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.

► A solver is developed based on an adaptive mesh refinement for multi-fluid flows, which can improve the computational accuracy without costing more computational time.
► A consistent and conservative scheme is employed to compute the Lorentz force and the current density, which can numerically conserve the charge and the momentum and can get accurate MHD results at high Hartmann number.
► A volume of fluid method is employed to capture the interface with grid adaptively refined near the interface with good resolution.
► Effect of magnetic field on the rising bubble under buoyancy is studied with vortex distribution and current density distribution shown for illustration.