A second-order time discretizing block-centered finite difference method for compressible wormhole propagation

In this paper, a second-order time discretizing block-centered finite difference method is introduced to solve the compressible wormhole propagation. The optimal second-order error estimates for the porosity, pressure, velocity, concentration and its flux are established carefully in different discrete norms on non-uniform grids. Then by introducing Lagrange multiplier, a novel bound-preserving scheme for concentration is constructed. Finally, numerical experiments are carried out to demonstrate the correctness of theoretical analysis and capability for simulations of compressible wormhole propagation.