Stability and accuracy analysis for viscous flow simulation by the moving particle semi-implicit method

Viscosity is an important property of fluids but it is not easy to simulate, especially for flows where viscous forces are dominant or comparable with other forces, because numerical viscosity may interfere. The paper mainly discusses the effect of setting up time step and space step on the stability and accuracy of the viscosity term in the moving particle semi-implicit (MPS) method. Two principles, the stability condition of the viscosity term and the accuracy condition of the viscosity term, are proposed for setting up time step and space step. The former can guarantee the stability of the viscous simulation by introducing extra numerical viscosity and the latter can produce a realistic and accurate simulation of the viscosity term without numerical viscosity interference. The simulated results for Poiseuille flow show that the simulation cases set up according to the stability condition of the viscosity term are stable and that the simulation cases set up according to the accuracy condition of the viscosity term are the most accurate. The proposed conditions can guide one to stable and accurate simulation for viscous flow by the MPS method.