Fully decoupled unconditionally stable Crank-Nicolson leapfrog numerical methods for the Cahn-Hilliard-Darcy system. (English) Zbl 07882735
Summary: We develop two totally decoupled, linear and second-order accurate numerical methods that are unconditionally energy stable for solving the Cahn-Hilliard-Darcy equations for two phase flows in porous media or in a Hele-Shaw cell. The implicit-explicit Crank-Nicolson leapfrog method is employed for the discretization of the Cahn-Hiliard equation to obtain linear schemes. Furthermore the artificial compression technique and pressure correction methods are utilized, respectively, so that the Cahn-Hiliard equation and the update of the Darcy pressure can be solved independently. We establish unconditionally long time stability of the schemes. Ample numerical experiments are performed to demonstrate the accuracy and robustness of the numerical methods, including simulations of the Rayleigh-Taylor instability, the Saffman-Taylor instability (fingering phenomenon).
© 2024 Wiley Periodicals LLC.
© 2024 Wiley Periodicals LLC.
MSC:
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 76Dxx | Incompressible viscous fluids |
| 76Mxx | Basic methods in fluid mechanics |
Keywords:
Cahn-Hilliard-Darcy system; Crank-Nicolson leapfrog scheme; Galerkin finite element method; second order accuracy; unconditional stabilityReferences:
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