Improved pressure calculation for the moving particle semi-implicit method

We developed a practical technique for calculating pressures and pressure gradients for the moving particle semi-implicit (MPS) method. Specifically, a new free-surface boundary condition for the pressure Poisson equation was developed by assuming that there are virtual particles over the surface. We treat the pressure of the virtual particles as a known value. A single liquid-phase flow is simulated taking into account the pressure of these virtual particles. A technique for detecting surface particles also was developed and used for accurately imposing the free-surface boundary condition. The pressure gradient model was modified to mitigate particle clustering and a single-layer wall model was developed to reduce the number of wall particles. We applied our technique to several problems, verifying that virtual surface particles suppress pressure oscillations and particle clusterings. The technique enables reliable differences in free-surface pressures to be taken and simulates instances of lower fluid pressure than that of a free surface.