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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 323-348 
    ISSN: 0271-2091
    Keywords: Incompressible flow ; Finite element method ; Segregated solution algorithms ; Iterative solvers ; Implicit 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: This paper presents results of an ongoing research program directed towards developing fast and efficient finite element solution algorithms for the simulation of large-scale flow problems. Two main steps were taken towards achieving this goal. The first step was to employ segregated solution schemes as opposed to the fully coupled solution approach traditionally used in many finite element solution algorithms. The second step was to replace the direct Gaussian elimination linear equation solvers used in the first step with iterative solvers of the conjugate gradient and conjugate residual type. The three segregated solution algorithms developed in step one are first presented and their integrity and relative performance demonstrated by way of a few examples. Next, the four types of iterative solvers (i.e. two options for solving the symmetric pressure type equations and two options for solving the non-symmetric advection-diffusion type equations resulting from the segregated algorithms) together with the two preconditioning strategies employed in our study are presented. Finally, using examples of practical relevance the paper documents the large gains which result in computational efficiency, over fully coupled solution algorithms, as each of the above two main steps are introduced. It is shown that these gains become increasingly more dramatic as the complexity and size of the problem is increased.
    Additional Material: 7 Tab.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 985-1000 
    ISSN: 0271-2091
    Keywords: Outflow boundary conditions ; Vortex shedding ; 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: The simulation of the von Karman vortex street behind a circular cylinder has long been used as a benchmark problem to test the performance of numerical algorithms for solving the Navier-Stokes equations. It is particularly suited for comparing different numerical outflow boundary conditions since the computational domain must necessarily be terminated in the vortex street itself. This paper presents detailed numerical results of the flow past a cylinder at a Reynolds number of 100 on a very fine mesh which has been purposely designed to extend past the typically used dimensions. Hopefully, these results can form a basis of a benchmark solution for the comparison of the effects of different outflow boundary conditions.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 103-120 
    ISSN: 0271-2091
    Keywords: free surface ; free boundary problem ; segregated method ; finite elements ; extrusion ; 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 to simulate steady, viscous free surface flows is presented in this paper. A Picard-type approach wherein the flow and free surface updates are performed alternately is utilized to iterate for a solution. The procedure is intended for large-scale two- or three-dimensional problems. A surface-intrinsic co-ordinate system which facilities representation of general free surface shapes is used. Using a Galerkin finite element method (GFEM), two free surface updates, namely kinematic and normal stress updates are formulated. It is shown that the effects of surface tension, surface tension gradients and imposition of contact angles can be simulated elegantly within the framework of the GFEM. A novel feature of the updates is that the deformations are sought in a direction normal to the current iterate free surface shape, with the result that the method is ideally suited when used in conjunction with an automatic mesh generator. With the normal stress update a volume constraint can also be imposed. A segregated method is utilized to solve iteratively one degree of freedom at a time for the solution of the flow variables. As a result, the memory and disc space requirements are minimal. Sample problems in extrusion, coating and crystal growth are presented to clearly illustrate the convergence behaviour and accuracy of the algorithm.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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