A Mass and Charge Conservative Fully Discrete Scheme for a 3D Diffuse Interface Model of the Two-phase Inductionless MHD Flows
Abstract
In this paper, we study the phase field model on a three-dimensional bounded domain for a two-phase, incompressible, inductionless magnetohydrodynamic (MHD) system, which is important for many engineering applications. To efficiently and accurately solve this multi-physics nonlinear system, we present a fully discrete scheme that ensures both mass and charge conservation. Making use of the discrete energy law, we demonstrate that the fully discrete scheme satisfies unconditional energy stability. Subsequently, by utilizing the Leray-Schauder principle, we establish the existence of solutions to the discrete scheme. As both mesh size and time step size tend to zero, we prove that the discrete solutions converge to the weak solution of the continuous problem. Finally, several three-dimensional numerical experiments, including the accuracy test, the bubble coalescence, the drop deformation and the Kelvin-Helmholtz (KH) instability, are performed to validate the reliability and efficiency of the proposed numerical scheme.
Recommended Citation
X. Wang et al., "A Mass and Charge Conservative Fully Discrete Scheme for a 3D Diffuse Interface Model of the Two-phase Inductionless MHD Flows," Computers and Mathematics with Applications, vol. 182, pp. 139 - 162, Elsevier, Mar 2025.
The definitive version is available at https://doi.org/10.1016/j.camwa.2025.01.020
Department(s)
Mathematics and Statistics
Keywords and Phrases
Cahn-Hilliard equation; Charge conservation; Convex splitting; Inductionless MHD equations; Mixed finite element method
International Standard Serial Number (ISSN)
0898-1221
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2025 Elsevier, All rights reserved.
Publication Date
15 Mar 2025
Comments
National Natural Science Foundation of China, Grant 12271514