Multiple-level Adaptive Particle Refinement for SPH Method

Abstract

Improving accuracy while reducing computational cost is the permanent challenge of Computational Fluid Dynamics (CFD). An extremely efficient technology dedicated to particle-based simulation methods such as the Smoothed-Particle Hydrodynamics (SPH) is the Adaptive Particle Refinement (APR). Particle local refinement consists in using fluid particles of different sizes, depending on the region of the flow. Critical regions are solved using small, refined particles, while regions of lower interest are solved only using a small number of coarse particles. With such techniques, the number of particles – therefore the computational cost – remains as low as possible, while the expected accuracy is met in required areas. Particle refinement techniques are challenging, as particles may move to and from areas of interest. Advanced algorithms are therefore required to subdivide coarse particles as they enter refinement areas, and merge small particles that are leaving it. When multiple-level refinement comes into play, the successive particle splits and merges become technically all-the-more challenging. Therefore, this capability, even though extremely valuable, remains out-of-reach for most open-source and commercial SPH software, and those implementing it rely on predefined fixed refinement areas. In many cases, the exact location of the zones of interest, and thus requiring potential refinement, is not known a priori and may also move time-after-time. Indeed, the critical refinement area location may depend on the resolved flow itself. In such cases, particle refinement areas need to be defined implicitly and not a priori. Criteria, such as “regions close to the free surface” or “regions nearby such body” are good examples of expected capabilities. When the local refinement technology automatically adapts to appropriately refine implicitly-defined areas, it is called Adaptive Local Refinement. We will expose in our presentation various APR techniques that can be implemented in SPH solvers, as well as results on different industrial test cases with the characteristics and advantages of the various refinement approaches.