A multigrid procedure for three-dimensional flows on non-orthogonal collocated grids

Authors

  • K. M. Smith,

    Corresponding author
    1. Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green, Urbana, IL 61801, U.S.A.
    • Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green, Urbana, IL 61801, U.S.A.
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  • W. K. Cope,

    1. Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green, Urbana, IL 61801, U.S.A.
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  • S. P. Vanka

    1. Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green, Urbana, IL 61801, U.S.A.
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Abstract

The development of a multigrid solution algorithm for the computation of three-dimensional laminar fully-elliptic incompressible flows is presented. The procedure utilizes a non-orthogonal collocated arrangement of the primitive variables in generalized curvilinear co-ordinates. The momentum and continuity equations are solved in a decoupled manner and a pressure-correction equation is used to update the pressures such that the fluxes at the cell faces satisfy local mass continuity. The convergence of the numerical solution is accelerated by the use of a Full Approximation Storage (FAS) multigrid technique. Numerical computations of the laminar flow in a 90° strongly curved pipe are performed for several finite-volume grids and Reynolds numbers to demonstrate the efficiency of the present numerical scheme. The rates of convergence, computational times, and multigrid performance indicators are reported for each case. Despite the additional computational overhead required in the restriction and prolongation phases of the multigrid cycling, the superior convergence of the present algorithm is shown to result in significantly reduced overall CPU times.

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