| Abstract: |
| In this talk, we present characteristic block-centered finite difference methods for solving the nonlinear Darcy-Forchheimer compressible miscible displacement problem in porous media. The block-centered finite difference method is used to discretize the miscible problem, where the pressure equation is described by the nonlinear Darcy-Forchheimer model, and the transport equation is addressed with the help of the characteristic method. Two-grid methods are developed for the nonlinear system. The nonlinear system is linearized using Newton`s method with a small positive parameter to ensure the differentiability of the nonlinear term in the Darcy-Forchheimer equation. A modified two-grid algorithm is proposed to further reduce the computational cost of the time-dependent problem. The proposed methods are rigorously analyzed, and a priori error estimates are provided for the rates of convergence of the velocity, pressure, concentration, and its flux. Finally, numerical experiments are conducted to demonstrate the effectiveness of the proposed methods by comparing the efficiency with that of other solvers, especially in terms of CPU time. |
|