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  • Journals
  • Articles  (56)
  • Finite elements  (56)
  • Wiley-Blackwell  (56)
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (56)
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  • Journals
  • Articles  (56)
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  • 1
    Electronic Resource
    Electronic Resource
    Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equationsBased on an invited lecture.Supported by NASA Langley Research Center under Grant NASA-NAG-1-361 and the IBM Almaden Research Center under Grant No. 604912. (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 1261-1275 
    Details
    ISSN: 0271-2091
    Keywords: Advection-diffusion equation ; Advective-diffusive systems ; Artificial-diffusion ; Compressible flows ; Discontinuous Galerkin method ; Entropy Error analysis ; Euler equations ; Finite elements ; Galerkin method ; Hyperbolic systems ; Incompressible flow ; Navier-Stokes equations ; Petrov-Galerkin method ; Space-time formulation ; Upwind methods ; Weighted residual 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: SUPG methods were originally developed for the scalar advection-diffusion equation and the incompressible Navier-Stokes equations. In the last few years successful extensions have been made to symmetric advective-diffusive systems and, in particular, the compressible Euler and Navier-Stokes equations. New procedures have been introduced to improve resolution of discontinuities and thin layers. In this paper a brief overview is presented of recent progress in the development and understanding of SUPG methods.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650071108
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  • 2
    Electronic Resource
    Electronic Resource
    A stable least-squares finite element method for non-linear hyperbolic problems (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 933-942 
    Details
    ISSN: 0271-2091
    Keywords: Least squares ; Finite elements ; Non-linear ; Hyperbolic ; 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 class of stable least-square finite element methods for non-linear hyperbolic problems is developed and some exploratory studies made. The methods are based on modifying the L2-norm of the. residual and a related approximation to the H1-norm of the residual. The effect of the additional terms in these residual functionals is to introduce a dissipative effect proportional to the solution gradient. This acts to stabilize the solution for non-linear hyperbolic problems which generate shocks. Numerical results for a one-dimensional nozzle and shock tube problem demonstrate the accuracy and stability of the method. Results are for an implicit scheme and calculations for linear, quadratic and cubic elements are given.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650080805
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  • 3
    Electronic Resource
    Electronic Resource
    Conjugate gradient methods and ILU preconditioning of non-symmetric matrix systems with arbitrary sparsity patterns (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 213-233 
    Details
    ISSN: 0271-2091
    Keywords: Preconditioning ; Conjugate gradients ; Non-symmetric matrices ; Finite elements ; Convective transport ; 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: Preconditioning techniques based on incomplete Gaussian elimination for large, sparse, non-symmetric matrix systems are described. A certain level of fill-in may be specified in the incomplete factorizations. All methods considered may be applied to matrices with arbitrary sparsity patterns, for instance those associated with the general preprocessor algorithms or adaptive mesh techniques. The preconditioners have been combined with five conjugate gradient-like methods and tested on finite element discretized scalar convection-diffusion equations in 2D and 3D. It is found from numerical experiments that an amount of fill-in corresponding to about 50% of the number of original non-zero matrix entries is the optimal choice for this class of preconditioners. The preconditioners show almost no sensitivity to grid distortion. In problems with significantly variable coefficients or anisotropy the preconditioners stabilize the basic iterative schemes in addition to reducing the computational work substantially, mostly by more than 90%. The modified preconditioning technique, where fill-in is added on the main diagonal, performs in general better than the standard incomplete LU factorization, but is inferior to the latter in 3D problems and for matrix systems with complicated sparsity patterns.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090207
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  • 4
    Electronic Resource
    Electronic Resource
    A Taylor-Galerkin-based algorithm for viscous incompressible flow (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 327-351 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Taylor-Galerkin algorithm ; Fractional step method ; Cavity 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: In this paper the development and behaviour of a new finite element algorithm for viscous incompressible flow is presented. The stability and background theory are discussed and the numerical performance is considered for some benchmark problems. The Taylor-Galerkin approach naturally leads to a time-stepping algorithm which is shown to perform well for a wide range of Reynolds numbers (1 ≤ Re ≤ 400).A conventional definition for Re is assumed. Various modifications to the algorithm are investigated, particularly with respect to their effects on stability and accuracy.
    Additional Material: 23 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100307
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  • 5
    Electronic Resource
    Electronic Resource
    Implicit finite element methods for two-phase flow in oil reservoirs (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 651-681 
    Details
    ISSN: 0271-2091
    Keywords: Porous media ; Two-phase flow ; Oil recovery ; Finite elements ; Preconditioning ; Conjugate gradients ; 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 equations governing immiscible, incompressible, two-phase, porous media flow are discretized by generalized streamline diffusion Petrov-Galerkin methods in space and by implicit differences in time. Systems of non-linear algebraic equations are solved by Newton-Raphson iteration employing ILU-preconditioned conjugate-gradient-like methods to the non-symmetric matrix system in each iteration. The resulting solution methods are robust, enable complex grids with irregular nodal orderings and allow capillary effects.Several numerical formulations are tested and compared for one-, two- and three-dimensional flow cases, with emphasis on problems involving saturation shocks, heterogeneous media and curved boundaries. For reservoirs consisting of multiple rock types with differing capillary pressure properties, it is shown that traditional Bubnov-Galerkin methods give poor results and the new Petrov-Galerkin formulations are required. Investigations regarding the behaviour of several preconditioned conjugate-gradient-like methods in these type of problems are also reported.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100605
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  • 6
    Electronic Resource
    Electronic Resource
    Simple test calculations concerning finite element applications to numerical weather prediction (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 209-226 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Atmospheric flow ; Petrov-Galerkin ; Staggered grids ; Hybrid 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: Different finite element schemes are investigated with respect to their application in numerical weather prediction. Different methods of staggering of variables are considered. The tests concern the accuracy of a Rossby wave prediction and the generation of noise in a geostrophic adjustment process. Theoretical results concerning the noise level of different schemes are confirmed by computations with a one-dimensional model. Favourable results were obtained by hybrid schemes, using different Galerkin treatments for different terms of the dynamic equations.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110207
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  • 7
    Electronic Resource
    Electronic Resource
    Finite element solution of flow between eccentric cylinders with viscous dissipation (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 849-865 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Navier-stokes ; Rotating cylinders ; Viscous dissipation ; 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 computational study of viscous flow between two eccentrically rotating cylinders is presented in which the effect of viscous dissipation is taken into account. The space discretization is based on piecewise linear finite elements with velocity stabilization, while the method of characteristics is used for time integration. Numerical results illustrate the efficiency of the adopted approach.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110610
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  • 8
    Electronic Resource
    Electronic Resource
    Finite element solution of the Navier-Stokes equations by a velocity-vorticity method (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 661-675 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Navier-Stokes ; Velocity-vorticity ; 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 velocity-vorticity formulation of the Navier-Stokes equations is presented as an alternative to the primitive variables approach. The velocity components and the vorticity are solved for in a fully coupled manner using a Newton method. No artificial viscosity is required in this formulation. The pressure is updated by a method allowing natural imposition of boundary conditions. Incompressible and subsonic results are presented for two-dimensional laminar internal flows up to high Reynolds numbers.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110511
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  • 9
    Electronic Resource
    Electronic Resource
    Three-dimensional hydrodynamics on finite elements. Part II: Non-linear time-stepping model (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 507-533 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Hydrodynamics ; Three-dimensional hydrodynamics ; Non-linear hydrodynamics ; Tidal hydrodynamics ; 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 development and application of a non-linear 3D hydrodynamic model are described. The model is based on the wave equation rearrangement of the primitive 3D shallow water equations with a general eddy viscosity formulation for the vertical shear. A Galerkin procedure is used to discretize these on simple sixnode elements: linear triangles in the horizontal with linear variations in the vertical. Resolution of surface, bottom and interfacial boundary layers is facilitated and total flexibility is preserved for specifying spatial and temporal variations in the vertical viscosity and density fields. A semi-implicit time-stepping algorithm allows the solutions for elevation and velocity to be uncoupled during each time step. The elevation solution is essentially a 2D wave equation calculation with a stationary sparse matrix representing the gravity waves. With nodal quadrature the subsequent velocity calculation is achieved by factoring only a tridiagonal diffusion matrix representing the vertical viscous terms. As a result the overall calculation scales computationally as only a 2D problem but provides the full 3D solution. Application to field-scale problems is illustrated for the English Channel/Southern Bight system and the Lake Maracaibo system.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120602
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  • 10
    Electronic Resource
    Electronic Resource
    The compressible Newtonian extrudate swell problem (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 255-261 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Compressible Newtonian flow ; Extrudate 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: We solve the compressible Newtonian extrudate swell problem in order to investigate the effect of compressiblity on the shape of the extrudate. We employ a first-order equation of state relating the density to the pressure and use finite elements for the numerical solution of the problem. Our results show that the shape of the extrudate and the final extrudate swell ratio are not significanlty affected even at high compressibility values.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650200305
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