A fully-decoupled artificial compressible Crank-Nicolson-leapfrog time stepping scheme for the phase field model of two-phase incompressible flows. (English) Zbl 1516.65098
Summary: In this paper, we consider efficient numerical approximations for the phase field model of two-phase incompressible flows. To develop easy-to-implement time stepping scheme, we introduce two types of nonlocal auxiliary variables to achieve highly efficient and fully-decoupled scheme based on the Crank-Nicolson-Leapfrog (CNLF) formula and artificial compression method. We prove that the scheme is linear and unconditionally energy stable. Ample numerical experiments are performed to demonstrate the accuracy, stability and efficiency.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin 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 |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 76T06 | Liquid-liquid two component flows |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
phase field model; two-phase incompressible flows; artificial compression method; Crank-Nicolson leapfrog; nonlocal variables; unconditionally energy stabilitySoftware:
FreeFem++References:
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