Numerical solutions of an accurate diffuse interface model of the incompressible resistive MHD free surface flow

Abstract

In this paper, we derive a new model to simulate the incompressible resistive magnetohydrodynamic (MHD) free surface flow. A thermodynamically consistent diffuse interface method is adopted to characterize the moving interface in the modeling process. The formal convergence of the proposed MHD free surface flow model to the sharp interface model is established via a matched asymptotic argument, and the model can be solved without the need for sophisticated free surface capturing schemes. We design a fully decoupled linear finite element scheme that preserves the divergence-free constraint of the magnetic field at a discrete level. The reliability and robustness of the proposed model and algorithm are validated through numerical investigations of the magnetic damping effect on bubble dynamics. In particular, we provide a quantitative numerical comparison of the present results with those obtained from an inductionless MHD model and a sharp interface arbitrary Lagrangian--Eulerian model.

References in corpus (4)

• A variational approach to the moving contact line hydrodynamics
• Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines
• MHD stability of large scale liquid metal batteries
• Efficient finite element schemes for a phase field model of two-phase incompressible flows with different densities