A new discontinuous Galerkin mixed finite element method for compressible miscible displacement problem. (15th September 2020)

• Record Type: Journal Article
• Authors: Zhang, Jiansong; Han, Huiran
• Is Part Of: Computers & mathematics with applications. Volume 80:issue 6(2020)
• Page Start: 1714
• Page End: 1725
• Publication Date: 2020-09-15
• Subjects: Splitting technique -- Discontinuous Galerkin method -- Convergence analysis -- Miscible displacement problem; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.08.008
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: A new combined discontinuous Galerkin method is proposed for compressible miscible displacement problem in porous media. Here, a splitting positive definite mixed finite element method is used for the pressure and Darcy velocity, while an interior penalty discontinuous Galerkin (IPDG) method is used for the transport equation. The stability and convergence of this algorithm are considered, and the optimal a priori error estimate in l ∞ ( L 2 ) for velocity, pressure and concentration are given. Finally we provide some numerical results to confirm our theoretical analysis, and simulate compressible fluid flows through homogeneous and isotropic porous media.