A 3D higher order Laplacian model for enhancement and stabilization of pressure calculation in 3D MPS-based simulations

A 3D higher order Laplacian model is proposed for enhancement and stabilization of pressure calculation by the MPS (Moving Particle Semi-implicit [1]) method. The 3D higher order Laplacian model is derived by taking the divergence of a particle-based gradient model [2] and is then applied for discretization of Laplacian of pressure corresponding to the Poisson Pressure Equation (PPE). The enhancing and stabilizing effect of the 3D higher order Laplacian model is shown through simulations of two benchmark tests, namely, designed exponentially excited sinusoidal pressure oscillations [3] and a schematic dam break with an obstacle [4].

► A 3D Laplacian model is proposed for pressure enhancement in the MPS method.
► The consistency of Laplacian model and PPE's discretized source term is highlighted.
► The enhancing and stabilizing effect of the 3D Laplacian model is verified.
► Verifications are performed in terms of pressure field and water surface evolution.