A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations
<|reference_start|>A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations: A high-order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the $Q_k$ finite element with mass lumping on rectangular grids, the second-order convex splitting method, and the pressure correction method. The unique solvability, unconditional stability, and bound-preserving properties are rigorously established. The key to bound-preservation is the discrete $L^1$ estimate of the singular potential. Ample numerical experiments are performed to validate the desired properties of the proposed numerical scheme.<|reference_end|>
@article{gao2024a,
    title={A high-order accurate unconditionally stable bound-preserving numerical
  scheme for the Cahn-Hilliard-Navier-Stokes equations},
    author={Yali Gao, Daozhi Han, Sayantan Sarkar},
    journal={arXiv preprint arXiv:2407.16498},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.16498},
    primaryClass={math.NA cs.NA math.AP}
}