Adaptive Compressible Smoothed Particle Hydrodynamics

Abstract: Modulating the number of particles in a region is key to accurately capturing the nuances in compressible flows with Smoothed Particle Hydrodynamics (SPH). This paper details the implementation of a volume-based adaptive refinement and derefinement procedure, incorporating state-of-the-art features such as automatic local adaptivity and solution adaptivity. A shock-aware particle shifting procedure is introduced to regularize the particle distribution while preserving the integrity of shocks. To our knowledge, this is the first demonstration of shock-based solution adaptivity and shock-aware particle shifting in the literature. A wide variety of test problems, which involve flow in and around boundaries, are employed to highlight the utility of these adaptivity features in improving the results and in making simulations faster. For instance, the adaptive resolution procedure is shown to deliver an order of magnitude speedup. We also demonstrate the effectiveness of the adaptivity procedure in resolving existing issues like errors due to interaction with differently spaced ghost particles at boundaries, formation of spot-like structures due to particle clumping, and poorly resolved low-density regions. In essence, the adaptivity technique presented in this paper is positioned as a powerful tool for simulating compressible flows with enhanced accuracy and efficiency.