Incompressible smoothed particle hydrodynamics (SPH) with reduced temporal noise and generalised Fickian smoothing applied to body–water slam and efficient wave–body interaction

Abstract

Incompressible smoothed particle hydrodynamics generally requires particle distribution smoothing to give stable and accurate simulations with noise-free pressures. The diffusion-based smoothing algorithm of Lind et al. (J. Comp. Phys. 231 (2012) 1499–1523) has proved effective for a range of impulsive flows and propagating waves. Here we apply this to body–water slam and wave–body impact problems and discover that temporal pressure noise can occur for these applications (while spatial noise is effectively eliminated). This is due to the free-surface treatment as a discontinuous boundary. Treating this as a continuous very thin boundary within the pressure solver is shown to effectively cure this problem. The particle smoothing algorithm is further generalised so that a non-dimensional diffusion coefficient is applied which suits a given time step and particle spacing.We model the particular problems of cylinder and wedge slam into still water. We also model wave-body impact by setting up undisturbed wave propagation within a periodic domain several wavelengths long and inserting the body. In this case, the loads become cyclic after one wave period and are in good agreement with experiment. This approach is more efficient than the conventional wave flume approach with a wavemaker which requires many wavelengths and a beach absorber.Results are accurate and virtually noise-free, spatially and temporally. Convergence is demonstrated. Although these test cases are two-dimensional with simple geometries, the approach is quite general and may be readily extended to three dimensions.