报告题目：三角网上多孔介质中可压缩混相驱替问题的高精度保界间断有限元格式

报 告 人：徐梓尧 博士生 密歇根理工大学应用数学系
报告时间：2018年5月19日（星期六）下午16：00-17：00
报告地点：文理楼254

报告人简介： 徐梓尧，在读博士，密歇根理工大学应用数学系。研究方向为油藏数值模拟，间断Galerkin方法。首次针对多孔介质多相渗流里混相驱问题的浓度变量进行了保界算法处理。

报告摘要：In this talk, we develop high-order bound-preserving (BP) discontinuous Galerkin (DG) methods for the coupled system of compressible miscible displacements on triangular meshes. We consider the problem with multi-component fluid mixture and the (volumetric) concentration of the j^th component, c_j,(j=1,2,…N) should be between 0 and 1. There are three main difficulties. Firstly, c_j does not satisfy a maximum-principle. Therefore, the traditional numerical techniques cannot be applied directly. The main idea is to apply the positivity-preserving techniques to all c_j's and enforce the sum of all c_j=1 simultaneously to obtain physically relevant approximations. By doing so, we have to choose suitable fluxes in the pressure and concentration equations. Secondly, the construction of high-order BP schemes on triangular meshes. We use IPDG methods for the concentration equations, and the first-order numerical fluxes are not easy to construct. Therefore, we will construct second-order BP schemes and then combine the second and high order fluxes to obtain a new one which further yields positive numerical cell averages. Finally, c_j are not the conservative variables, as a result, the classical slope limiter cannot be applied. Moreover, for fluid mixture with more than one components, we cannot simply set the upper bound of each c_j to be 1. Therefore, a suitable limiter for multi-component fluid will be introduced. Numerical experiments will be given to demonstrate the high-order accuracy and good performance of the numerical technique.

理学院 科技处 国际合作与交流处

2018-05-17