Conclusions and Prospect
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In order to improve the performance of the numerical methodologies in studying the incompressible MHD flows, a new solver is developed and implemented into the open source Gerris code. The new Gerris-MHD solver, which is based on the Cartesian grids and the AMR technique, is able to simulate the single-phase MHD flows respectively of being bounded by electrically insulating or conducting walls with a cut-cell approach. In addition, by using the VOF method, the solver is also able to solve the multi-phase MHD flows and the discontinuities of the physical properties across the fluid-fluid interface can be handled very well. After that, the single bubble motion with or without the influence of the MF is investigated numerically, and the physical mechanisms are discussed in details.