Optimized Refinement for Spatially Adaptive SPH

Abstract

In this article, we propose an improved refinement process for the simulation of incompressible low-viscosity turbulent flows using Smoothed Particle Hydrodynamics, under adaptive volume ratios of up to 1 : 1, 000, 000. We derive a discretized objective function, which allows us to generate ideal refinement patterns for any kernel function and any number of particles a priori without requiring intuitive initial user-input. We also demonstrate how this objective function can be optimized online to further improve the refinement process during simulations by utilizing a gradient descent and a modified evolutionary optimization. Our investigation reveals an inherent residual refinement error term, which we smooth out using improved and novel methods. Our improved adaptive method is able to simulate adaptive volume ratios of 1 : 1, 000, 000 and higher, even under highly turbulent flows, only being limited by memory consumption. In general, we achieve more than an order of magnitude greater adaptive volume ratios than prior work.