Efficient finite element schemes for a phase field model of two-phase incompressible flows with different densities
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arXiv
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| Natura: | Preprint |
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2024
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| _version_ | 1866917744234987520 |
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| author | Wang, Jiancheng Li, Maojun Wang, Cheng |
| author_facet | Wang, Jiancheng Li, Maojun Wang, Cheng |
| contents | In this paper, we present two multiple scalar auxiliary variable (MSAV)-based, finite element numerical schemes for the Abels-Garcke-Gr{ü}n (AGG) model, which is a thermodynamically consistent phase field model of two-phase incompressible flows with different densities. Both schemes are decoupled, linear, second-order in time, and the numerical implementation turns out to be straightforward. The first scheme solves the Navier-Stokes equations in a saddle point formulation, while the second one employs the artificial compressibility method, leading to a fully decoupled structure with a time-independent pressure update equation. In terms of computational cost, only a sequence of independent elliptic or saddle point systems needs to be solved at each time step. At a theoretical level, the unique solvability and unconditional energy stability (with respect to a modified energy functional) of the proposed schemes are established. In addition, comprehensive numerical simulations are performed to verify the effectiveness and robustness of the proposed schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04371 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficient finite element schemes for a phase field model of two-phase incompressible flows with different densities Wang, Jiancheng Li, Maojun Wang, Cheng Numerical Analysis In this paper, we present two multiple scalar auxiliary variable (MSAV)-based, finite element numerical schemes for the Abels-Garcke-Gr{ü}n (AGG) model, which is a thermodynamically consistent phase field model of two-phase incompressible flows with different densities. Both schemes are decoupled, linear, second-order in time, and the numerical implementation turns out to be straightforward. The first scheme solves the Navier-Stokes equations in a saddle point formulation, while the second one employs the artificial compressibility method, leading to a fully decoupled structure with a time-independent pressure update equation. In terms of computational cost, only a sequence of independent elliptic or saddle point systems needs to be solved at each time step. At a theoretical level, the unique solvability and unconditional energy stability (with respect to a modified energy functional) of the proposed schemes are established. In addition, comprehensive numerical simulations are performed to verify the effectiveness and robustness of the proposed schemes. |
| title | Efficient finite element schemes for a phase field model of two-phase incompressible flows with different densities |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2408.04371 |