Work

Error Analysis of Second‐Order Decoupled Scheme for Two‐Phase Magnetohydrodynamic Diffuse Interface Model

Year: 2025

Type: article

Abstract: ABSTRACT In this paper, we construct error analysis of second‐order decoupled scheme for the two‐phase magnetohydrodynamic diffuse interface model. First, we construct a second‐order time‐discrete scheme in which the time derivative term is treated by the second‐order backward difference formulation, the scalar auxiliary variable (SAV) method is used to linearize the nonlinear energy potential, and the other nonlinear terms are treated by semi‐implicit method. Importantly, we use Gauge–Uzawa method to decouple velocity and pressure. The proposed scheme have two distinct features: It does not need to give an initial value of the pressure; it does not require artificial boundary conditions on pressure, thus saving additional computational cost. Second, the unconditional stability of the second‐order scheme is proved. Then, through rigorous error analysis, we provide suboptimal convergence orders. Finally, some numerical experiments demonstrate the accuracy and effectiveness of the proposed scheme. It is also proved that the proposed scheme is superior to other classical second‐order scheme.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.11061

Authors: Zhaowei Wang, Danxia Wang, Jun Zhang, Hongen Jia

Institutions: Taiyuan University of Technology, Guizhou University of Finance and Economics

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: bronze

Funders: National Natural Science Foundation of China, Shanxi Scholarship Council of China

Awards: G105819990, G3897772806, G4046957608, G4596838107, G49992873