Sharp interface algorithm for large density ratio incompressible multiphase magnetohydrodynamic flows

A numerical algorithm and the corresponding paralleled implementation for the study of magnetohydrodynamics (MHD) of large density ratio, three-dimensional multiphase flows at low magnetic Reynolds numbers have been developed. The algorithm employs the method of front tracking for the propagation of material interfaces and the embedded interface method for solving elliptic-parabolic problems associated with approximations of incompressible fluids and low magnetic Reynolds numbers. The use of embedded interface method supports arbitrary discontinuities of density and other physics properties across interfaces and significantly improves methods that smear interface discontinuities across several grid cells. The numerical algorithm has been implemented as an MHD extension of FronTier, a parallel front tracking hydrodynamic code, verified using asymptotic solutions and validated through the comparison with experiments on liquid metal jets. The FronTier-MHD code has been used for simulations of liquid mercury targets for the proposed muon collider / neutrino factory, ablation of pellets in tokamaks, and processes in hybrid magnetoinertial fusion.