Accuracy analysis of moving particle semi-implicit method

The viscous and pressure gradient terms, which can be solved by Green Function method theoretically, are calculated separately in MPS method. Through the analysis of kernel function, an accuracy condition of viscous term is proposed and the reasonable match between spatial and time step will increase the accuracy and stability of MPS method. Poiseuille flow is simulated and the accuracy condition is validated. In the analysis of the source term of Pressure Poisson equation, the particle number density (PND), which is very sensitive to the relative configuration of particles, yields the deviation of velocity profile from the theoretical solution. It is the fluctuation in PND that causes the spurious fluctuation of pressure.