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Local preconditioning and variational multiscale stabilization for Euler compressible steady flow
Ist Teil von
Computer methods in applied mechanics and engineering, 2016-06, Vol.305, p.468-500
Ort / Verlag
Elsevier B.V
Erscheinungsjahr
2016
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
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.