A new two-step projection method in an ISPH model for free surface flow computations

In this study, we propose a new two-step projection method in connection with an ISPH model. Compared to the traditional ISPH model that uses the future time step pressure to calculate the intermediate velocity, in the present study the pressure at both current time step and future time step is employed. In addition, the velocity and pressure obtained at the end step of the projection method are re-projected onto the updated particle locations using an interpolation method. While the use of current time step pressure provides a better energy conserving property of the numerical scheme, the interpolation smooths the velocity field and ensures a more stringent constraint for incompressibility condition. The accuracy of the model is further enhanced by implementing C2 consistency kernel approximation for variable and derivative calculation. The model is first calibrated by using the still water and liquid sloshing tests. It is then validated against a series of benchmark tests of linear wave and solitary wave propagation in constant water depth, followed by the case of nonlinear wave transformation over a submerged breakwater. The numerical results are compared to available theories, experimental data, and previously published simulation results. It is shown that the present model can achieve a much better energy conservation than the traditional ISPH model, even with the use of a much larger time step.