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High Order Accurate direct arbitrary-lagrangian-eulerian ADER-MOOD Finite Volume Schemes for Non-Conservative Hyperbolic Systems with Stiff Source Terms

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Communications in Computational Physics 2017年第1期21卷 271-312页

作者： Walter Boscheri Raphael Loubere Laboratory of AppliedMathematics Department of CivilEnvironmental and Mechanical EngineeringUniversity of TrentoI-38123 TrentoItaly CNRS and Institut de Mathematiques de Toulouse(IMT)Universite Paul-Sabatier ToulouseFrance

In this paper we present a 2D/3D high order accurate finite volume scheme in the context of direct arbitrary-lagrangian-eulerian algorithms for general hyperbolic systems of partial differential equations with non-conservative products and stiff source *** scheme is constructed with a single stencil polynomial reconstruction operator,a one-step space-time ADER integration which is suitably designed for dealing even with stiff sources,a nodal solver with relaxation to determine the mesh motion,a path-conservative integration technique for the treatment of non-conservative products and an a posteriori stabilization procedure derived from the so-called Multidimensional Optimal Order Detection(MOOD)*** this work we consider the seven equation Baer-Nunziato model of compressible multi-phase flows as a representative model involving non-conservative products as well as relaxation source terms which are allowed to become *** new scheme is validated against a set of test cases on 2D/3D unstructured moving meshes on parallel machines and the high order of accuracy achieved by the method is demonstrated by performing a numerical convergence *** Riemann problems and explosion problems with exact solutions are simulated in 2D and *** overall numerical code is also profiled to provide an estimate of the computational cost required by each component of the whole algorithm.

关键词： direct arbitrary-lagrangian-eulerian a posteriori MOOD stabilization Baer-Nunziato model stiff source terms non-conservative products unstructured mesh ADER high order of accuracy in space and time high performance computing(HPC) hyperbolic conservation laws

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