A Second-Order Fully Decoupled Scheme And Its Optimal Finite Element Error Estimate For A Two-Phase Magnetohydrodynamics Model
Abstract
This paper proposes a fully decoupled, linear, second-order accurate, fully discrete numerical scheme with unconditional energy stability for the reformulated two-phase magnetohydrodynamics model. The reformulation itself is achieved by unifying the scalar auxiliary variable (SAV) and zero-energy-contribution (ZEC) methods via a time-dependent auxiliary variable. The scheme achieves second-order temporal accuracy by second-order backward differential formula (BDF2), realizes decoupling and linearity among the phase, flow, and magnetic fields via the unified SAV–ZEC method and a fully explicit treatment of the nonlinear terms and their coefficients, and attains intra-field decoupling within the flow field by the second-order pressure-correction projection method. The unconditional energy stability and optimal (Formula presented.) error estimate of the scheme are established. One simplification in the phase-field analysis involves embedding the inverse of discrete Laplacian into the test functions. This embedding induces an (Formula presented.) – (Formula presented.) norm transformation, which allows the associated terms to be estimated directly. One technique to achieve second-order temporal accuracy involves an auxiliary function that incorporates a first-order temporal pressure approximation for canceling the lower-order temporal terms. The introduction of a Stokes quasi-projection operator similarly prevents the loss of the spatial convergence rate. Four numerical examples are presented to verify the efficacy of the proposed scheme.
Recommended Citation
D. Duan et al., "A Second-Order Fully Decoupled Scheme And Its Optimal Finite Element Error Estimate For A Two-Phase Magnetohydrodynamics Model," International Journal for Numerical Methods in Engineering, vol. 127, no. 18, article no. e70433, Wiley, Sep 2026.
The definitive version is available at https://doi.org/10.1002/nme.70433
Department(s)
Mathematics and Statistics
Publication Status
Full Access
Keywords and Phrases
fully decoupled; optimal L2$$ {L}^2 $$ error estimate; second-order accurate; two-phase magnetohydrodynamics model; zero-energy-contribution method
International Standard Serial Number (ISSN)
1097-0207; 0029-5981
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 Wiley, All rights reserved.
Publication Date
30 Sep 2026
Comments
National Natural Science Foundation of China, Grant 15305325