More Stable SPH-based Fluid Simulation

Abstract

The simulation of fluid is a field largely discussed, from the viewpoint of engineering, in the so-called compu tational fluid dynamics (CFD). A problem that occurs repeatedly in the literature of CFD is the stability of the simulation. One of the elements that introduce instability in any CFD model is the temporal integration method. Among the most commonly used CFD techniques, both in the field of engineering and in the computer graphics, is SPH, which is particularly relevant to its computational simplicity. However, this technique adds stability pro blems due to the treatment of viscous and pressure terms arising from the formulation of Navier–Stokes. SPH also introduces greater instability by the need to use interpolation functions appropriate to the phenomena that occur in fluid dynamics. We present solutions to these four problems of inestability mentioned: treatment of the terms of pressure and viscosity that appear in the Navier–Stokes, the formulation of the characteristic interpolation function of SPH and treatment of temporal integration