Decoupled, Linear, and Unconditionally Energy Stable Fully Discrete Finite Element Numerical Scheme for a Two-Phase Ferrohydrodynamics Model

Abstract

We consider in this paper numerical approximations of a phase field model for twophase ferrofluids, which consists of the Navier-Stokes equations, the Cahn-Hilliard equation, the magnetostatic equations, and the magnetic field equation. By combining the projection method for the Navier-Stokes equations and some subtle implicit-explicit treatments for coupled nonlinear terms, we construct a linear, decoupled, fully discrete finite element scheme to solve the highly nonlinear and coupled multiphysics system efficiently. The scheme is provably unconditionally energy stable and leads to a series of decoupled linear equations to solve at each time step. Through numerous numerical examples in simulating benchmark problems such as the Rosensweig instability and droplet deformation, we demonstrate the stability and accuracy of the numerical scheme.

Department(s)

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Comments

National Science Foundation, Grant DMS-1720212

Keywords and Phrases

Ferrofluid; Ferrohydrodynamics; Magnetic field; Phase field; Unconditional energy stability

International Standard Serial Number (ISSN)

1064-8275; 1095-7197

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 Society for Industrial and Applied Mathematics (SIAM), All rights reserved.

Publication Date

01 Jan 2021

Link to Full Text

Share

 
COinS