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

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-06-10 DOI:10.1016/j.apnum.2025.06.004

Yali Gao , Daozhi Han , Sayantan Sarkar

引用次数: 0

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 for 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.

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Cahn-Hilliard-Navier-Stokes方程的高阶精确无条件稳定保界数值格式

提出了一种求解具有Flory-Huggins势的Cahn-Hilliard-Navier-Stokes方程的高阶数值方法。该方案基于矩形网格质量集总的Qk有限元、二阶凸分裂法和压力修正法。严格地建立了唯一可解性、无条件稳定性和保界性。保持边界的关键是奇异势的离散L1估计。进行了大量的数值实验来验证所提出的数值格式的预期性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.