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Comparison of Several Dissipation Algorithms for Central Difference Schemes.pdf

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Comparison of Several Dissipation Algorithms for Central Difference Schemes

NASA Contractor Report 201726 ICASE Report No. 97-40 COMPARISON OF SEVERAL DISSIPATION ALGORITHMS FOR CENTRAL DIFFERENCE SCHEMES R. C. Swanson R. Radespiel E. Turkel NASA Contract No. NAS1-19480 August 1997 Institute for Computer Applications in Science and Engineering NASA Langley Research Center Hampton, VA 23681-0001 Operated by Universities Space Research Association National Aeronautics and Space Administration Langley Research Center Hampton, Virginia 23681-0001 COMPARISON OF SEVERAL DISSIPATION ALGORITHMS FOR CENTRAL DIFFERENCE SCHEMES R. C. Swanson Aerodynamic and Acoustic Mcthods Branch NASA Langley Research Center Hampton, VA R. Radespiel, E. Turkel DLR, Institute of Design Aerodynamics ICASE, NASA Langley Braunschweig, Germany and Department of Mathematics Tel-Aviv University, Tel-Aviv, Israel * Abstract Several algorithms for introducing artificial dissipation into a central difference approx- imation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretiza- tion and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical results are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme. *This research was supported in part by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the first author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-0001. In