Improvement of a projection-based particle method in free-surface flows by improved Laplacian model and stabilization techniques

Abstract

This paper incorporates an improved Laplacian model for the pressure Poisson equation, a stabilization technique and a newly proposed advanced conditional collision force model in a projection-based particle method of the Moving Particle Semi-implicit (MPS) method. The Laplacian model is used to calculate pressure field and is able to predict more accurate results. The stabilization technique is used to eliminate density variation, which is developed from the continuity equation and transport theorem. The conditional collision force model is developed to handle approaching particles in simulations. With the conditional collision force model and the stabilization technique, the density calculation is improved in the dam-breaking flow and the number of separate jumping particles in the flow is greatly reduced due to the stabilization technique. By using the conditional collision force model, the Laplacian model can calculate the rotation of a square fluid patch. The stabilization technique further enhances the calculation, allowing the method to predict the evolution of the fluid patch in long duration. Including the three techniques, the present MPS is able to predict accurate pressure in the dam-breaking flow and rotation of the fluid patch. The energy variation in the impact of two rectangular fluid patches is also reproduced by the implemented techniques.