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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

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

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.

An Unconventional Divergence Preserving Finite-Volume Discretization of Lagrangian Ideal MHD

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Communications on Applied Mathematics and Computation 2024年第3期6卷 1665-1719页

作者： Walter Boscheri raphael loubere Pierre-Henri Maire Dipartimento di Matematica e Informatica University of FerraraFerraraItaly Institut de Mathématiques de Bordeaux(IMB) University of BordeauxTalenceFrance CEA-CESTA Le BarpFrance

We construct an unconventional divergence preserving discretization of updated Lagrangian ideal magnetohydrodynamics(MHD)over simplicial *** cell-centered finite-volume(FV)method employed to discretize the conservation laws of volume,momentum,and total energy is rigorously the same as the one developed to simulate hyperelasticity *** construction this moving mesh method ensures the compatibility between the mesh displacement and the approximation of the volume flux by means of the nodal velocity and the attached unit corner normal vector which is nothing but the partial derivative of the cell volume with respect to the node coordinate under *** is precisely the definition of the compatibility with the Geometrical Conservation Law which is the cornerstone of any proper multi-dimensional moving mesh FV *** momentum and the total energy fluxes are approximated utilizing the partition of cell faces into sub-faces and the concept of sub-face force which is the traction force attached to each sub-face impinging at a *** observe that the time evolution of the magnetic field might be simply expressed in terms of the deformation gradient which characterizes the Lagrange-to-Euler *** this framework,the divergence of the magnetic field is conserved with respect to time thanks to the Piola ***,we solve the fully compatible updated Lagrangian discretization of the deformation gradient tensor for updating in a simple manner the cell-centered value of the magnetic ***,the sub-face traction force is expressed in terms of the nodal velocity to ensure a semi-discrete entropy inequality within each *** conservation of momentum and total energy is recovered prescribing the balance of all the sub-face forces attached to the sub-faces impinging at a given *** balance corresponds to a vectorial system satisfied by the nodal *** always admits a unique solution which provides the nodal velocit

关键词： Cell-centered Lagrangian finite-volume(FV)schemes Hyper-elasticity Ideal magnetohydrodynamics(MHD)equations Moving unstructured meshes A posteriori MOOD limiting

晚上新世冰期发动的渐进模式——北大西洋深海岩心证据

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地质科技情报 1989年第3期8卷 56-60,50页

作者： Paul loubere 彭雪萍杨星

对北大西洋深海钻探计划(DSDP)548号孔的浮游有孔虫组合,及晚上新世底栖有孔虫氧同位素的详细分析表明:北半球冰期是通过一系列冷暖循环逐渐开始的.这个结果与其它地点(DSDP)的研究相抵触.后者表明在2.4~2.5Ma间,冰期以跳跃方式突然发生... 详细信息

对北大西洋深海钻探计划(DSDP)548号孔的浮游有孔虫组合,及晚上新世底栖有孔虫氧同位素的详细分析表明:北半球冰期是通过一系列冷暖循环逐渐开始的.这个结果与其它地点(DSDP)的研究相抵触.后者表明在2.4~2.5Ma间,冰期以跳跃方式突然发生.在此以前,古气候状况一直是稳定的,两者的区别可以用取样亲间距与沉积间断来解释.由于沉积间断,其它位置上晚上新世冰期开始时间变得模糊不清,看起来,像是以跳跃式开始的.548号孔研究表明:北半球冰川作用之发端,与其说在地质历史上是一个突发古气候事件,不如说是气候逐步恶化的结果.

关键词：上新世底栖有孔虫浮游有孔虫深海钻探计划古地磁地层学氧同位素沉积间断冰川作用生物地层冷水种

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小微信贷的政策悖论:推动发展与制造不平等

文化纵横 2019年第1期 108-118,M0004页

作者：卢宁() 杨龙(译) 徐书鸣(译) 瑞典隆德大学东亚与东南亚研究中心不详

引言长期以来,中国城乡关系一直被视作二元对立的——乡村代表着僻壤、边缘和不发达的地区,城市则是中心、现代和繁荣的象征。尤其是改革开放以来,伴随经济私有化不断拓展,中国政府愈发意识到这种城乡二元结构对国家的整体发展构成严峻... 详细信息

引言长期以来,中国城乡关系一直被视作二元对立的——乡村代表着僻壤、边缘和不发达的地区,城市则是中心、现代和繁荣的象征。尤其是改革开放以来,伴随经济私有化不断拓展,中国政府愈发意识到这种城乡二元结构对国家的整体发展构成严峻挑战。

关键词：小微信贷普惠金融城乡关系