High-order bound-preserving discontinuous Galerkin methods for compressible miscible displacements in porous media on triangular meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:378

Article

Chuenjarern, Nattaporn¹  Xu, Ziyao¹  Yang, Yang¹ 

[1] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

关键词: Compressible miscible displacements;    Bound-preserving;    Discontinuous Galerkin method;    Triangular meshes;    Multi-component fluid;    Flux limiter;   

DOI  :  10.1016/j.jcp.2018.11.003

来源: Elsevier

【 摘 要 】

In this paper, 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 jth component, c(j), should be between 0 and 1. There are three main difficulties. Firstly, c(j) does not satisfy a maximum-principle. Therefore, the numerical techniques introduced in Zhang and Shu (2010) [44] cannot be applied directly. The main idea is to apply the positivity-preserving techniques to all C'(s)(j) and enforce Sigma(j)c(j) = 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 and choose suitable fluxes in the pressure and concentration equations. Secondly, it is not easy to construct first-order numerical fluxes for interior penalty DG methods on triangular meshes. One of the key points in the high-order BP technique applied in this paper is the combination of high-order and lower-order numerical fluxes. We will construct second-order BP schemes and use the second-order numerical fluxes as the lower-order one. Finally, the classical slope limiter cannot be applied to c(j). To construct the BP technique, we will not approximate c(j) directly. Therefore, a new limiter will be introduced. Numerical experiments will be given to demonstrate the high-order accuracy and good performance of the numerical technique. (C) 2018 Elsevier Inc. All rights reserved.

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