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Fourier stability analysis and local Courant number of the preconditioned variational multiscale stabilization (P-VMS) for Euler compressible flow

AuthorsMoragues Ginard, Margarida; Bernardino, Gabriel; Vazquez, Mariano; Houzeaux, Guillaume
KeywordsVariational multiscale stabilization
Local preconditioning
Compressible flow, Fourier stability analysis, Local Courant–Friedrichs–Lewy number
Finite elements
Issue Date2016
CitationComputer Methods in Applied Mechanics and Engineering 301: 28- 51 (2016)
AbstractThe results of a Fourier stability analysis of the preconditioned variational multiscale stabilization (P-VMS) method introduced in Moragues et al. (2015) are presented in this paper. P-VMS combines a variational multiscale stabilized finite elements discretization together with local preconditioning. In this work, we deal with the P-VMS method using van Leer-Lee-Roe's (vanLeer et al., 1991) and Choi-Merkle's (Choi and Merkle, 1993) local preconditioners. We solve the Euler equations of compressible flow for steady problems. We concentrate on explicit time integration schemes. The stability analysis is performed on a two dimensional simplified problem with a structured mesh and its conclusions are applied to two and three dimensional general problems with unstructured meshes. As a result of this analysis a local Courant-Friedrichs-Lewy number is defined for the computation of the time step. The convergence rate is evaluated, and compared with the traditional constant Courant-Friedrichs-Lewy number for various test cases spanning a large range of Mach numbers. © 2015 Elsevier B.V.
Identifiersdoi: 10.1016/j.cma.2015.12.008
issn: 0045-7825
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