High Order Accurate Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD Finite Volume Schemes for Non-Conservative Hyperbolic Systems with Stiff Source Terms

作     者：Walter Boscheri Raphael Loubere 

作者机构：Laboratory of AppliedMathematicsDepartment of CivilEnvironmental and Mechanical EngineeringUniversity of TrentoI-38123 TrentoItaly CNRS and Institut de Mathematiques de Toulouse(IMT)Universite Paul-SabatierToulouseFrance 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2017年第21卷第1期

页      面：271-312页

核心收录：

学科分类：07[理学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：W.B.has been financed by the European Research Council(ERC)under the European Union’s Seventh Framework Programme(FP7/2007-2013)with the research project STiMulUs,ERC Grant agreement no.278267 R.L.has been partially funded by the ANR under the JCJC project“ALE INC(ubator)3D”JS01-012-01 the“International Centre for Mathematics and Computer Science in Toulouse”(CIMI)partially supported by ANR-11-LABX-0040-CIMI within the program ANR-11-IDEX-0002-02.The authors would like to acknowledge PRACE for awarding access to the SuperMUC supercomputer based in Munich,Germany at the Leibniz Rechenzentrum(LRZ).Parts of thematerial contained in this work have been elaborated,gathered and tested while W.B.visited the Mathematical Institute of Toulouse for three months and R.L.visited the Dipartimento di Ingegneria Civile Ambientale e Meccanica in Trento for three months 

主　　题：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 

摘      要：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.