An ALE Method for Compressible Multifluid flows: Application to Underwater Explosion

摘要

In the present study an ALE scheme is proposed for the multilateral flows in which a gas-phase zone is separated from a liquid-phase zone by an immiscible interface. In the proposed scheme the material boundary between the two phases remains Lagrangian and the ALE behaviors is only allowed within materials. For the 1D and spherically symmetric problems the interface tracking is straightforward and it is suffice to move the grid of interface with its right velocity. This velocity is obtained from the exact solution of a Riemann problem at the gas-liquid interface using a proper equation of state for each phase. Element degeneracy is then prevented by moving the neighboring grids in the gas and liquid zones by an appropriate velocity field. In the present work, the Laplacian equation is solved for the mesh velocity using the interface velocity as boundary conditions. The new grid position is then updated in each time step using the grid velocity field. The accuracy of this technique is demonstrated by presenting some results. This contains the solution to several gas-water Riemann problems and a simplified model for the spherically symmetric underwater explosion. In the later case the different stages of the bubble dynamics can be seen clearly in the simulation.