impossible in general to derive simple enough expressions which can lead to an efficient calculation of fluxes. The key point here is the definition of approximate Riemann invariants to alleviate this difficulty.Some of the properties of this new numerical flux are discussed. We give 1D and 2D applications to illustrate the robustness and capability of this new solver. We show by numerical examples that the main properties of Osher's solver are preserved; in particular, no entropy fix is needed even for hypersonic applications.
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  • 21
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    International Journal for Numerical Methods in Fluids 14 (1992) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 22
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1009-1018 
    ISSN: 0271-2091
    Keywords: Mathematical modeling ; Shock capturing ; Upwind schemes ; Flux difference splitting ; Open channel flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An upwind finite difference scheme based on flux difference splitting is presented for the solution of the equations governing unsteady open channel hydraulics. An approximate Jacobian needed for splitting the flux differences is defined that satisfies the conditions required to construct a first-order upwind conservative discretization of the equations. Added limited second-order corrections make the resulting scheme robust and accurate for the computation of all regimes of open channel flow. Some numerical results and comparisons with other classical schemes under exacting conditions are presented.
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  • 23
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1037-1062 
    ISSN: 0271-2091
    Keywords: Eccentric cylinders ; Fluid convection ; Rotation ; Low-Prandtl-number fluids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical experiments are performed to study rotational effects on the mixed convection of low-Prandtlnumber fluids enclosed between the annuli of concentric and eccentric horizontal cylinders. The inner cylinder is assumed to be heated and rotating. The rotational Reynolds number considered is in the range where the effect of Taylor vortices is negligible. The Prandtl number of the fluid considered is in the range 0·01-1·0. The Rayleigh number considered is up to 106. A non-uniform mesh transformation technique coupled with the introduction of ‘false transient’ parameters to the vorticity and streamfunction-vorticity expressions was used to solve the governing set of equations. Results show that when the inner cylinder is made to rotate, the multicellular flow patterns observed in stationary cylindrical annuli subside in a manner depending on the Prandtl number of the fluids. Eventually the flow tends toward a uniform flow similar to that of a solid body rotation. For a fixed Rayleigh number and with a Prandtl number of the order of 1·0, when the inner cylinder is made to rotate, the mean Nusselt number is observed to decrease throughout the flow. For lower Prandtl number of the order 0·1-0·01 the mean Nusselt number remained fairly constant when the inner cylinder was made to rotate. The mean Nusselt numbers obtained were also compared with available data from other investigators.
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  • 24
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1134-1134 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 25
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1135-1149 
    ISSN: 0271-2091
    Keywords: Free surface flow ; Non-linear effects ; Free surface boundary layer ; BEM ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The fully non-linear free surface potential flow past a 2D non-lifting body is computed. The numerical method is based on the simple layer integral formulation; the non-linear solution is obtained by means of an iterative procedure. Under some hypotheses, viscosity effects at the free surface are considered. All the numerical results obtained have been tested against analytical solutions and experimental results.
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  • 26
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1219-1243 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new finite element technique for the analysis of wave run-up is presented in this paper. In this finite element approach, the movement of the shoreline is expressed by that of the nodal points at the wave front, and an auto mesh generation technique is effectively used. The present method is tested by the comparison with the experimental result of a channel with uniform slope, and two numerical examples are reported to show the efficiency of this method. As a final example, the tsunami run-up caused by the 1983 Nihonkai-Chubu earthquake is analysed and compared with actual records of the flooded area.
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  • 27
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1245-1257 
    ISSN: 0271-2091
    Keywords: Advection modeling ; Streamline upwind ; Finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A streamline upwind formulation is presented for the treatment of the advection terms in the general transport equation. The formulation is monotone and conservative and is based on the discontinuous nature of the advection mechanism. The results of there benchmark test cases for the full range of flow Peclet numbers are presented. The new formulation is shown to accurately model the advection phenomenon with significantly smaller numerical diffusion than the existing methods. The results are also free of all spatial oscillations. Considerable savings in computer storage and execution time have been achieved by employing the three-noded triangular element for which exact integrations exist. The formulation is straightforward and can be readily incorporated into any finite element code using the conventional Galerkin approach.
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  • 28
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 595-612 
    ISSN: 0271-2091
    Keywords: 2D Navier-Stokes equation ; Streamfunction-Vorticity formulation ; Regular boundary element method ; Linearity invariance under homotopy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Based on regular boundary element method and a kind of linearity invariance under homotopy, a kind of numerical scheme of 2D steady-state Navier-Stokes equation in streamfunction-vorticity formulation is described. The flow inside a square cavity is used to illustrate this numerical scheme.
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  • 29
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 613-623 
    ISSN: 0271-2091
    Keywords: Large sparse non-symmetric linear system ; Multilevel iteration ; Generalized minimal residual method ; Parallel computing ; Distributed memory ; Computational fluid dynamics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Linearization of the non-linear systems arising from fully implicit schemes in computational fluid dynamics often result in a large sparse non-symmetric linear system. Practical experience shows that these linear systems are ill-conditioned if a higher than first-order spatial discretization scheme is used. To solve these linear systems, an efficient multilevel iterative method, the α-GMRES method, is proposed which incorporates a diagonal preconditioning with a damping factor α so that a balanced fast convergence of the inner GMRES iteration and the outer damping loop can be achieved. With this simple and efficient preconditioning and damping of the matrix, the resulting method can be effectively parallelized. The parallelization maintains the effectiveness of the original scheme due to the algorithm equivalence of the sequential and the parallel versions.
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  • 30
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    International Journal for Numerical Methods in Fluids 15 (1992) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 31
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 649-671 
    ISSN: 0271-2091
    Keywords: Multigrid ; Runge-Kutta ; Conservation laws ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: It is known that Jameson's scheme is a pseudo-second-order-accurate scheme for solving discrete conservation laws. The scheme contains a non-linear artificial dissipative flux which is designed to capture shocks. In this paper, it is shown that the, shock-capturing of Jameson's scheme for the Euler equations can be improved by replacing the Lax-Friedrichs' type of dissipative flux with Roe's dissipative flux. This replacement is at a moderate expense of the calculation time.
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  • 32
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 673-691 
    ISSN: 0271-2091
    Keywords: Turbulent ; Lag-entrainment ; Boundary layer ; Separation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The lag-entrainment method, which is a well-established integral method for predicting the development of turbulent boundary layers, is used in this study to predict two-dimensional turbulent separated flow. The method is used in an inverse mode, in which the displacement thickness is specified together with other integral parameters of the boundary layer. It is concluded that the prediction of two-dimensional separated flow by an integral method is feasible, but there is a need for accurate data for both equilibrium and general separated flows for making a comparison.
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  • 33
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 773-789 
    ISSN: 0271-2091
    Keywords: Finite difference method ; Newtonian jet swell ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite difference technique that incorporates a numerical mapping has been successfully applied to analyse both planar and axisymmetric Newtonian jets. A pressure gradient equation and a free-surface slope equation have been derived for free-surface iteration. The computation of pressure inside the jet surface using the pressure gradient equation is stable and accurate at high Reynolds numbers. The free-surface slope equation is needed for updating the free surface and is applicable for jets with strong surface tension effects. The present development can simulate the Newtonian jets for Reynolds numbers as high as 2000 and capillary number as low as 10-5. Numerical predictions by the present technique are close to the results of previous finite element simulations.
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  • 34
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 791-798 
    ISSN: 0271-2091
    Keywords: Generalized differential quadrature ; Incompressible flows ; Navier-Stokes equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A global method of generalized differential quadrature is applied to solve the two-dimensional incompressible Navier-Stokes equations in the vorticity-stream-function formulation. Numerical results for the flow past a circular cylinder were obtained using just a few grid points. A good agreement is found with the experimental data.
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  • 35
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 799-816 
    ISSN: 0271-2091
    Keywords: Large eddy simulation ; Finite volume methods ; Compressible turbulence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Large eddy simulation of compressible, homogeneous, isotropic, decaying turbulence in a rectangular box is performed using finite volume techniques. An analysis of the energy spectra obtained from the simulations shows that an agreement with the Kolmogorov law for the inertial range is found only when an appropriate spatial discretization method is used. This agreement is obtained both for a low (0·05) and a moderate (0·6) Mach number when Smagorinsky's subgrid model is employed.
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  • 36
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 1059-1071 
    ISSN: 0271-2091
    Keywords: Turbulence model ; Deep ocean ; Radionuclide ; Three-dimensional modelling ; Eddy viscosity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this study the adequacy of the k-∊ turbulence model and the feasibility of the three-dimensional hydrodynamic-transport models TEMPEST and FLESCOT for deep ocean radionuclide disposal assessment were evaluated qualitatively. TEMPEST and FLESCOT were applied to a hypothetical, two-dimensional, deep ocean case with and without stratifications. TEMPEST with the k-∊ model was applied to obtain quasi-steady state eddy viscosity distributions. With calculated eddy viscosity distributions as part of the input, FLESCOT then calculated distributions of velocity, water temperature, sediment and the dissolved and sediment-sorbed radionuclide, assuming that the radionuclide was disposed on the ocean bottom.Results revealed that the computed eddy viscosity increased almost linearly with vertical distance near the ocean bottom, then rapidly decreased towards a molecular viscosity value when the vertical gradient of the velocity distribution became very small. The results also demonstrate the importance of the density gradient to suppress the turbulent kinetic energy production, resulting in reduced eddy viscosity, producing the maximum computed eddy viscosity of 0·2 Pa s, which compares well with the reported value of 0·07 Pa s in the deep ocean. Thus the k-∊ turbulence model appears to be qualitatively applicable to the deep ocean environment.
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 1145-1146 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 38
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 1073-1118 
    ISSN: 0271-2091
    Keywords: Space-time ; Finite elements ; Incompressible flows ; Galerkin/least-squares ; Deforming spatial domain ; Oscillating cylinder ; Pitching aerofoil ; Clustered element-by-element ; GMRES ; Vortex shedding ; Vortex-induced oscillations ; Lock-in ; Hysteresis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present our numerical results for certain unsteady flows past oscillating cylinders and aerofoils. The computations are based on the stabilized space-time finite element formulation. The implicit equation systems resulting from the space-time finite element discretizations are solved using iterative solution techniques.One of the problems studied is flow past a cylinder which is forced to oscillate in the horizontal direction. In this case we observe a change from an unsymmetric mode of vortex shedding to a symmetric one. An extensive study was carried out for the case in which a cylinder is mounted on lightly damped springs and allowed to oscillate in the vertical direction. In this case the motion of the cylinder needs to be determined as part of the solution, and under certain conditions this motion changes the vortex-shedding pattern of the flow field significantly. This non-linear fluid-structure interaction exhibits certain interesting behaviour such as ‘lock-in’ and ‘hysteresis’, which are in good agreement with the laboratory experiments carried out by other researchers in the past. Preliminary results for flow past a pitching aerofoil are also presented.
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 1147-1148 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 15 (1992) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 1149-1170 
    ISSN: 0271-2091
    Keywords: Coastal upwelling ; Turbulence energy ; Exchange coefficient ; Roughness length ; Co-ordinate transformation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A three-dimensional numerical model has been applied to study the impact of freshwater discharge from a river on the coastal circulation in the western Bay of Bengal. The basic dynamical framework of the model follows closely that described by Johns et al.1 for the simulation of coastal upwelling off the east coast of India. Using this model, experiments have been performed to investigate the impact of the freshwater discharge at the location of Godavari river along the east coast of India. A comparison of the model results, with and without the inclusion of river discharge, shows that the river discharge into the western Bay of Bengal suppresses the upwelling near the river mouth. Though there are no detailed observations on the flow structure near the mouth of the Godavari river, the computed results are in qualitative agreement with the observations documented by Rao and Jayaraman2 and Rao,3 who have shown that during monsoon period the upwelling off Godavari estuary is suppressed.
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 1171-1196 
    ISSN: 0271-2091
    Keywords: Advection ; Diffusion ; Finite difference schemes ; Numerical modelling ; Solute transport ; Stability ; Truncation error ; Computer applications ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In recent years the QUICK finite difference scheme has been increasingly used in solving the advection-diffusion equation, particularly for water quality modelling studies relating to coastal and estuarine flows. This scheme has the benefits of mass conservation, reasonably high accuracy and computational efficiency in comparison with many other higher-order-accurate schemes reported in the recent literature. A von Neumann stability analysis showed that the explicit QUICK scheme has a severe stability constraint which depends upon the diffusion coefficient. It can be proved that this scheme is numerically unstable for the case of pure advection. Various modified forms of the implicit QUICK scheme have been formulated and their numerical stability properties have been studied and analysed. The modified QUICK schemes considered have been tested for transient simulations for the cases of pure advection and of advection and diffusion in an idealized one-dimensional basin using three different initial boundary conditions: (a) a sharp front concentration gradient, (b) a Gaussian concentration distribution and (c) a plug source. Details of the comparisons between these modified schemes and with other typical second-order-accurate difference schemes are given, together with comparisons with the analytical solutions for each case. A two-dimensional version of the semi-time-centred QUICK scheme (ADI-QUICK), has also been applied to a two-dimensional test case using the standard ADI technique and has been shown to be attractive in comparison with other comparable second-order schemes.
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 1213-1237 
    ISSN: 0271-2091
    Keywords: Physical component ; Lie derivative ; Physical curvilinear space ; Riemannian geometry ; Lagrangian front tracking ; Free surface ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a systematic and theoretically consistent approach for the analysis of free-surface flow, making use of a number of established ideas such as physical component, boundary-fitted co-ordinate (BFC) and Lagrangian front tracking. The approach extends, theoretically as well as numerically, the use of physical component to general non-orthogonal moving grids and provides a numerically stable BFC method with little labour of free-surface positioning, grid generation and grid renewal. The approach conserves mass even at the free surface and allows time step of the order of the Coulant number. The main body of the present paper starts with the definition of analytical space and Riemannian geometry intrinsic to the physical component by applying to it the theorems of differential geometry and manifold theory. Then the governing equations of flow and free surface for the physical component are defined in the general 3D form with the notation of the new Riemannian geometry. Numerical procedures and the fully discrete equations are also presented for the benefit of potential users. Finally, several 2D examples demonstrate the basic performance of the present method by showing the computability of complex free-surface motion.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 109-124 
    ISSN: 0271-2091
    Keywords: Numerical tidal model ; Spectral method ; Arakawa grids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Three-dimensional algorithms for the numerical computation of flows caused by tides or meteorological forcing are developed for four of Arakawa's spatial grid types using a spectral method in the vertical dimension. Three of the grids, in which the velocity components are computed at the same grid points, offer potential advantages over the commonly used C-grid. The computed results from the four grids are compared for three test problems based on the linearized hydrodynamical equations. It is concluded that the B-grid provides a viable alternative to the C-grid, with significant advantages when a spectral method is used.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 175-187 
    ISSN: 0271-2091
    Keywords: Parallel computing ; Transputer ; CFD ; Fire simulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper describes the implementation of a fire field model in the parallel computing environment offered by multiple transputers. The fire model is built into the general purpose SIMPLE-based CFD code HARWELL-FLOW3D. The technique of domain decomposition has been applied tb convert the conventional serial version of FLOW3D into a code capable of efficiently utilizing an arbitrary number of transputers. Fire simulations consisting of up to 24 000 computational cells are performed on parallel systems with up to 15-processors. The run time for this simulation has been reduced from over 4 days on a single processor to just over 8 h on the 15-processor system. An interactive graphics system has also been developed which runs in parallel with the main computations.
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  • 46
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 289-298 
    ISSN: 0271-2091
    Keywords: Stokes equations ; Mixed finite elements ; Stabilization ; Uzawa-type algorithm ; Preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We study the behaviour of a conjugate gradient Uzawa-type method for a stabilized finite element approximation of the Stokes problem. Many variants of the Uzawa algorithm have been described for different finite elements satisfying the well-known Inf-Sup condition of Babuška and Brezzi, but it is surprising that developments for unstable ‘low-order’ discretizations with stabilization procedures are still missing. Our paper is presented in this context for the popular (so-called) Q1-P0 element.First we show that a simple stabilization technique for this element permits us to retain the property of a convergence factor bounded independently of the discretization mesh size. The second contribution of this work deals with the construction of a less costly preconditioner taking full advantages of the block diagonal structure of the stabilization matrix. Its efficiency is supported by 2D and. 3D numerical results.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 375-377 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 379-401 
    ISSN: 0271-2091
    Keywords: Characteristics ; Currents ; Finite difference techniques ; Three-dimensional modeling ; Tides ; Wind-induced flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Certain free surface flows exhibit in nature negligible vertical accelerations and as a result the pressure within the fluid remains hydrostatic. The method of characteristics is developed as a solution technique for the integration of the partial differential equations describing this kind of flow. The equations are integrated over the depth to provide a two-dimensional model which is then tested and validated by comparing its results with tide-induced flows occurring in a number of cases where either analytical or observational data are available for comparison. On the basis of the results of the 2D model, a finite difference 3D model is developed which provides the values of the unknown velocities u, v and w along the three axes x, y and z. This combined 2D-3D model is verified by applying it in cases of wind-induced flow inside closed or open basins for which the classical Ekman solution may be used as a testing means.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 981-1003 
    ISSN: 0271-2091
    Keywords: Co-ordinate mapping ; Finite element method ; Free-boundary ; Solidification ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new boundary-conforming mapping is developed for the calculation of highly deformed cellular solidification interfaces in a model of directional solidification of a binary alloy. The mapping is derived through a variational fomulation that is designed so that the grid penetrates the grooves between cells along the interface without causing a loss of ellipticity of the mapping equations. A finite element/Newton method is presented for simultaneous solution of the free boundary problem described by the solutal model of directional solidification and the mapping equations. Results are compared to previous calculations and demonstrate the importance of accurate representation of the interface shape for understanding the solution structure.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1063-1086 
    ISSN: 0271-2091
    Keywords: Boundary element method ; Local mesh refinement ; Convergence ; Small interparticle gap ; Adaptive subdomain integration ; Superparametric ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A second-order boundary element technique was developed to simulate the 3D hydrodynamic interactions between multiple particles of arbitrary shape. This paper reports the results of an extensive validation procedure aimed at demonstrating the convergence characteristics of the technique, especially in cases where the particles are in close proximity. The quadratic elements are superior to the lower-order elements in terms of accuracy, computer storage and CPU time required, thus resulting in a significant improvement in the overall computational efficiency. Superparametric discretization improves the accuracy over isoparametric discretization but lowers the convergence rate of the method. When the interparticle gap becomes very small (less than 1% of the particle radius), the numerical solution diverges owing to inaccurate determination of the element contributions in the gap region. An adaptive subdomain integration scheme was developed that dramatically improved the integration accuracy and provided convergent solutions for problems of very small gaps down to 0-01% of the particle diameter.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1131-1133 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1111-1130 
    ISSN: 0271-2091
    Keywords: Non-linear waves ; Diffraction ; Wave forces ; Circular cylinder ; Grid generation ; Numerical simulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The interaction of two-dimensional water waves with a fixed submerged cylinder is studied using a finite difference scheme with boundary-fitted co-ordinates. A mixed Eulerian-Lagrangian (MEL) formulation is used to satisfy the fully non-linear free surface conditions. The diffraction of small-amplitude water waves by a cylinder is examined for various wavelengths and amplitudes of the incident wave. Fourier analyses of the incident and diffracted waves are performed to determine their spectra. An example of a large-amplitude wave breaking over a cylinder is also studied. The non-linear numerical solutions are compared with those of experiments and linear theory where appropriate.
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    International Journal for Numerical Methods in Fluids 14 (1992) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 757-774 
    ISSN: 0271-2091
    Keywords: Viscoelastic fluid ; Finite differences ; Shooting method ; Stagnation point flow ; Stretching sheet ; Rotating disk ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A hybrid method for computing the flow of viscoelastic and second-order fluids is presented. It combines the features of the finite difference technique and the shooting method. The method is accurate because it uses central differences. Its convergence is at least superlinear.The method is applied to obtain the solutions to three problems of flow of Walters' B' fluid: (a) flow near a stagnation point, (b) flow over a stretching sheet and (c) flow near a rotating disk. Numerical results reveal some new characteristics of flows which are not easy to demonstrate using the perturbation technique.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1289-1310 
    ISSN: 0271-2091
    Keywords: Vortex method ; Free surface flows ; Body-wave interaction ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Vortex methods have found wide applications in various practical problems. The use of vortex methods in free surface flow problems, however, is still very limited. This paper demonstrates a vortex method for practical computation of non-linear free surface flows produced by moving bodies. The method is a potential flow formulation which uses the exact non-linear free surface boundary condition at the exact location of the instantaneous free surface. The position of the free surface, on which vortices are distributed, is updated using a Lagrangian scheme following the fluid particles on the free surface. The vortex densities are updated by the non-linear dynamic boundary condition, derived from the Euler equations, with an iterative Lagrangian numerical scheme.The formulation is tested numerically for a submerged circular cylinder in unsteady translation. The iteration is shown to converge for all cases. The results of the unsteady simulations agree well with classical linearized solutions. The stability of the method is also discussed.
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  • 56
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1261-1287 
    ISSN: 0271-2091
    Keywords: Finite difference method ; Separating flow ; Ocean current ; Vortex ; Zoning method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite difference simulation method is developed for 3D flow about a body of complex geometry. The Navier-Stokes equation is approximated by a high-order-accurate difference scheme in the framework of rectangular co-ordinate systems. The configuration of the 3D body is represented by use of both surface porosity and volume porosity and the no-slip body boundary conditions are approximately implemented on the boundary cells. The validity of the method is demonstrated by a numerical test of flow past a sphere at a Reynolds number of 1000. The complicated structure of separated vortices is well revealed by this test computation. The versatility of the method is shown by application to an ocean-engineering problem of flow about a bay with an island.
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  • 57
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 579-593 
    ISSN: 0271-2091
    Keywords: Split operator scheme ; Method of characteristics ; Ocean waves ; Wave spectrum ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A coupled discrete spectral model was developed for the prediction of ocean waves by solving the energy conservation equation of the two-dimensional wave spectrum. The model includes the dispersion correction terms in the governing equation to account for the dispersive effect due to the frequency-dependent velocities of waves. A split operator scheme is used to deal with the numerical problems arising from different terms of the governing equation. The advection terms are solved by the proven accurate minimax characteristics method to avoid excessive numerical damping or oscillations. The dispersion correction terms are solved by central differencing. The source and sink terms are solved by a quasi-second-order explicit scheme with limitation on energy growth per time step to allow the use of a large time step. The model was verified by ideal test cases and wave-hindcasting studies under typhoon conditions in the South China Sea near Hong Kong.
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  • 58
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 975-984 
    ISSN: 0271-2091
    Keywords: Natural convection ; Forced convection ; Porous medium ; Numerical modelling ; CFD package ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A PC-based system for modelling of convection in enclosures on the basis of the Navier-Stokes equations is described and a number of test results are given. New examples of mixed convection in a square chamber and thermal convection in ordinary and porous (isotropic and anisotropic) vertical layers are presented which may be of interest in civil and building engineering.
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  • 59
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 967-974 
    ISSN: 0271-2091
    Keywords: Permeable walls ; Bulk friction ; Time-dependent ; Incompressible Navier-Stokes ; Pressure correction ; Projection ; Semi-implicit ; Finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Computer simulations may contribute significantly to the optimal design of air-conditioning systems. To capture the effects of partially permeable walls such as bookshelves on the movement of air and heat, it is necessary to extend the density-dependent Navier-Stokes equations by an additional friction term. The finite element technique is convenient to approximate the extended equations in spatial co-ordinates. For the time co-ordinate a recently proposed semi-implicit finite difference method is very efficient in terms of accuracy and computational complexity. A pressure correction approach is most appropriate to decouple the primitive variables in the extended Navier-Stokes equations. The resulting algorithm has the interesting feature that small symmetric positive definite systems of equations can be solved sequentially for each of the primitive variables. Iterative solution of the systems of equations with preconditioned conjugate gradients combined with a compressed storage scheme allows fine grid computations at affordable costs. As an example a two-dimensional version of the code was applied to an enclosure which was heated from the side and contained a porous wall. The time-dependent computational results are compared with measurement data.
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  • 60
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 1383-1406 
    ISSN: 0271-2091
    Keywords: Incompressible flow ; Co-volume method ; Upwind ; Voronoi tessellation ; Networks ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The dual variable method for Delaunay triangulations is a network-theoretic method that transforms a set of primitive variable finite difference or finite element equations for incompressible flow into an equivalent system which is one-fifth the size of the original. Additionally, it eliminates the pressures from the system and produces velocities that are exactly discretely divergence-free. In this paper new discretizations of the convection term are presented for Delaunay triangulations, the dual variable method is extended to tessellations that contain obstacles, and an efficient algorithm for the solution of the dual variable system is described.
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 1417-1419 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 15 (1992), S. 1421-1422 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 63
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 13-24 
    ISSN: 0271-2091
    Keywords: Streamlined finite elements ; Extrusion ; Free surface flows ; Die design ; Three-dimensional flows ; Three-dimensional finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A method to determine three-dimensional die shapes from extrudate swell and vice versa is presented using a three-dimensional Galerkin finite element method based on a streamlined formulation with the fluid velocities and pressures represented by triquadratic and trilinear basis functions respectively. The three-dimensional streamlined method, an extension of the two-dimensional formulation, uses successive streamsurfaces to form a boundary-conforming co-ordinate system. This produces a fixd, computational domain leaving the spatial location of the elements as unknowns to be determined with the standard primary variables (u, v, w, p). The extrudate produced by a die of a given shape is considered for moderate Reynolds numbers. Finally, the method is extended to address the problem of die design, where a die profile is sought to produce a target extrudate shape.
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  • 64
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 25-45 
    ISSN: 0271-2091
    Keywords: Partial differential equations ; Non-linear equations ; Coupled system ; Numerical methods ; Finite elements ; Adaptive grid ; Flow in porous media ; Groundwater contamination ; Multiphase flow ; Immiscible flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A straightforward moving grid finite element method is developed to solve the one-dimensional coupled system of non-linear partial differential equations (PDEs) governing two- and three-phase flow in porous media. The method combines features from a number of self-adaptive grid techniques. These techniques are the equidistribution, the moving grid finite element and the local grid refinement/coarsening methods. Two equidistribution criteria, based on solution gradient and curvature, are employed and nodal distributions are computed iterativcly. Using the developed approach, an intermingle-free nodal distribution is guaranteed. The method involves examination of a single representative gradient to facilitate the application of moving grid algorithms to solve a non-linear coupled set of PDEs and includes a feature to limit mass balance error during nodal redistribution. The finite element part of the developed algorithm is verified against an existing finite difference model. A numerical simulation example involving a single-front two-phase flow problem is presented to illustrate model performance. Additional simulation examples are given in Part 2 of this paper. These examples include single and double moving fronts in two- and three-phase flow systems incorporating source/sink terms. Simulation sensitivity to the moving grid parameters is also explored in Part 2.
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  • 65
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 443-457 
    ISSN: 0271-2091
    Keywords: Turbulent oscillating flows ; Finite element method ; The method of averaging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The time-dependent turbulent Navier-Stokes equations are solved numerically by a finite element method with an algebraic eddy viscosity model (Baldwin-Lomax formulation) for oscillating turbulent channel flows. The method of averaging is used to analyse the resulting periodic motion of the fluid. Numerical results are obtained for various Strouhal numbers and relative amplitudes. A comparison is made between the numerical and published experimental results. It appears that for low relative amplitudes in a certain range of frequencies the agreement is satisfactory.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 459-475 
    ISSN: 0271-2091
    Keywords: Impinging twin jet ; Fountain upwash flow ; Cross-flow ; Lift force ; κ-∊ model ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Theoretical research to simulate twin-jet impingement with cross-flow has been undertaken. An impinging twin jet coupled with cross-flow in closed ground effect has been studied by using the compressible Navier-Stokes equation with a Jones-Launder κ-∊ two-equation turbulence model. The velocity results without cross-flow were compared with the data of Saripalli et al. and found to show good agreement. The calculated results show that several recirculating zones are distributed around the flow field. Their size and location are closely related to the jet exit height above the ground, the nozzle space and the strength of cross-flow. In addition, a fountain upwash flow occurs between the nozzles, and two low-pressure recirculating zones are induced by the interaction between the nozzle mainstream and the fountain upwash flow. This induce a loss of lift force of the aircraft. The effects of the cross-flow induce the sudden decrease in the lift force of the aircraft; the stronger the cross-flow, the lower is the lift force of the flow field.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 125-126 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 68
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 361-374 
    ISSN: 0271-2091
    Keywords: Rapidly varied flow ; Open channel ; Numerical simulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new method combining the Preissmann four-point scheme and the Holly-Preissmann reach-back scheme is introduced to solve the rapidly varied flow problem in an open channel. The Preissmann four-point scheme is well known for the computation of one-dimensional unsteady flow. The Holly-Preissmann reach-back scheme integrates the Holly-Preissmann two-point scheme with the concept of reach-back characteristics, which allows the characteristics to project several time steps beyond the current time level. A spontaneous surge formation case is used to demonstrate and evaluate the applicability of the new method. It has been found that the results from this method are quite compatible with those of Preissmann four-point scheme. In addition, with the appropriate choice of the number of reach-back time steps, this new method can always avoid the numerical oscillation which usually exists when one uses the Preissmann four-point scheme for the condition of Courant number not close to unity.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 423-441 
    ISSN: 0271-2091
    Keywords: Finite volume method ; Non-orthogonal co-ordinates ; Turbulent recircalating flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A general numerical method for the solution of the complete Reynolds-averaged Navier-Stokes equations for 2D or 3D flows is described. The method uses non-orthogonal co-ordinates, Cartesian velocity components and a pressure-velocity-coupling algorithm adequate for non-staggered grid systems. The capability of the method and the overall performance of the κ-∊ eddy viscosity model are demonstrated by calculations of 2D and 3D flow over a hill. Solution error estimations based on fine grids, e.g. 320 × 192 control volumes, together with comparisons with standard turbulence model modifications, low-Reynoldsnumber or streamline curvature effects, have allowed the investigation of model drawbacks in predicting turbulent flows over surface-mounted hills.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 529-537 
    ISSN: 0271-2091
    Keywords: Boundary element method ; Cavity flow ; Riabouchinsky flow ; Free surface flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a boundary element formulation for solution of planar Riabouchinsky cavity flow problems. An iterative procedure for adjusting the free surface position is developed and shown to be stable and convergent. Numerical results are compared with finite difference and finite element solutions, showing the superior accuracy of the BEM models.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 557-585 
    ISSN: 0271-2091
    Keywords: Multivariant finite element ; Incompressible flow ; Pressure modes ; Shape functions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Within multivariant elements, which have restricted degrees of freedom at some nodes, different velocity components have different variations. Shape functions for the multivariant elements Q1+ Po and R2+ Po are developed. With such shape functions the value of a velocity component within a multivariant element is shown to depend upon all the independent components of velocity at the nodes of the element.The use of the Q1 P0 element to simulate flows with discontinuous boundary conditions generated disturbance throughout the flow domain, giving erroneous pressure and velocity distributions. The Q1+ Po element restricted the disturbance due to such discontinuities to a small region near the singular points, whereas the P2+ Po element completely eliminated the fluctuations. Flows with discontinuous boundary conditions were simulated with reasonable accuracy by partially relaxing the no-slip condition on the Q1 Po elements near the singular points.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 587-608 
    ISSN: 0271-2091
    Keywords: Open boundary conditions ; Backward-facing step ; Unbounded flow ; Free boundary condition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Boundary conditions come from Nature. Therefore these conditions exist at natural boundaries. Often, owing to limitations in computing power and means, large domains are truncated and confined between artificial synthetic boundaries. Then the required boundary conditions there cannot be provided naturally and there is a need to fabricate them by intuition, experience, asymptotic behaviour and numerical experimentation. In this work several kinds of outflow boundary conditions, including essential, natural and free boundar conditions, are evaluated for two flow and heat transfer model problems. A new outflow boundary condition, called hereafter the free boundary condition, is introduced and tested. This free boundary condition is equivalent to extending the validity of the weak form of the governing equations to the synthetic outflow instead of replacing them there with unknown essential or natural boundary conditions. In the limit of zero Reynolds number the free boundary condition minimizes the energy functional among all possible choices of outflow boundary conditions. A review of results from applications of the same boundary conditions to several other flow situations is also presented and discussed.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 631-664 
    ISSN: 0271-2091
    Keywords: Unsteady 2D flow ; Dam-break flood waves ; Body-fitted co-ordinates ; Implicit scheme ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Sudden total collapse of a dam holding back a reservoir of water, whenever it occurs, becomes formidably impressive in the extent of destruction with which it is associated. The movement on a dry bed of a two-dimensional flood wave resulting from the break of a dam has been one of the most important and challenging subjects in rapidly varied unsteady flows from the computational point of view. An implicit time-marching finite volume numerical scheme was developed and subsequently applied for the solution of the two-dimensional unsteady open channel flow equations written in conservation form. In order to avoid the problems associated with a conventional grid system, a body-fitted non-orthogonal local co-ordinate system was utilized. The proposed numerical technique was applied to determine the stage hydrographs, water surface profiles and velocities of flood flows resulting from suddenly breached storage dams. Predictions were compared with an analytical solution, with available numerical solutions using MacCormack's two-step explicit scheme and with experimental measurements. Agreement between predictions and measurements regarding the wave front advancement and stage hydrographs is considered to be satisfactory.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 756-756 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 477-493 
    ISSN: 0271-2091
    Keywords: Bed friction ; Hydrodynamics ; Shallow sea ; Galerkin ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The mathematical formulation of a three-dimensional shallow sea model using a modal expansion in the veitical is briefly described.The importance of the time discretization of the vertical diffusion term and bottom friction term is discussed in some detail. Both stability theory and numerical calculations show the importance of time centring or evaluating the modal form of the viscosity term at the higher time step in order to develop a numerically efficient algorithm. Similar analysis and calculations show that in shallow water it is essential to time centre or evaluate bottom friction at the higher time step. In the case of linear bottom friction it is shown that this condition can be readily accomplished. However, using a quadratic friction formulation (a more physically realistic form), this cannot be readily achieved. A new algorithm is presented whereby a stable solution can be obtained even in shallow water using quadratic bottom friction.
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    International Journal for Numerical Methods in Fluids 14 (1992) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 539-556 
    ISSN: 0271-2091
    Keywords: Thin film flows ; Free boundary problems ; Parabolic differential equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The numerical solution of the thin film flow surrounding a horizontal cylinder resulting from a single vertical cylindrical jet is obtained. This is effected by transforming the domain of the flow, which contains a free surface, onto a rectangular parallelepiped and using a marching strategy to solve the ensuing parabolic equations. The flow terminates at a finite distance along the cylinder, its position depending on the velocity and mass flux of the jet. A comparison with the usual two-dimensional model in which the jet is replaced by a vertical sheet shows that such a representation is valid provided the overall width of the flow is not too large. In particular, the differences in heat transfer characteristics amount to a few per cent, thus validating the use of the two-dimensional model when applied to heat exchanger tubes. A comparison with the more usual multicolumn case is also considered.
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 907-918 
    ISSN: 0271-2091
    Keywords: Elliptic solution ; Mean pressure ; Plane turbulent jet ; Algebraic stress model ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical prediction is obtained for the mean pressure field in the similarity region of a plane turbulent jet. An algebraic stress model, which introduces non-isotropic relations for the Reynolds stress components, is used to close the mean momentum equation. The full two-dimensional form of the transport equations is retained and the resultant equation set solved elliptically. The numerical prediction simulates many of the characteristics of the pressure field measured by experimental studies. However, the overall level of the predicted field is lower than the experimental values. The level obtained for the mean pressure field depends strongly on the prediction for the transverse normal Reynolds stress component 〈u2u2〉. The pressure field is shown to represent a small negative contribution to the net strearnwise momentum balance.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1005-1007 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 961-980 
    ISSN: 0271-2091
    Keywords: Vorticity-streamfunction ; Turbulent flow ; Control volume ; κ-∊ model ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical procedure to solve turbulent flow which makes use of the κ-∊ model has been developed. The method is based on a control volume finite element method and an unstructured triangular domain discretization. The velocity-pressure coupling is addressed via the vorticity-streamfunction and special attention is given to the boundary conditions for the vorticity. Wall effects are taken into account via wail functions or a low-Reynolds-number model. The latter was found to perform better in recirculation regions. Source terms of the κ and ε transport equations have been linearized in a particular way to avoid non-realistic solutions. The vorticity and streamfunction discretized equations are solved in a coupled way to produce a faster and more stable computational procedure. Comparison between the numerical predictions and experimental data shows that the physics of the flow is correctly simulated.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1019-1036 
    ISSN: 0271-2091
    Keywords: Natural convection ; Phase change ; Heat source method ; Solidification ; Melting ; Square cavity ; Water ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The problem of phase change in the presence of natural convection has been investigated. A model has been proposed based on the treatment of the release/absorption of latent heat as a heat source/sink in combination with the standard Galerkin finite element method with a primitive variable formulation on a fixed grid. To demonstrate the capabilities of the model, three cases of phase change of an aluminium alloy in the presence of natural convection arc considered, i.e. solidification, melting and combined solidification and melting. The solidification of water in a square cavity is modelled as another example, taking into account the density extremum, and the results are compared with a previously published work.
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1259-1259 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 84
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 817-841 
    ISSN: 0271-2091
    Keywords: Mixed convection ; Finite elements ; CVD ; Iterative methods ; Preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An algorithm is presented for the finite element solution of three-dimensional mixed convection gas flows in channels heated from below. The algorithm uses Newton's method and iterative matrix methods. Two iterative solution algorithms, conjugate gradient squared (CGS) and generalized minimal residual (GMERS), are used in conjunction with a preconditioning technique that is simple to implement. The preconditioner is a subset of the full Jacobian matrix centered around the main diagonal but retaining the most fundamental axial coupling of the residual equations. A domain-renumbering scheme that enhances the overall algorithm performance is proposed on the basis of and analysis of the preconditioner. Comparison with the frontal elimination method demonstrates that the iterative method will be faster when the front width exceeds approximately 500. Techniques for the direct assembly f the problem into a compressed sparse row storage format are demonstrated. Elimination of fixed boundary conditions is shown to decrease the size of the matrix problem by up to 30%. Finally, fluid flow solutions obtained with the numerical technique are presented. These solutions reveal complex three-dimensional mixed convection fluid flow phenomena at low Reynolds numbers, including the reversal of the direction of longitudinal rolls in the presence of a strong recirculation in the entrance region of the channel.
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  • 85
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 861-881 
    ISSN: 0271-2091
    Keywords: Grid generation ; Tri-tree ; Unstructured ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new method for generating finite element grids in two and three dimensions is developed. The method is based on a new search tree structure. The search tree is built upon triangles in two dimensions and tetrahedra in three dimensions. The density of elements can be varied throughout the computational domain. Efficient search algorithms for finding points in space and for finding the boundary of the domain have been developed. The speed of the grid algorithm will permit adaptive gridding during computation. The grid algorithm is generally applicable to both hydrodynamic as well as aerodynamic finite element computations. The technique has been used with success for gridding the North Sea-Skagerrak area.
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  • 86
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1-12 
    ISSN: 0271-2091
    Keywords: Helmholtz pressure equation ; Unsteady incompressible flow ; Time-implicit algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A time-implicit numerical method for solving unsteady incompressible viscous flow problems is introduced. The method is based on introducing intermediate compressibility into a projection scheme to obtain a Helmholtz equation for a pressure-type variable. The intermediate compressibility increases the diagonal dominance of the discretized pressure equation so that the Helmholtz pressure equation is relatively easy to solve numerically. The Helmholtz pressure equation provides an iterative method for satisfying the continuity equation for time-implicit Navier-Stokes algorithms. An iterative scheme is used to simultaneously satisfy, within a given tolerance, the velocity divergence-free condition and momentum equations at each time step. Collocated primitive variables on a non-staggered finite difference mesh are used. The method is applied to an unsteady Taylor problem and unsteady laminar flow past a circular cylinder.
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  • 87
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 83-93 
    ISSN: 0271-2091
    Keywords: Phase change material (PCM) ; Finite element analysis ; Enclosures ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is devoted to the finite element analysis of heat transfer during melting in rectangular enclosures. The effects of aspect ratio and subcooling on the motion of the interface and the Nusselt number have been investigated. The different schemes employed in the present work throw useful light on the choice of the appropriate method for dealing with such phase change problems.
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  • 88
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 127-146 
    ISSN: 0271-2091
    Keywords: Numerical simulation ; Slug flow ; Turbulence ; Dissipation ; Open surface ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Steps towards the numerical simulation of the flow behind the slug front in horizontal slug flow performed with a streamfunction-vorticity representation of the mean flow and an energy dissipation model for the turbulence are discussed. The flow field consists of two vortices, one saddle point and four stagnation regions. Attention is focused on the following boundary conditions: moving wall jet, moving wall, free jet velocity discontinuity and vertical liquid-gas open surface. A dissipation flux boundary condition is suggested to simulate the interaction of the turbulent eddies with the open surface. A method to assess the necessity to use a transport model equation for the dissipation rather than a geometric specification of a length is suggested. Three different ways to characterize the mixing zone length are proposed.
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  • 89
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1325-1345 
    ISSN: 0271-2091
    Keywords: κ-∊ ; Wall functions ; Finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An extended κ-∊ model (to include low-Reynolds-number regions) employing weighting functions is presented. Wall functions for the near-wall zones are developed giving correct boundary values for the Shear stress and κ-∊. A finite element model using a penalty formulation for incompressible turbulent flow is applied to Solve a flow between two plates. Results with mesh boundaries situated in the near-wall region and a: the wall are compared with measured values.
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  • 90
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1347-1365 
    ISSN: 0271-2091
    Keywords: Water waves ; Wave reflection and transmission ; Boundary element method ; Asymptotic theory ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We study numerically the linear water wave equations for shallow channels with rapidly varying bottom topography. We do not use the shallow water approximation because it is not valid when the bottom is rapidly varying. We use the boundary element method because it allows accurate tracking of the surface waves for long times. We present the results of a range of numerical validation experiments and a comparison between propagation over a periodic and a random rough bottom topography.
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  • 91
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1367-1376 
    ISSN: 0271-2091
    Keywords: Finite elements ; Viscoelastic flow ; Convergence failure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents an algorithm for two-dimensional Steady viscoelastic flow Simulation in which the Solution of the momentum and continuity equations is decoupled from that of the constitutive equations. The governing equations are discretized by the finite element method, with 3 × 3 element subdivision for the stress field approximation. Non-consistent Streamline upwinding is also used. Results are given for flow through a converging channel and through an abrupt planar 4:1 contraction.
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  • 92
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1311-1323 
    ISSN: 0271-2091
    Keywords: Steady Navier-Stokes equations ; Flux difference splitting ; Multigrid methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The steady Navier-Stokes equations in primitive variables are discretized in conservative form by a vertex-centred finite volume method Flux difference splitting is applied to the convective part to obtain an upwind discretization. The diffusive part is discretized in the central way.In its first-order formulation, flux difference splitting leads to a discretization of so-called vector positive type. This allows the use of classical relaxation methods in collective form. An alternating line Gauss-Seidel relaxation method is chosen here. This relaxation method is used as a smoother in a multigrid method. The components of this multigrid method are: full approximation scheme with F-cycles, bilinear prolongation, full weighting for residual restriction and injection of grid functions.Higher-order accuracy is achieved by the flux extrapolation method. In this approach the first-order convective fluxes are modified by adding second-order corrections involving flux limiting. Here the simple MinMod limiter is chosen. In the multigrid formulation the second-order discrete system is solved by defect correction.Computational results are shown for the well known GAMM backward-facing step problem and for a channel with a half-circular obstruction.
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  • 93
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1377-1382 
    ISSN: 0271-2091
    Keywords: Finite elements ; Viscoelastic flow ; Convergence failure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present the results of some numerical experiments which were carried out in order to investigate the general characteristics of the algorithm described in Part I of this paper.
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  • 94
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1383-1385 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 95
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1386-1386 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 96
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    International Journal for Numerical Methods in Fluids 14 (1992) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 97
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1387-1389 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 98
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1391-1405 
    ISSN: 0271-2091
    Keywords: Artificial dissipation schemes ; Central difference schemes ; Compressible flow ; Euler equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The influence of artificial dissipation schemes on the accuracy and stability of the numerical solution of compressible flow is extensively examined. Using an implicit central difference factored scheme, an improved form of artificial dissipation is introduced which highly reduces the errors due to numerical viscosity. A function of the local Mach number is used to scale the amount of numerical damping added into the solution according to the character of the flow in several flow regimes. The resulting scheme is validated through several inviscid flow test cases.
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  • 99
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1407-1419 
    ISSN: 0271-2091
    Keywords: Adaptive mesh refinement ; Finite elements ; Compressible flow ; Transient problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An adaptive finite element scheme for transient problems is presented. The classic h-enrichment/coarsening is employed in conjunction with a tetrahedral finite element discretization in three dimensions. A mesh change is performed every n time steps, depending on the Courant number employed and the number of ‘protective layers’ added ahead of the refined region. In order to simplify the refinement/coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved by pre-sorting the elements and then performing the refinement/coarsening groupwise according to the case at hand. Further reductions in CPU requirements arc realized by optimizing the identification and sorting of elements for refinement and deletion. The developed technology has been used extensively for shock-shock and shock-object interaction runs in a production mode. A typical example of this class of problems is given.
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  • 100
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    International Journal for Numerical Methods in Fluids 14 (1992), S. 1437-1452 
    ISSN: 0271-2091
    Keywords: Vortex flow aerodynamics ; High angle of attack ; Delta wing ; Viscous vortex models ; Vortex separation and bursting ; Computational fluid dynamics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new computational approach is developed for the analysis of vortex-dominated flow fields around highly swept wings at high angles of attack. In this approach an inviscid Euler technology is coupled with viscous models, similar to inviscid/boundary layer coupling. The viscous nature of the vortex core is represented by an algebraic model derived from the Navier-Stokes equations. The approach also accounts for the effects of the viscous shear layer near a wing surface through a modified surface boundary condition. The inviscid/viscous coupling consistently provides improved predictions of leading edge separation, vortex bursting and secondary vortex formation at relatively low computational cost. Results for several cases are compared with wind tunnel tests and other Euler and Navier-Stokes solutions.
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