Abstract
This paper focuses on the unconditionally optimal error estimates of a fully discrete decoupled scheme for two-phase magnetohydrodynamic (MHD) model with different viscosities and electric conductivities, by using the zero-energy-contribution (ZEC) method for the temporal discretization and mixed finite elements for the spatial discretization. Based on the ZEC property of the nonlinear and coupled terms of the model, an ordinary differential equation is designed to introduce a nonlocal scalar auxiliary variable which will play a key role in the design and the energy stability of the decoupled scheme. Combining fully explicit treatment on the nonlinear and coupled terms with the stabilization method for nonlinear potential, a decoupled temporal discrete scheme is proposed. Utilizing mixed finite elements for the spatial discretization in this temporal discrete scheme, a fully discrete scheme is proposed. Both schemes are proved to be mass-conservative and unconditionally energy stable. The unconditionally optimal error estimates of the temporal discrete scheme are derived for two dimensional and three dimensional (2D/3D) cases. Utilizing a modified Maxwell projection with variable electric conductivities, the superconvergence of its negative norm estimates, mathematical induction, and the unconditional stability of the numerical scheme, we also derive the optimal error estimates in L2-norm for the fully discrete scheme in 2D/3D cases, without any restriction on the time step size and mesh size. Finally, numerical experiments are provided to verify the theoretical results.
Recommended Citation
J. Yang et al., "Unconditionally Optimal Convergent Zero-Energy-Contribution Scheme for Two Phase MHD Model," Journal of Scientific Computing, vol. 102, no. 2, article no. 55, Springer, Feb 2025.
The definitive version is available at https://doi.org/10.1007/s10915-024-02773-1
Department(s)
Mathematics and Statistics
Keywords and Phrases
Decoupled scheme; Energy stability; Error estimates; Two-phase MHD flows; Zero-energy-contribution method
International Standard Serial Number (ISSN)
1573-7691; 0885-7474
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2025 Springer, All rights reserved.
Publication Date
01 Feb 2025
Comments
National Natural Science Foundation of China, Grant 12271514