Two-phase SPH model based on an improved Riemann solver for water entry problems

There are challenges in simulating two-phase flows with large density ratios using traditional SPH. Taking full advantages of Riemann solver in dealing with contact discontinuity problems and combining two-phase flow SPH method with Riemann solver, a new model of two-phase flow coupling with structure based on an improved Riemann solver is described for the water entry problems with the effect of air. The flow momentum equation of the Riemann form is improved to decrease the Riemann dissipation and simulate the two-phase flows with different viscosity ratios. One-sided Riemann problem considering the free-slip and no-slip conditions at a wall is used to deal with the fluid-body interaction. A switch-function-based Riemann solver dissipation is used to improve the instability of interface owing to the strong impact. In order to test the accuracy of the model in fluid-structure coupling problems, five cases, including dam break, sinking of a rectangle body, water entry of a wedge, flat plate slamming on water and water entry of a catamaran, are numerically simulated. The agreements between the present results and other reference results demonstrate that the proposed method is robust and stable to simulate the water entry problems with the air.