A remedy for numerical oscillations in weakly compressible smoothed particle hydrodynamics

Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) can lead to non-physical oscillations in the pressure and density fields when simulating incompressible flow problems. This in turn may result in tensile instability and sometimes divergence. In this paper, it is shown that this difficulty originates from the specific form of spatial discretization used for the pressure term when solving the mass conservation equation. After describing the pressure-velocity decoupling problem associated with the so-called colocated grid methods, a modified approach is presented that overcomes this problem using a different discretization scheme for the second derivative of pressure. The modified scheme is employed for solving a number of benchmark problems including both single-phase and two-phase test cases. Copyright (C) 2010 John Wiley & Sons, Ltd.