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On central-difference and upwind schemes. (English) Zbl 0757.76044
Summary: A class of numerical dissipation models for central-difference schemes constructed with second- and fourth-difference terms is considered. The notion of matrix dissipation associated with upwind schemes is used to establish improved shock capturing capability for these models. In addition, conditions are given that guarantee that such dissipation models produce a TVD scheme. Appropriate switches for this type of model to ensure satisfaction of the TVD property are presented. Significant improvements in the accuracy of a central-difference scheme are demonstrated by computing both inviscid and viscous transonic airfoil flows.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76H05 Transonic flows
65N06 Finite difference methods for boundary value problems involving PDEs
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