A skewed kernel approach for the simulation of shocks using SPH

Abstract

SummaryA wide variety of jump discontinuities, such as shock fronts, are abound in high‐speed flows. An accurate approximation of these fronts may require higher order techniques either under mesh‐based methods or mesh‐free methods. In the latter class, the smoothed particle hydrodynamics (SPH) is becoming popular as a promising method. However, the standard approach in SPH (like any other discrete methods) can result in highly diffusive solutions because of the inevitable use of artificial viscosity to suppress numerical oscillations. On the other hand, the SPH formulation allows innovative ways to model complicated phenomena. In this paper, we introduce the novel idea of a skewed Gaussian kernel, to improve the shock capturing capability in high speed flows. Here, the standard Gaussian kernel function is modified, and its ‘shape’ is altered with a predesigned tunable skewness parameter, while the basic unity property of the kernel function is still preserved. The SPH with the proposed skewed Gaussian kernel is then applied on a number of benchmark problems in computational fluid dynamics, featuring shocks. The simulations have shown significantly better shock capture through the skewed kernel approach as against the standard techniques, with almost no increase in computational time. Copyright © 2016 John Wiley & Sons, Ltd.