Improved MPS models for simulating free surface flows

Two improved Laplacian models are introduced in this study for more accurate simulation of free surface flows in the context of the moving particle semi-implicit (MPS) method, a well-known mesh-less approach. The Euler equations are the governing equations of these flows without considering viscous forces which are solved in the Lagrangian frame by the MPS and two-step projection methods for spatial and temporal discretization, respectively. Considering the similarity between the MPS and SPH (smoothed particle hydrodynamics) methods, one of the introduced Laplacian models is formulated by a corrective matrix firstly proposed in an improved SPH method [28]. The other modified Laplacian model is also derived from the divergence of a newly developed MPS gradient model proposed for solving elasticity problems [33]. The higher accuracy of these methods compared to the classic SPH, MPS and even three modified SPH and MPS Laplacian models [7, 34, 44] is verified by solving 2D Poisson equations. Moreover, the excellent performance of the Laplacian models and the improved gradient model in obtaining smooth pressure field is validated by solving three benchmark free surface flows. Furthermore, the problem of wave damping in the original MPS computations can be resolved by using the applied models.