Imposing accurate wall boundary conditions in corrective-matrix-based moving particle semi-implicit method for free surface flow

Corrective matrix that is derived to restore consistency of discretization schemes can significantly enhance accuracy for the inside particles in the Moving Particle Semi-implicit method. In this situation, the error due to free surface and wall boundaries becomes dominant. Based on the recent study on Neumann boundary condition (Matsunaga et al, CMAME, 2020), the corrective matrix schemes in MPS are generalized to straightforwardly and accurately impose Neumann boundary condition. However, the new schemes can still easily trigger instability at free surface because of the biased error caused by the incomplete/biased neighbor support. Therefore, the existing stable schemes based on virtual particles and conservative gradient models are applied to free surface and nearby particles to produce a stable transitional layer at free surface. The new corrective matrix schemes are only applied to the particles under the stable transitional layer for improving the wall boundary conditions. Three numerical examples of free surface flows demonstrate that the proposed method can help to reduce the pressure/velocity fluctuations and hence enhance accuracy further.

Automated summary

Corrective matrix schemes are used in the MPS method to improve the accuracy of internal particles, especially in dealing with errors caused by free surface and wall boundaries. New corrective schemes are developed for Neumann boundary conditions, but instability issues remain, requiring the use of existing stable schemes. By applying stable schemes to the free surface and nearby particles and new corrective schemes to particles under a stable transitional layer, accuracy can be significantly enhanced.