Efficient second-order, linear, decoupled and unconditionally energy stable schemes of the Cahn-Hilliard-Darcy equations for the Hele-Shaw flow. (English) Zbl 1512.65190
The authors establish two efficient numerical schemes to solve the Cahn-Hilliard-Darcy equations based on the IEQ (Invariant Energy Quadratization) method and one scheme based on the SAV (Scalar Auxiliary Variable) method. These schemes are (i) second-order accurate in time, (ii) unconditionally energy stable, (iii) linear and decoupled. Some numerical examples are presented to support the theoretical results.
Reviewer: Abdallah Bradji (Annaba)
MSC:
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N08 | Finite volume methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 76S05 | Flows in porous media; filtration; seepage |
| 76D27 | Other free boundary flows; Hele-Shaw flows |
| 76U05 | General theory of rotating fluids |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
decoupled; Cahn-Hilliard-Darcy; Hele-Shaw; invariant energy quadratization; second-order; unconditional energy stabilityReferences:
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