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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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A New Family of High Order Unstructured MOOD and ADER Finite Volume Schemes for Multidimensional Systems of Hyperbolic Conservation Laws

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Communications in Computational Physics 2014年第8期16卷 718-763页

作者： raphael loubere Michael Dumbser Steven Diot CNRS and Institut de Mathematiques de Toulouse(IMT)Universite Paul-Sabatier ToulouseFrance Department of Civil Environmental and Mechanical EngineeringUniversity of TrentoVia Mesiano77-38123 TrentoItaly Fluid Dynamics and Solid Mechanics(T-3) Los Alamos National LaboratoryNM 87545 USA.

In this paper,we investigate the coupling of the Multi-dimensional Optimal Order Detection(MOOD)method and the Arbitrary high order DERivatives(ADER)approach in order to design a new high order accurate,robust and computationally efficient Finite Volume(FV)scheme dedicated to solve nonlinear systems of hyperbolic conservation laws on unstructured triangular and tetrahedral meshes in two and three space dimensions,*** Multi-dimensional Optimal Order Detection(MOOD)method for 2D and 3D geometries has been introduced in a recent series of papers for mixed unstructured *** is an arbitrary high-order accurate Finite Volume scheme in space,using polynomial reconstructions with a posteriori detection and polynomial degree decrementing processes to deal with shock waves and other *** the following work,the time discretization is performed with an elegant and efficient one-step ADER *** so,we retain the good properties of the MOOD scheme,that is to say the optimal high-order of accuracy is reached on smooth solutions,while spurious oscillations near singularities are *** ADER technique permits not only to reduce the cost of the overall scheme as shown on a set of numerical tests in 2D and 3D,but it also increases the stability of the overall scheme.A systematic comparison between classical unstructured ADER-WENO schemes and the new ADER-MOOD approach has been carried out for high-order schemes in space and time in terms of cost,robustness,accuracy and *** main finding of this paper is that the combination of ADER with MOOD generally outperforms the one of ADER and WENO either because at given accuracy MOOD is less expensive(memory and/or CPU time),or because it is more accurate for a given grid resolution.A large suite of classical numerical test problems has been solved on unstructured meshes for three challenging multi-dimensional systems of conservation laws:the Euler equations of compressible gas dynamics

关键词： Finite Volume high-order conservation law polynomial reconstruction ADER MOOD hyperbolic PDE unstructured meshes finite volume one-step time discretization local continuous space-time Galerkin method WENO Euler equations MHD equations relativistic MHD equations.

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Staggered Lagrangian Discretization Based on Cell-Centered Riemann Solver and Associated Hydrodynamics Scheme

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Communications in Computational Physics 2011年第9期10卷 940-978页

作者： Pierre-Henri Maire raphael loubere Pavel Vachal CEA-CESTA BP 233114Le BarpFrance Institut de Mathematiques de Toulouse(IMT)Universite Paul-Sabatier and CNRS ToulouseFrance FNSPE Czech Technical University(CTU)in PragueCzech Republic

The aim of the present work is to develop a general formalism to derive staggered discretizations for Lagrangian hydrodynamics on two-dimensional unstructured *** this end,we make use of the compatible discretization that has been initially introduced by *** et al.,in ***.,146(1998).Namely,momentum equation is discretized by means of subcell forces and specific internal energy equation is obtained using total energy *** main contribution of this work lies in the fact that the subcell force is derived invoking Galilean invariance and thermodynamic *** is,we deduce a general form of the sub-cell force so that a cell entropy inequality is *** subcell force writes as a pressure contribution plus a tensorial viscous contribution which is proportional to the difference between the nodal velocity and the cell-centered *** cell-centered velocity is a supplementary degree of freedom that is solved by means of a cell-centered approximate Riemann *** satisfy the second law of thermodynamics,the local subcell tensor involved in the viscous part of the subcell force must be symmetric positive *** subcell tensor is the cornerstone of the *** particular expression of this tensor is given.A high-order extension of this discretization is *** tests are presented in order to assess the efficiency of this *** results obtained for various representative configurations of one and two-dimensional compressible fluid flows show the robustness and the accuracy of this scheme.

关键词： Lagrangian scheme Riemann solver artificial viscosity hydrodynamics compressible flow

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