Conservative Local Discontinuous Galerkin Method for Compressible Miscible Displacements in Porous Media

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© 2017, Springer Science+Business Media, LLC. In Guo et al. (Appl Math Comput 259:88–105, 2015), a nonconservative local discontinuous Galerkin (LDG) method for both flow and transport equations was introduced for the one-dimensional coupled system of compressible miscible displacement problem. In this paper, we will continue our effort and develop a conservative LDG method for the problem in two space dimensions. Optimal error estimates in L∞(0, T; L2) norm for not only the solution itself but also the auxiliary variables will be derived. The main difficulty is how to treat the inter-element discontinuities of two independent solution variables (one from the flow equation and the other from the transport equation) at cell interfaces. Numerical experiments will be given to confirm the accuracy and efficiency of the scheme.

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Journal of Scientific Computing