A Compact Eulerian Interface-Capturing Algorithm for Compressible Multimaterial Elastic-Plastic Flows with Mie-Gr uneisen Equation of State  

作　　者：Xiang Li Dong-Jun Ma Nan-Sheng Liu Pei Wang 

机构地区：[1]Institute of Applied Physics and Computational Mathematics,Beijing 100094,China [2]Department of Modern Mechanics,University of Science and Technology of China,Hefei,Anhui 230027,China [3]Center for Applied Physics and Technology,Peking University,Beijing 100871,China

出　　处：《Advances in Applied Mathematics and Mechanics》2023年第2期485-521,共37页应用数学与力学进展（英文）

基　　金：This work was funded by the Natural Science Foundation of China under Grant Nos.11772065 and 11702028;the Science Challenge Project(Grant No.TZ2016001);The work of the first author was supported by the Postdoctoral Science Foundation of China(Grant No.2020M670226).

摘　　要：This paper presents an Eulerian diffuse-interface method using a high-order compact difference scheme for simulating elastic-plastic flows with the Mie–Gruneisen(MG)equation of state(EoS).For simulations of multimaterial problems,numerical errors were generated in the material discontinuities owing to inconsistent treatment of the convective terms.Based on the normal-stress-based mechanical equilibrium assumption for elastic-plastic solids,we introduce an improved form of the consistent localized artificial diffusivity(LAD)method to ensure an oscillation-free interface for velocity and normal stress.The proposed algorithm uses a hyperelastic model.A mixture type of the model system was formed by combining the conservation equations for the basic conserved variables,an equation of a unified deviatoric tensor describing solid deformation,and an additional set of equations for solving the material quantities in the MG EoS.Several one-and two-dimensional problems with various discontinuities,including the elastic-plastic Richtmyer–Meshkov instability,were considered for testing the proposed method.

关 键 词：Multimaterial elastic-plastic flow Eulerian solid-dynamics high-order accurate schemes compact finite difference localized artificial diffusivity 

分 类 号：O343[理学—固体力学]