Spatially adaptive Smoothed Particle Hydrodynamics

Fluid mechanics is an important area of research in many fields, e.g., special effects in movies, coastal structure design in engineering or the simulation of astrophysical phenomena. While each of these problems involve very different scenarios, they all use the same underlying physical model for fluid flows, and the simulation approaches used to simulate the fluid in each problem are also the same. One commonly used approach is the Smoothed Particle Hydrodynamics method, which is a Lagrangian approach to solving the Navier-Stokes equations.
To obtain better computational performance and more detailed simulations, the achievable resolution of the simulation should be made as high as possible. Uniform, global increases in resolution are however computationally prohibitive, whereas existing methods utilizing local changes in resolution suffer from various issues. This dissertation presents research on spatially adaptive Smoothed Particle Hydrodynamics to address many of these issues, including fundamental problems, e.g., simulation stability, and practical problems, e.g., computational performance. The findings presented in this dissertation allow simulations to have adaptivity orders of magnitudes higher than that in prior work.
The primary focus of the research in this dissertation is on the process of splitting a single particle with low resolution into many particles with higher resolution. By introducing a continuous adaptive process with a novel temporal blending process and a new concept of resolution sharing, simulations were shown to have adaptivity three orders of magnitude higher than what was previously possible. These processes were then further improved using a novel optimization strategy for refinement that can be carried out a priori and also during the simulation itself, with the latter utilizing evolutionary optimization, as well as an enhanced temporal blending scheme. The improved methods significantly stabilize spatially adaptive simulations, allowing for more practical and reliable simulations.
Another important focus of the presented research is on boundary handling for spatially adaptive simulations. By assuming the local boundaries are flat, an analytic solution for flat boundary geometries was used to develop a scale-invariant boundary handling approach that can readily be utilized for spatially adaptive simulations. Boundary handling for non-adaptive simulations was also significantly improved by this approach as it allows for more accurate interactions with boundary features below particle resolution.
Finally, this dissertation also covers research on GPU-based acceleration structures and algorithms that enable the efficient implementation and on-the-fly rendering of spatially adaptive fluids. Mechanisms to both handle anisotropic Smoothed Particle Hydrodynamics simulations and to significantly reduce the memory usage of both adaptive and non-adaptive simulations are also presented.