Stable and accurate schemes for the compressible Navier-Stokes equations
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. (c) 2007 Elsevier Inc. All rights reserved.
compressible navier-stokes equations minimal stencil width schemes numerical stability boundary conditions second-derivatives