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

In this paper, a high-order numerical scheme by using fourth-order implicit Runge-Kutta method and block-centered finite difference method is constructed to solve the compressible wormhole propagation. For the evolution of porosity, high-order interpolation technique and cut-off approach are applied to achieve high-order and bound-preserving. Finally, some numerical experiments are presented to demonstrate the correctness and capability of the given scheme.