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Local Discontinuous Galerkin Method with Implicit–Explicit Time Marching for Incompressible Miscible Displacement Problem in Porous Media

  • Haijin Wang
  • Jingjing Zheng
  • Fan Yu
  • Hui Guo
  • Qiang Zhang
Article

Abstract

In this paper, we shall present two fully-discrete local discontinuous Galerkin methods, coupled with multi-step implicit–explicit time discretization up to second order, for solving the two-dimensional incompressible miscible displacement problem. To avoid the solving of nonlinear algebraic systems, the extrapolation linearization is adopted to diffusion–dispersion tensor. Under weak temporal-spatial conditions, the optimal error estimates in \(L^{\infty }(L^{2})\) norm for both concentration and velocity are derived. Numerical experiments are also given to demonstrate the theoretical results.

Keywords

Local discontinuous Galerkin method Implicit–explicit time-marching scheme Incompressible miscible displacement problem Extrapolation linearization Error estimates 

Mathematics Subject Classification

65M12 65M15 65M60 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of ScienceNanjing University of Posts and TelecommunicationsNanjingPeople’s Republic of China
  2. 2.College of ScienceChina University of PetroleumQingdaoPeople’s Republic of China
  3. 3.Department of MathematicsNanjing UniversityNanjingPeople’s Republic of China

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