Wednesday August 23rd, at 11:00AM Math Conference room

August 20, 2016 by Duan Chen
Categories: Spring 2022
Yang Yang, Department of Mathematical Sciences, Michigan Tech University
Title:Bound-preserving discontinuous Galerkin method for compressible miscible displacement problem in porous media
Abstract: In this talk, I will talk about the bound-preserving discontinuous Galerkin (DG) methods for the coupled system of compressible miscible displacement problems. We consider the problem with two components and the (volumetric) concentration of the ith component of the fluid mixture, c_i, should be between 0 and 1. However, c_i does not satisfy the maximum-principle due to the existence of the source terms. Therefore, the numerical techniques introduced in (X. Zhang and C.-W. Shu, Journal of Computational Physics, 229 (2010), 3091-3120) cannot be applied directly. The main idea is to apply the positivity-preserving techniques to both c_1 and c_2, respectively and enforce c_1+c_2=1 simultaneously to obtain physically relevant approximations. By doing so, we have to treat the time derivative of the pressure dp/dt as a source in the concentration equation. Moreover, c_i’s are not the conservative variables, as a result, the classical bound-preserving limiter in (X. Zhang and C.-W. Shu, Journal of Computational Physics, 229 (2010), 3091-3120) cannot be applied directly. Therefore, another limiter will be introduced. Numerical experiments will be given to demonstrate the good performance of the numerical technique.