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

Abstract

AbstractIn 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.