Stabilization and smoothing of pressure in MPS method by Quasi-Compressibility

In this paper, a method to stabilize simulations and suppress the pressure oscillation in Moving Particle Semi-implicit method for an incompressible fluid is presented. To make the pressure smooth in terms of both of space and time, a new representation of the incompressible condition is proposed. The incompressible condition consists of two parts: the Divergence-Free condition and the Particle Number Density condition. The Divergence-Free condition has the effect of making the pressure smooth in terms of both space and time. The Particle Number Density condition is necessary to keep the fluid volume constant. In this work, the Quasi-Compressibility is also introduced for stabilization. A dam break is simulated more stably and the space distribution and the time variation of pressure are evaluated more smoothly than the traditional method. Moreover, surface particles are detected more accurately. Nevertheless the proposed method is computationally cheaper. Some simulations such as a Fluid-Structure Interaction are supposed to be more accurate using this method.