Efficient finite element schemes for a phase field model of two-phase incompressible flows with different densities
<|reference_start|>Efficient finite element schemes for a phase field model of two-phase incompressible flows with different densities: In this paper, we present two multiple scalar auxiliary variable (MSAV)-based, finite element numerical schemes for the Abels-Garcke-Gr{\"u}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.<|reference_end|>
@article{wang2024efficient,
    title={Efficient finite element schemes for a phase field model of two-phase
  incompressible flows with different densities},
    author={Jiancheng Wang and Maojun Li and Cheng Wang},
    journal={arXiv preprint arXiv:2408.04371},
    year={2024},
    doi={10.1016/j.jcp.2024.113331},
    archivePrefix={arXiv},
    eprint={2408.04371},
    primaryClass={math.NA cs.NA}
}