3D extension of the particle-attached element interpolation in Smoothed Particle Hydrodynamics

Abstract

Random pressure and density oscillations in Smoothed Particle Hydrodynamics (SPH) often lead to degradation of numerical stability and accuracy of the entire simulation. Shepard filter is the most commonly used technique to alleviate such an issue, but the major problem with this method is that it is highly sensitive to the smoothing frequency and tends to over-smooth the density field when applied too frequently. To overcome this problem, a new density correction method was proposed by Seo for 2D problems, where density of each particle is reinitialized using particle-attached element and the corresponding shape functions. As an extension to his work, this paper presents a 3D implementation of the new density correction method. Similar to the 2D method which uses a 4-node square element, a 8-node cubic element with linear shape functions are employed for interpolation of the density field within the smoothing domain. Variable smoothing domain size is selected for each particle in each smoothing step, which enables the simulation to avoid over-smoothing and have converged solutions regardless of the smoothing frequency. The major portion of the calculation is carried out using a graphics processing unit (GPU) for faster simulation and three benchmark problems are solved to verify the feasibility of the method in 3D.