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A characteristic block-centered finite difference method for Darcy-Forchheimer compressible miscible displacement problem. (English) Zbl 1489.65153

Summary: In this paper, we construct, analyze, and numerically validate a characteristic block-centered finite difference method for 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. A decoupled algorithm is designed for solving the resulting nonlinear system combined with Picard iteration. Our method is shown to be effective with the established theoretical analysis and several supporting numerical experiments.

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
35Q35 PDEs in connection with fluid mechanics

Software:

GitHub; FEALPy
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Full Text: DOI

References:

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