An enhanced weakly-compressible MPS method for free-surface flows

Abstract

Similar to other particle methods, the Weakly-Compressible MPS (WC-MPS) is known to suffer from numerical instabilities and unphysical pressure fluctuations. Here we develop, adapt and evaluate a series of enhancement techniques to improve the stability and accuracy of this numerical approach. This includes a new conservative pressure gradient formulation and its conjugate form of the continuity equation supplied with a new diffusive term to reduce the numerical error related to the false diffusion. As a regularization technique, we have also adapted and modified the particle shifting algorithm (with near-surface special treatment) in combination with the pair-wise particle collision method to avoid particle clustering and associated noises. The impact of each of these enhancement techniques is evaluated and quantified using popular benchmark cases, i.e. hydrostatic pressure tank, elliptical water drops, rotating square patch of fluid, and dam-break problems. While the results confirm the effectiveness of all the enhancement techniques, the additional diffusive term is found to play a key role in increasing stability and eliminating the high-frequency pressure noises. Furthermore, results show that for the cases with large interfacial deformations, the developed particle shifting algorithm is essential for maintaining the smoothness of the free-surface region and avoiding unwanted fragmentation.