Improvement and application of weakly compressible moving particle semi-implicit method with kernel-smoothing algorithm (R)

The moving particle semi-implicit method (MPS) is a well-known Lagrange method that offers advantageous in addressing complex fluid problems, but particle distribution is an area that requires refinement. For this study, a particle smoothing algorithm was developed and incorporated into the weakly compressible MPS (sWC-MPS). From the definition and derivation of basic MPS operators, uniform particle distribution is critical to numerical accuracy. Within the framework of sWC-MPS, numerical operators were modified by implementing coordinate transformation and smoothing algorithm. Modifying numerical operators significantly improved particle clustering, smoothed pressure distributions, and reduced pressure oscillations. To validate the numerical feasibility of the method, several cases were numerically simulated to compare sWC-MPS to the weakly compressible MPS (WC-MPS): a pre-defined two-dimensional (2-D) analytical function, Poiseuille's flow, Taylor Green vortex, and dam break. The results showed a reduction of errors caused by irregular particle distribution with lower particle clustering and smaller pressure oscillation. In addition, a larger Courant number, which represents a larger time step, was tested. The results showed that the new sWC-MPS algorithm achieves numerical accuracy even using a larger Courant number, indicating improved computational efficiency.