Development of MHD solver based on an adaptive mesh refinement technique

An accurate model is developed for numerical simulation of 3D magnetohydrodynamic multiphase flows at a low magnetic Reynolds number, in which a consistent and conservative scheme has been applied to calculate the Lorentz force and continuous surface force model is used to calculate the surface tension based on the volume of fluid method for capturing the interface using a PLIC (Piecewise Linear Interface Calculation) to reconstruct the interface. An adaptive mesh refinement technique is used to improve the accuracy and efficiency by automatically refining (relaxing) the meshes near (outside of) the surface, the Hartmann layers and side layers, respectively. Multi-grid method is utilized to accelerate the convergence of Poisson equations. Numerical results are compared with the theoretical or experimental results to validate and verify the numerical solver. A bubble rising in a stagnant liquid metal with/without the influence of magnetic field is simulated and compared with the experimental works.