Premium
Robustness versus accuracy in shock‐wave computations
Author(s) -
Gressier Jérémie,
Moschetta JeanMarc
Publication year - 2000
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/1097-0363(20000615)33:3<313::aid-fld7>3.0.co;2-e
Subject(s) - riemann solver , inviscid flow , riemann hypothesis , mathematics , compressible flow , mach number , mach reflection , transonic , roe solver , riemann problem , computational fluid dynamics , compressibility , mathematical analysis , finite volume method , classical mechanics , physics , aerodynamics , mechanics , mach wave
Despite constant progress in the development of upwind schemes, some failings still remain. Quirk recently reported (Quirk JJ. A contribution to the great Riemann solver debate. International Journal for Numerical Methods in Fluids 1994; 18 : 555–574) that approximate Riemann solvers, which share the exact capture of contact discontinuities, generally suffer from such failings. One of these is the odd–even decoupling that occurs along planar shocks aligned with the mesh. First, a few results on some failings are given, namely the carbuncle phenomenon and the kinked Mach stem . Then, following Quirk's analysis of Roe's scheme, general criteria are derived to predict the odd–even decoupling. This analysis is applied to Roe's scheme (Roe PL, Approximate Riemann solvers, parameters vectors, and difference schemes, Journal of Computational Physics 1981; 43 : 357–372), the Equilibrium Flux Method (Pullin DI, Direct simulation methods for compressible inviscid ideal gas flow, Journal of Computational Physics 1980; 34 : 231–244), the Equilibrium Interface Method (Macrossan MN, Oliver. RI, A kinetic theory solution method for the Navier–Stokes equations, International Journal for Numerical Methods in Fluids 1993; 17 : 177–193) and the AUSM scheme (Liou MS, Steffen CJ, A new flux splitting scheme, Journal of Computational Physics 1993; 107 : 23–39). Strict stability is shown to be desirable to avoid most of these flaws. Finally, the link between marginal stability and accuracy on shear waves is established. Copyright © 2000 John Wiley & Sons, Ltd.