A front-tracking method with projected interface conditions for compressible multi-fluid flows

A front-tracking method for compressible multi-fluid flows is presented, where marker points are used both for tracking fluid interfaces and also for constructing the Riemann problem on the interfaces. The Riemann problem between the two fluid phases (defined in the interface normal direction) is solved using the exact Riemann solver on the marker points. The solutions are projected onto fixed grid points and then extrapolated into the corresponding ghost-fluid regions, to be used as boundary conditions. Each fluid phase is solved separately as in the ghost-fluid method. The proposed procedures, especially the projection of the exact Riemann solutions onto the fluid grids, are designed to be simple and consistent in any spatial dimensions. Several multi-fluid problems, including the breakup of a water cylinder induced by the passage of a shock wave were computed in order to demonstrate the capability of the proposed method.