A Space‐Time Fourth‐Order Compact Finite Difference Scheme for Semilinear Compressible Darcy–Brinkman Model

ABSTRACT A high‐order algorithm targeting the two‐dimensional semilinear compressible Darcy–Brinkman equation is proposed in porous media. This method combines block‐centered and compact difference techniques in spatial discretization with the implicit‐explicit (IMEX) fourth‐order backward difference formula (BDF4) scheme for temporal discretization. The stability and error estimates for both the solution and flux of the provided scheme are demonstrated. Numerical experiments for model problems validate that this approach achieves fourth‐order convergence in both space and time while exhibiting high accuracy and relatively ideal efficiency.