Semi-Implicit Incompressible SPH Fluid Simulation in a Marine Simulator

We present a predictive-corrective semi-implicit incompressible smoothed particle hydrodynamics (SPH) approach. At the first stage of the explicit computation, the fluid density is predicted using a continuous density method, which takes the velocity as the source term and considers the relative velocity effect. At the second stage of implicit computation, the ratio of the pressure to the square of the density obtained by the predictive-corrective method is directly used to correct the fluid velocity. As there are larger density errors in fluid particles near or on the boundary, more iteration numbers are required. The boundary handling method is applied to modify the density of fluid particles near or on the boundary. For density invariant conditions, the relaxation method and optimal initial value are adopted to improve the convergence speed. Our proposed approach can achieve semi-implicit incompressible SPH, solve the particle deficiency problem and realize the simulation of small-scale ocean scenes. While ensuring stability, the approach allows large time steps, controls the density deviation below 0.01% and improves the overall efficiency.