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    Distributed Relaxation Multigrid and Defect Correction Applied to the Compressible Navier-Stokes Equations (1999)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: The distributed-relaxation multigrid and defect- correction methods are applied to the two- dimensional compressible Navier-Stokes equations. The formulation is intended for high Reynolds number applications and several applications are made at a laminar Reynolds number of 10,000. A staggered- grid arrangement of variables is used; the coupled pressure and internal energy equations are solved together with multigrid, requiring a block 2x2 matrix solution. Textbook multigrid efficiencies are attained for incompressible and slightly compressible simulations of the boundary layer on a flat plate. Textbook efficiencies are obtained for compressible simulations up to Mach numbers of 0.7 for a viscous wake simulation.
    Keywords: Numerical Analysis
    Type: AIAA Paper 99-3334 , 14th Computational Fluid Dynamics Conference; Jun 28, 1999 - Jul 01, 1999; Norfolk, VA; United States
    Format: application/pdf
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  • 2
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    An O(Nm(sup 2)) Plane Solver for the Compressible Navier-Stokes Equations (1999)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: A hierarchical multigrid algorithm for efficient steady solutions to the two-dimensional compressible Navier-Stokes equations is developed and demonstrated. The algorithm applies multigrid in two ways: a Full Approximation Scheme (FAS) for a nonlinear residual equation and a Correction Scheme (CS) for a linearized defect correction implicit equation. Multigrid analyses which include the effect of boundary conditions in one direction are used to estimate the convergence rate of the algorithm for a model convection equation. Three alternating-line- implicit algorithms are compared in terms of efficiency. The analyses indicate that full multigrid efficiency is not attained in the general case; the number of cycles to attain convergence is dependent on the mesh density for high-frequency cross-stream variations. However, the dependence is reasonably small and fast convergence is eventually attained for any given frequency with either the FAS or the CS scheme alone. The paper summarizes numerical computations for which convergence has been attained to within truncation error in a few multigrid cycles for both inviscid and viscous ow simulations on highly stretched meshes.
    Keywords: Numerical Analysis
    Type: AIAA Paper 99-0785 , 37th AIAA Aerospace Sciences Meeting and Exhibit; Jan 11, 1999 - Jan 14, 1999; Reno, NV; United States
    Format: application/pdf
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