An efficient dynamically regularized Lagrange multiplier method for the incompressible MHD equations

Abstract

This paper proposes an efficient numerical scheme for solving incompressible magnetohydrodynamic (MHD) equations based on the dynamically regularized Lagrange multiplier (DRLM) method. By introducing dynamically regularized Lagrange multipliers, we construct a new system that not only captures the energy evolution process but also remains equivalent to the original system. Building upon this framework, we employ backward differentiation formulas (BDF) for temporal discretization to establish first-order and second-order DRLM schemes, respectively. Theoretical analysis demonstrates that both the proposed first-order and second-order DRLM schemes possess unconditional energy stability. Numerical experiments validate the computational accuracy, energy dissipation characteristics, and numerical robustness of the proposed schemes.