A moving particle semi-implicit method for free surface flow: Improvement in inter-particle force stabilization and consistency restoring

The moving particle semi-implicit (MPS) method has been widely applied in free surface flows. However, the implementation of MPS remains limited because of compressive instability occurred when the particles are under compressive stress states. This study proposed an inter-particle force stabilization and consistency restoring MPS (IFS-CR-MPS) method to overcome this numerical instability. For inter-particle force stabilization, a hyperbolic-shaped quintic kernel function is developed with a non-negative and smooth second order derivative to satisfy the stability criterion under compressive stress state. Then, a contrastive study is conducted on the contradiction between the common understanding of the conventional MPS hyperbolic-shaped kernel function and its performance. The result shows that the conventional MPS hyperbolic-shaped kernel function can easily cause violent repulsive inter-particle force and then lead to the compressive instability. Therefore, the first order derivative of the modified hyperbolic-shaped quintic kernel function is recommended as the form of the contribution of the neighbor particles to achieve a more stable inter-particle repulsive force. For consistency restoring, the Taylor series expansion and the hyperbolic-shaped quintic kernel are combined to improve the accuracy of the viscosity and pressure calculation. The IFS-CR-MPS algorithm is subsequently verified by the inviscid hydrostatic pressure, jet impacting, and viscous droplet impacting problems. These results can be used for choosing kernel function and the contribution of neighbor particles in particle methods.