题  目：可压缩欧拉方程的高阶ALE间断有限元算法研究

（A High Order ALE-DG Method for Solving Compressible Euler Equations）

报告人：蔚喜军 研究员 北京应用物理与计算数学研究所

时  间：7月16日（周五下午） 15：30—16：30

地  点：文理楼290会议室

摘要：The compressible Euler equations can be used to describe the complex fluid flow problems such as implosion dynamics, ICF, interfacial instability and so on. These problems have the characteristics of dynamic boundary, strong discontinuity, large deformation, nonlinear, multimedia and so on. It is very difficult and challenging to solve these problems numerically. We study using Arbitrary Lagrangian-Eulerian (ALE) discontinuous Galerkin (DG) method for compressible Euler equations and construct a grid containing velocity ALE scheme, namely when the grid velocity is equal to the fluid velocity, It is the Lagrangian scheme; when the grid velocity is equal to zero, it is the Eulerian scheme. In one dimensional case, the speed of the grid is based on the Roe averaging method, which is characterized by the ability to accurately track the material interface. In the two-dimensional case, the speed of the grid is based on the method of solving the elliptic equation, and we have made a correction to it. The advantage of the scheme is that the new grid can be solved explicitly through computing physical quantities at the last time, avoiding the format iteration and interpolation process, and the grid distribution is more intensive on neighborhood of contact discontinuities and shock waves which it has some kind of grid adaptive function. Compared with the Lagrangian scheme, because grid speed is introduced into the scheme, we can avoid stopping calculation of pure Lagrangian scheme due to grid distortion. The numerical flux of the scheme is selected the HLLC flux. And to eliminate physical quantity non physical numerical oscillation by using discontinuous Galerkin method, the TVB slope limiter or WENO reconstruction is selected. The scheme can maintain the conservation of mass, momentum and total energy. Some numerical examples of single medium fluid flow and multimedia fluid flow show that the scheme has high accuracy, robustness and essential non oscillation.

报告人简介：

蔚喜军，北京应用物理与计算数学研究所，计算物理国防科技重点实验室，研究员，博士生导师，兼职中国科技大学和东北师范大学博士生导师。现任《空气动力学学报》和《Journal of Mathematical Research and Applications (JMRA)》杂志编委，曾任《计算物理》编委。长期以来主要从事流体力学数值方法研究，特别在流体力学有限元数值方法研究方面，取得国内一流原创性科研成果，发表学术论文100余篇，主持完成国家自然科学基金10余项，中物院基金、重点实验室基金等11项，参与完成国家863计划项目等多项，撰写“十二五”国家重点图书出版规划项目专著一本《多介质流体动力学计算方法》（科学出版社）。

中国石油大学（华东）理学院

2021年7月14日