Analysis and Application of Reformulated Smoothed Particle Hydrodynamics
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During the study of geophysical flows, some software packages (such as TITAN2D, GeoClaw) have been developed to simulate the behavior of geophysical flows of lava, avalanche, and mudslide. While these packages have led a better understanding of geophysical flows, there are some impediments which limit the widespread acceptance of these packages in practice. For example, some of the current programs (e.g. TITAN2D) are based on the depth average model and such a methodology can be computationally challenging when dealing with boundary conditions. With the development of computational fluid mechanics, a mesh free method called Smoothed Particle Hydrodynamics (SPH) has been introduced by Gingold and Monaghan. Because of the limitation of classical SPH, Reformulated Smoothed Particle Hydrodynamics (RSPH) has been derived from convolution integral of the original hydrodynamics equations. Such a framework uses a Riemann Solver to determine the force acting on each fluid particle and is recently recognized to be more efficient and accurate for tracking particle movements, making it possible to capture the behavior of fluids under strong shock. This dissertation focuses on implementation of RSPH for simulation of large scale of geophysical flows. The 1-D and 2-D cases were first discussed to confirm the advantage of using Riemann Solver, followed by the development of a formula to determine where to use Riemann Solver. For the cases without boundary conditions, a Von Neumann stability analysis was conducted to assess the stability and benefit of RSPH in comparison with standard SPH. For the cases with boundary conditions, the GKSO theory (a theory given by Gustaffson, Kreiss, Sundstrom and Osher) was used to analyze the stability of SPH. The framework of RSPH for use in materials with plastic viscosity was also developed together with a discussion of its stability under different boundary conditions. At last, stability of the SPH with corrected derivative and weight smoothing was addressed. This work provides building blocks for further implementation of RSPH technique in engineering fluid mechanics.