A second-order semi-implicit spectral deferred correction scheme for Cahn-Hilliard-Navier-Stokes equation

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-05-12 DOI:10.1016/j.apnum.2025.05.003

Xin Liu , Dandan Xue , Shuaichao Pei , Hong Yang

引用次数: 0

Abstract

In this paper, a second-order and energy stable numerical scheme is developed to solve the Cahn-Hilliard-Navier-Stokes phase field model with matching density. This scheme is based on the second-order semi-implicit spectral deferred correction method and the energy stable first-order convex splitting approach. A fully discretized scheme with finite elements for the spatial discretization is developed to solve this coupled system. The energy stability of our scheme is theoretically proven, and its convergence is verified numerically. Numerical experiments are conducted to demonstrate the stability and reliability of the proposed scheme.

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Cahn-Hilliard-Navier-Stokes方程的二阶半隐式谱延迟校正格式

本文建立了具有匹配密度的Cahn-Hilliard-Navier-Stokes相场模型的二阶能量稳定数值格式。该方案基于二阶半隐式谱延迟校正方法和能量稳定的一阶凸分裂方法。为求解该耦合系统，提出了一种空间离散化的有限元全离散化方案。理论证明了该方案的能量稳定性，数值验证了其收敛性。数值实验验证了该方法的稳定性和可靠性。

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.