Numerical solutions of an accurate diffuse interface model of the incompressible resistive MHD free surface flow
Provides a thermodynamically consistent and numerically efficient approach for simulating MHD free surface flows, relevant to engineering and physics applications.
The authors derive a new diffuse interface model for incompressible resistive MHD free surface flow, prove its convergence to the sharp interface model, and validate it via numerical simulations of magnetic damping on bubble dynamics, showing quantitative agreement with existing models.
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.