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  • Articles  (14)
  • Stability  (14)
  • Wiley-Blackwell  (14)
  • Annual Reviews
  • 1990-1994  (12)
  • 1980-1984  (2)
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (14)
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  • Articles  (14)
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  • Wiley-Blackwell  (14)
  • Annual Reviews
  • Springer  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Advection-diffusion modelling using the modified QUICK scheme (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 1171-1196 
    Details
    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.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650151003
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  • 2
    Electronic Resource
    Electronic Resource
    Iterative stabilization of the bilinear velocity-constant pressure element (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 125-140 
    Details
    ISSN: 0271-2091
    Keywords: Incompressible flow ; Finite element ; Stability ; 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: Some finite element approximations of incompressible flows, such as those obtained with the bilinear velocity-constant pressure element (Q1-P0), are well known to be unstable in pressure while providing reasonable results for the velocity.We shall see that there exists a subspace of piecewise constant pressures that leads to a stable approximation. The main drawback associated with this subspace is the necessity of assembling groups of elements, the so-called ‘macro-elements’, which increases dramatically the bandwidth of the system.We study a variant of Uzawa's method which enables us to work in the desired subspace without increasing the bandwidth of the system. Numerical results show that this method is efficient and can be made to work at a low extra cost. The method can easily be generalized to other problems and is very attractive in three-dimensional cases.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100202
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  • 3
    Electronic Resource
    Electronic Resource
    Stabilization of a time integrator for the 3D shallow water equations by smoothing techniques (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 475-490 
    Details
    ISSN: 0271-2091
    Keywords: 3D shallow water equations ; Method of lines ; Time integrators ; Smoothing ; Stability ; Vector and parallel computers ; 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 smoothing technique is applied to improve the stability of a semi-implicit time integrator for the three-dimensional shallow water equations. In this method the terms involving the vertical direction are treated implicitly. The stability condition on the time step depends only on the horizontal mesh sizes; therefore in the horizontal-direction a smoothing operator is added. Owing to the smoothing, the maximally stable time step increases considerably while the accuracy is hardly affected. Moreover, it turns out that the smoothing operator is efficient on vector and parallel computers.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120505
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  • 4
    Electronic Resource
    Electronic Resource
    A time-splitting method for the three-dimensional shallow water equations (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 519-534 
    Details
    ISSN: 0271-2091
    Keywords: Three-dimensional shallow water equations ; Method of lines ; Time integrators ; Stability ; Vector and parallel computers ; 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 describe a time-splitting method for the three-dimensional shallow water equations. The stability of this method neither depends on the vertical diffusion term nor on the terms describing the propagation of the surface waves. The method consists of two stages and requires the solution of a sequence of linear systems. For the solution of these systems we apply a Jacobi-type iteration method and a conjugate gradient iteration method. The performance of both methods is accelerated by a technique based on smoothing. The resulting method is mass-conservative and efficient on vector and parallel computers. The accuracy, stability and computational efficiency of this method are demonstrated for wind-induced problems in a rectangular basin.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130409
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  • 5
    Electronic Resource
    Electronic Resource
    Buoyancy-driven instability in a vertical cylinder: Binary fluids with Soret effect. Part I: General theory and stationary stability results (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 79-117 
    Details
    ISSN: 0271-2091
    Keywords: Fluid mechanics ; Stability ; Soret effect ; Buoyancy-driven ; Double diffusive ; 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: Buoyancy-driven instability of a monocomponent or binary fluid which is completely contained in a vertical circular cylinder is investigated, including the influence of the Soret effect for the binary mixture. The Boussinesq approximation is used, and the resulting linear stability problem is solved using Galerkin's technique. The analysis considers various types of fluid mixtures, ranging from gases to liquid metals, in cylinders with a variety of radius-to-height ratios. The flow structure is found to depend strongly on both the cylinder aspect ratio and the magnitude of the Soret effect. Comparisons are made with experiments and other theories, and the predicted stability limits are shown to agree closely with observations.
    Additional Material: 22 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100106
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  • 6
    Electronic Resource
    Electronic Resource
    Stability analysis of finite difference schemes for two-dimensional advection-diffusion problems (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 579-597 
    Details
    ISSN: 0271-2091
    Keywords: Diffusion-convection ; Fourier analysis ; Stability ; Artificial 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: This paper develops a stability analysis of second-order, two- and three-time-level difference schemes for the 2D linear diffusion-convection model problem. The corresponding 1D schemes have been extensively analysed in two previous papers by the same author. Most of these 2D schemes obviously generalize 1D schemes, i.e. their stencil only uses the nearest points and defines ‘product difference schemes’; however, the stability results are not always the exact generalization of the 1D stability properties. Moreover, the 1D nonviscous MFTCS scheme may only be generalized if one uses a nine-point scheme. Numerical experiments for different values of the cell Reynolds number allow a comparison to be made between the theoretical and numerical stability limits.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130504
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  • 7
    Electronic Resource
    Electronic Resource
    The stability of explicit Euler time-integration for certain finite difference approximations of the multi-dimensional advection-diffusion equation (1984)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 853-897 
    Details
    ISSN: 0271-2091
    Keywords: Stability ; Advection-diffusion ; von Neumann method ; Matrix method ; Explicit Euler ; 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 comprehensive study is presented regarding the numerical stability of the simple and common forward Euler explicit integration technique combined with some common finite difference spatial discretizations applied to the advection-diffusion equation. One-dimensional results are obtained using both the matrix method (for several boundary conditions) and the classical von Neumann method of stability analysis and arguments presented showing that the latter is generally to be preferred, regardless of the type of boundary conditions. The less-well-known Godunov-Ryabenkii theory is also applied for a particular (Robin) boundary condition. After verifying portions of the one-dimensional theory with some numerical results, the stabilities of the two- and three-dimensional equations are addressed using the von Neumann method and results presented in the form of a new stability theorem. Extension of a useful scheme from one dimension, where the pure advection limit is known variously as Leith's method or a Lax-Wendroff method, to many dimensions via finite elements is also addressed and some stability results presented.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650040905
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  • 8
    Electronic Resource
    Electronic Resource
    Stability of flow over a rotating disk (1984)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 989-996 
    Details
    ISSN: 0271-2091
    Keywords: Galerkin ; Spline ; Stability ; 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: The perturbation equations which characterize the stability of flow over a rotating infinite disk are derived via strict order of magnitude analysis. These equations contain viscous terms not considered by Stuart,1 curvature and Coriolis terms not considered by Brown,2 and axial velocity terms not considered by Kobayashi et al.3 The strategy for reducing the problem to an algebraic system is Galerkin's method with B-spline discretization. In comparison with the Poiseuille flow solutions of Orszag,4 the method is shown to perform well without placing undue demands on computing capability. Critical values of Reynolds number, wave length, vortex orientation and number of spiral vortices calculated by the present method compare favourably with experimental data of Kobayashi et al.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650041007
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  • 9
    Electronic Resource
    Electronic Resource
    Numerical analysis of time-dependent Boussinesq models (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 1235-1250 
    Details
    ISSN: 0271-2091
    Keywords: Numerical analysis ; Stability ; Boussinesq 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: In this paper we analyse numerical models for time-dependent Boussinesq equations. These equations arise when so-called Boussinesq terms are introduced into the shallow water equations. We use the Boussinesq terms proposed by Katapodes and Dingemans. These terms generalize the constant depth terms given by Broer. The shallow water equations are discretized by using fourth-order finite difference formulae for the space derivatives and a fourth-order explicit time integrator. The effect on the stability and accuracy of various discrete Boussinesq terms is investigated. Numerical experiments are presented in the case of a fourth-order Runge-Kutta time integrator.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650131004
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  • 10
    Electronic Resource
    Electronic Resource
    A stable high-order method for the heated cavity problem (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 1313-1332 
    Details
    ISSN: 0271-2091
    Keywords: A fourth-order method ; Navier-Stokes equation ; Stability ; Finite difference ; 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 fourth-order method, without using extrapolation, is developed for the steady-state solution of a non-linear system of three simultaneous partial differential equations for the flow of a fluid in a heated closed cavity. The method is a finite difference method which has converged for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. The results are presented and compared with some of the accurate results available in de Vahl Davis and Jones, Shay and Schultz, and Dennis and Hudson. The method used to develop the fourth-order method presented in this paper can be used to develop high-order methods for other partial differential equations. The method was developed to be stable without using the upwinding technique.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650151106
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  • 11
    Electronic Resource
    Electronic Resource
    A decoupling numerical method for fluid flow (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 659-682 
    Details
    ISSN: 0271-2091
    Keywords: NAVIER-STOKES equations ; 3-Point exponential upwind ; Pressure perturbation ; Stability ; Curved channel ; Laminar flow ; Square-driven cavity ; 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 first-order non-conforming numerical methodology, Separation method, for fluid flow problems with a 3-point exponential interpolation scheme has been developed. The flow problem is decoupled into multiple one-dimensional subproblems and assembled to form the solutions. A fully staggered grid and a conservational domain centred at the node of interest make the decoupling scheme first-order-accurate. The discretization of each one-dimensional subproblem is based on a 3-point interpolation function and a conservational domain centred at the node of interest. The proposed scheme gives a guaranteed first-order accuracy. It is shown that the traditional upwind (or exponentially weighted upstream) scheme is less than first-order-accurate. The pressure is decoupled from the velocity field using the pressure correction method of SIMPLE. Thomas algorithm (tri-diagonal solver) is used to solve the algebraic equations iteratively. The numerical advantage of the proposed scheme is tested for laminar fluid flows in a torus and in a square-driven cavity. The convergence rates are compared with the traditional schemes for the square-driven cavity problem. Good behaviour of the proposed scheme is ascertained.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650160802
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  • 12
    Electronic Resource
    Electronic Resource
    Buoyancy-driven instability in a vertical cylinder: Binary fluids with Soret effect. Part II: Weakly non-linear solutions (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 755-786 
    Details
    ISSN: 0271-2091
    Keywords: Stability ; Soret ; Buoyancy ; Bifurcation ; Non-linear ; 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 buoyancy-driven instability of a monocomponent or binary fluid that is completely contained in a vertical circular cylinder is investigated, including the influence of the Soret effect for the binary mixture. The Boussinesq approximation is used, and weakly-non-linear solutions are generated via Galerkin's technique using an expansion in the eigensolutions of the associated linear stability problem. Various types of fluid mixtures and cylindrical domains are considered. Flow structure and associated heat transfer are computed and experimental observations are cited when possible.
    Additional Material: 32 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650170903
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  • 13
    Electronic Resource
    Electronic Resource
    Semi-implicit Skew Upwind Method for problems in environmental hydraulics (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 803-823 
    Details
    ISSN: 0271-2091
    Keywords: Numerical diffusion ; Skew upwind ; Convective transport ; Stability ; 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 method is presented for reducing numerical diffusion in environmental fluid problems. This method, which is referred to as the Semi-Implicit Skew Upwind Method (SISUM), is a robust solution procedure for the conditional convergence of the discretized transport equations. The method retains the advantage of the low numerical diffusion of the conventional skew upwind schemes but does not suffer from over- or under-shooting often found in these methods due to the improved interpolation schemes. The effectiveness of SISUM is demonstrated in several examples. The comparison of the results of a hybrid scheme and SISUM with field observations of convection-dominated pollutant transport in strongly curvilinear river flow shows that SISUM successfully eliminates the high numerical diffusion produced by the hybrid scheme. The robustness of the method was tested by solving the hydrodynamics of a circular clarifier model with a large density gravity source term in the vertical-momentum equation.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650170905
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  • 14
    Electronic Resource
    Electronic Resource
    A technique for analysing finite element methods for viscous incompressible flow (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 935-948 
    Details
    ISSN: 0271-2091
    Keywords: Stokes equations ; Mixed Finite elements ; Stability ; Patch test ; 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 give a self-contained presentation of our macroelement technique for verifying the stability of finite element discretizations of the Navier-Stokes equations in the velocity-pressure formulation.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110615
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