A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow

作     者：Xiaolong Zhao Xijun Yu Zupeng Jia Shijun Zou Meilan Qiu 

作者机构：School of Mathematics and StatisticsZhengzhou UniversityZhengzhouHenan 450001China Laboratory of Computational PhysicsInstitute of Applied Physics and Computational MathematicsBeijing 100088China School of Mathematical SciencesCapital Normal UniversityBeijing 100048China School of Mathematics and StatisticsHuizhou UniversityHuizhouGuangdong 516007China Institute of Applied Physics and Computational MathematicsBeijing 100088China 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2024年第16卷第1期

页      面：181-207页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by Natural Science Foundation of Guangdong province of China(Grant No.2018A030310038) National Natural Science Foundation of China(Grant Nos.11571002,11772067,11702028 and 12071046) 

主　　题：Vertex-centered arbitrary Lagrangian-Eulerian sub-cells multi-material flows 

摘      要：In this paper,we present a new vertex-centered arbitrary LagrangianEulerian(ALE)finite volume scheme for two-dimensional compressible *** our scheme,the momentum equation is discretized on the vertex control volume,while the mass equation and the energy equation are discretized on the sub-cells which are included in the vertex control *** attain the average of the fluid velocity on the vertex control volume directly by solving the conservation *** we can obtain the fluid velocity at vertex with the reconstructed polynomial of the *** fluid velocity is chosen as the mesh velocity,which makes the mesh move in a Lagrangian *** WENO(Weighted Essentially Non-Oscillatory)reconstructions for the density(the total energy)and the velocity are used to make our scheme achieve the anticipated *** with the general vertexcentered schemes,our scheme with the new approach for the space discretization can simulate some multi-material flows which do not involve large *** addition,our scheme has good robustness,and some numerical examples are presented to demonstrate the anticipated accuracy and the good properties of our scheme.