Local preconditioning and variational multiscale stabilization for Euler compressible steady flow

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• 作者：Margarida Moragues Ginard^a ; ^{margarida.moragues@bsc.es" class="auth_mail" title="E-mail the corresponding author} ; Mariano Vá ; zquez^a ; ^b ; Guillaume Houzeaux^a
• 关键词：Local preconditioning ; Variational multiscale method ; Finite elements ; Euler equations ; Compressible flow ; Steady flow problems
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2016
• 出版时间：15 June 2016
• 年：2016
• 卷：305
• 期：Complete
• 页码：468-500
• 全文大小：5214 K

文摘

This paper introduces a preconditioned variational multiscale stabilization (P-VMS) method for compressible flows. In this introductory paper we focus on inviscid flow and steady state problems. The Euler equations are solved on fully unstructured grids and discretized using the finite element method. The P-VMS method can be decomposed into three parts. First, a local preconditioner is applied to the continuous equations to reduce the stiffness while covering a wide range of Mach numbers. Then, the resulting preconditioned system is discretized in space using finite elements and stabilized with a variational multiscale stabilization method adapted for the preconditioned equations. In this paper, the solution is advanced in time using a fully explicit time discretization, although P-VMS is general and can be applied to fully implicit solvers. The proposed method is assessed by comparing convergence and accuracy of the solutions between the non-preconditioned and preconditioned cases, in particular for van Leer–Lee–Roe’s (1991) and Choi-Merkle’s (1993) preconditioners, in some selected examples covering a large range of Mach numbers.