The linear, decoupled and fully discrete finite element methods for simplified two-phase ferrohydrodynamics model

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-12-14 DOI:10.1016/j.apnum.2024.12.004

Xiaoyong Chen , Rui Li , Jian Li

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引用次数: 0

Abstract

In this paper, we consider numerical approximations of a phase field model for simplified two-phase ferrofluids. This model is a highly nonlinear and coupled multiphysics PDE system with Cahn-Hilliard equations, Navier-Stokes equations, magnetization equation and magnetostatic equation. By combining the artificial compressibility method for the Navier-Stokes equations, the convex splitting method or the stabilize explicit method for Cahn-Hilliard systems, the subtle implicit-explicit treatments and some extra stabilization terms for nonlinear coupling terms, we construct two linear, decoupled and fully discrete finite element methods to solve multiphysics system efficiently. The proposed schemes do not enforce any artificial boundary condition on the pressure. Furthermore, the energy stability and unique solvability are obtained for the proposed schemes. In order to accurately capture the diffuse interface, we apply the adaptive mesh strategy. Finally, a series of numerical experiments verify the theory and illustrate the efficiency and effectiveness of these methods.

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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.