Characteristic splitting mixed finite element analysis of compressible wormhole propagation

Abstract

A combined method is provided for simulating the compressible wormhole propagation, in which, the splitting mixed finite element (SMFE) method is applied for the parabolic-type pressure equation, the modified mass-conservative characteristic (MCC) method is presented for the convection-diffusion type solute transport equation, and the traditional finite element method is applied for the porosity equation. The application of the splitting mixed element method results in a symmetric positive definite coefficient matrix of the separated mixed element system and the mass-conservative characteristic finite element method not only does well in handling convection-dominant diffusion problem but also keeps mass balance globally. The convergence of this method is considered and the optimal L2-norm error estimate is also derived. Finally, some numerical examples are provided to confirm theoretical analysis and effectiveness of the proposed method.