An h-Adaptive Local Discontinuous Galerkin Method for Simulating Wormhole Propagation with Darcy-Forcheiner Model

In this paper, we apply local discontinuous Galerkin methods to the compressible wormhole propagation. With high velocity, Darcy-Forchheimer model is used instead of classical Darcy framework. Optimal error estimates for the pressure, velocity, porosity and concentration in different norms are established on non-uniform rectanglular grids. To capture the propagation of the wormhole accurately and save computations, adaptive mesh is applied. Numerical experiments are presented to verify the theoretical analysis and show the good performance of the LDG scheme for compressible wormhole propagation.