Stable and accurate schemes for the compressible Navier-Stokes equations

Authors:
K. Mattsson;M. Svärd;M. Shoeybi
Affiliations:
Center for Turbulence Research, Building 500, Stanford University, Stanford, CA 94305-3035, United States and Department of Information Technology, Uppsala University, Uppsala, SE 751 05 Uppsala, ...;Center for Turbulence Research, Building 500, Stanford University, Stanford, CA 94305-3035, United States and Centre of Mathematics for Applications, University of Oslo, P.B 1053, Blindern N-0316 ...;Center for Turbulence Research, Building 500, Stanford University, Stanford, CA 94305-3035, United States
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

Minimal stencil width discretizations of combined mixed and non-mixed second-order derivatives are analyzed with respect to accuracy and stability. We show that these discretizations lead to stability for Cauchy problems. With a careful boundary treatment, we also show that the stability holds for initial-boundary value problems. The analysis is verified by numerical simulations of Burgers' and Navier-Stokes equations in two and three space dimensions.