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A second order in time, decoupled, unconditionally stable numerical scheme for the Cahn-Hilliard-Darcy system. (English) Zbl 1407.65158
Summary: We propose a novel second order in time, fully decoupled and unconditionally stable numerical scheme for solving the Cahn-Hilliard-Darcy system which models two-phase flow in porous medium or in a Hele-Shaw cell. The scheme is based on the ideas of second order convex-splitting for the Cahn-Hilliard equation and pressure-correction for the Darcy equation. The computation of order parameter, pressure and velocity is completely decoupled in our scheme. We show that the scheme is uniquely solvable, unconditionally energy stable and mass-conservative. Ample numerical results are presented to gauge the efficiency and robustness of our scheme.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76T99 Multiphase and multicomponent flows
76S05 Flows in porous media; filtration; seepage
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
35Q35 PDEs in connection with fluid mechanics
76D27 Other free boundary flows; Hele-Shaw flows
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