A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations

Yali Gao; Daozhi Han; Sayantan Sarkar

A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations

Numerical Analysis 2024-07-24 v1 Numerical Analysis Analysis of PDEs

Authors: Yali Gao , Daozhi Han , Sayantan Sarkar

Abstract

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.

Keywords

Cahn-Hilliard-Navier-Stokes equations high-order scheme bound-preserving convex splitting Flory-Huggins potential

Cite

@article{arxiv.2407.16498,
  title  = {A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations},
  author = {Yali Gao and Daozhi Han and Sayantan Sarkar},
  journal= {arXiv preprint arXiv:2407.16498},
  year   = {2024}
}

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