Enhancement of Pressure and Curvature Calculation for the Moving Particle Semi-Implicit Method

<jats:p>This paper aims at illustrating a number of methods for stabilizing pressure solution and improving surface curvature calculation for the simulation using the moving particle semi-implicit (MPS) method. The unphysical numerical oscillation of pressure originated from the original MPS method can be suppressed by adjusting the collision coefficient in the collision model and using a specific weight function for avoiding the occurrence of excessive pressure value when particles get closer. The pressure gradient solver and the poison pressure equations (PPE) are also modified by implementing a mixed source term of velocity divergence and a corrective matrix, respectively. In addition to the pressure field, the surface tension force is essential for correctly deforming the fluid interface between different phases. The curvature calculation is improved with high accuracy by utilizing a contoured continuum surface model where a new scheme for computing the partial derivatives of the mollified color function is proposed. The Gaussian function for smoothing the color function is specified to ensure a better coincidence of the local contour of mollified color values with the interface. Compared to the original MPS method, both modifications and extensions for the pressure and curvature solver can generate more stable and accurate results, which are presented by a few numerical examples, including the hydrostatic pressure, dam break and bubble rising models.</jats:p>