An accelerated conservative sharp-interface method for multiphase flows simulations

In this paper, we develop an accelerated conservative sharp-interface method for multiphase flows simulations. Traditional multiphase simulation methods use the minimum time step of all fluids obtained according to the CFL conditions to evolve the fluid states, which limits the computational efficiency, as the sound speed of one fluid may be much larger than of others. To address this issue, based on the original conservative sharpinterface methods, the present method is proposed by solving the governing equations of each individual fluid with the corresponding time step. Without violating the numerical stability requirement, the states of one fluid containing larger time-scale features will be evolved with a larger time step. The interaction step between two fluids is solved for synchronization, which is handled by interpolating the intermediate states of the fluid with larger time steps. In addition, an interfacial flux correction is applied to maintain the conservative property. The present algorithm has be coupled with a wavelet-based adaptive multi-resolution (MR) algorithm to achieve additional computational efficiency. A number of numerical tests indicate that the accuracy of the results obtained by the present method is comparable to of the original costly method, with a significant speedup. The speedup increases with the dimensions and resolution, which indicates its applications in 3D high resolution simulations of multiphase flows. (C) 2020 Elsevier Inc. All rights reserved.