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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 429-442 
    ISSN: 0271-2091
    Keywords: Uzawa algorithm ; Preconditioning ; Incomplete factorization ; Three-dimensional ; 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 new iterative algorithm for the solution of the three-dimensional Navier-Stokes equations by the finite element method is presented. This algorithm is based on a combination of the Uzawa and the Arrow-Hurwicz algorithms and uses a preconditioning technique to enhance convergence. Numerical tests are presented for the cubic cavity problem with two elements, namely the linear brick Q1-P0 and the enriched linear brick Q1+ - P1. It is shown that the proposed methodology is optimal with the enriched element and that the CPU time varies as NEQ1·44, where NEQ is the number of equations.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 275-294 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Fully-coupled solution ; Iterative solvers ; Finite-element methods ; Parallel algorithm ; Block diagonal preconditioning ; CFD ; 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 the parallelization aspects of a solution method for the fully coupled 3D compressible Navier-Stokes equations. The algorithmic thrust of the approach, embedded in a finite element code NS3D, is the linearization of the governing equations through Newton methods, followed by a fully coupled solution of velocities and pressure at each non-linear iteration by preconditioned conjugate gradient-like iterative algorithms. For the matrix assembly, as well as for the linear equation solver, efficient coarse-grain parallel schemes have been developed for shared memory machines, as well as for networks of workstations, with a moderate number of processors. The parallel iterative schemes, in particular, circumvent some of the difficulties associated with domain decomposition methods, such as geometry bookkeeping and the sometimes drastic convergence slow-down of partitioned non-linear problems.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 447-457 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new algorithm for the solution of the three-dimensional Navier-Stokes equation using the mixed formulation and an incomplete factorization technique is presented. The linear system obtained at each modified Newton-Raphson iteration is solved by the preconditioned conjugate residual method (PCR) using an out-of-core incomplete LU factorization as preconditioning. This factorization is performed on a matrix stored by a new static storage method called the packed skyline method. The performance of the proposed algorithm is assessed for the wall-driven cubic cavity problem using the Q1+ -P1 enriched element.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 3 (1987), S. 223-233 
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several new elements are compared to the standard trilinear velocity-constant pressure element (Q1 - P0) for the solution of the three-dimensional Navier-Stokes equations by the finite element method. The test problem is the cubic wall-driven cavity with solution sought at Reynolds numer of 400 and 3200. It is shown that the Q1 - P0 can be advantageously replaced by better elements and a choice among these elements is proposed.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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