A Stable Hybrid Potential–SPH Technique to Enforce the Fluid Incompressibility

Abstract

The SPH method has extensively used in fluid flow simulation. Through SPH the fluid is modelled by a particles system whose mutual interaction is weighed by a function, named kernel function, whose limits define the neighbouring of each particle. In spite of the high capabilities of SPH for simulate complex environments, it shows shortcomings specially if the fluid is subject to high changes in the pressure, the velocity and the density as occur in phenomena such as shock–tube, blast–wave or in the boundary and discontinuities where the number of neighbour particles is relatively low. In this case, the pressure gradient is inaccurate. As consequence, the simulation is instable with an erratic behaviour of particles. To avoid this problem, we propose a hybrid technique. This one consists in formulating the pressure gradient from a potential defined on each particles pair. Thus, the pressure gradient is immune to the low number of neighbour particles. Also, our proposal allows enforcing the fluid incompressibility. To show the improvements obtained we will carry out a set of simulation