A decoupled, unconditionally stable numerical algorithm for phase transition in aluminum under electromagnetic levitation

In this paper, we provide an efficient decoupled numerical algorithm for solving the phase transition in aluminum (Al) under electromagnetic levitation (EML) conditions. This work includes threefolds: (i) Models. The Maxwell equations, heat transfer equations, and the incompressible Navier-Stokes (NS) equations are involved in a whole electromagnetic-heat-flow system. (ii) Algorithm (main contribution). We solve the electromagnetic equation based on the magnetic potential vector A ; the time-filter (TF) technique is employed to the heat equations to improve the temporal step. For the fluid part, a consistent splitting scheme to decouple the velocity and pressure with the TF technique is utilized. The algorithm exhibits unconditional stability. The finite element method is dragged into spatial discretization. (iii) Numerical experiments. We first present a numerical test to check the second-order temporal accuracy of the incompressible NS equations. We then compare the results with those by the proposed algorithm and the commercial software COMSOL, which confirm the accuracy of our algorithm. Finally, the phase transition processes of aluminum under EML are simulated, and also we compare them with the data from the literature [Cai et al., Int. J. Heat Mass Transfer 151, 119386 (2020)] to further demonstrate the robustness and efficiency of the proposed algorithm.