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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.
This book is based on results obtained over a decade of study and research. It questions the use of dynamic molecular models in the continuum scale providing alternative solutions to open problems in the literature. It provides a physical-mathematical understanding of the differential equations that govern fluid flow and energy transport, serving as a reference to the application of Smoothed Particle Hydrodynamics in continuum fluid mechanics and transport phenomena. The physical-mathematical modelling of the problems in the continuum scale and the employment of the SPH method for solving the equations are presented. Examples of applications in continuum fluid mechanics with numerical results and discussions are also provided. This literature defends the concepts of continuum mechanics and the application of boundary treatment techniques that do not violate the laws of physics.
Predictive Modeling of Dynamic Processes provides an overview of hydrocode technology, applicable to a variety of industries and areas of engineering design. Covering automotive crash, blast impact, and hypervelocity impact phenomena, this volume offers readers an in-depth explanation of the fundamental code components. Chapters include informative introductions to each topic, and explain the specific requirements pertaining to each predictive hydrocode. Successfully blending crash simulation, hydrocode technology and impact engineering, this volume fills a gap in the current competing literature available.
This is the first-ever book on smoothed particle hydrodynamics (SPH) and its variations, covering the theoretical background, numerical techniques, code implementation issues, and many novel and interesting applications. It contains many appealing and practical examples, including free surface flows, high explosive detonation and explosion, underwater explosion and water mitigation of explosive shocks, high velocity impact and penetration, and multiple scale simulations coupled with the molecular dynamics method. An SPH source code is provided and coupling of SPH and molecular dynamics is discussed for multiscale simulation, making this a friendly book for readers and SPH users.
This book presents the SPH method for fluid modelling from a theoretical and applied viewpoint. It explains the foundations of the method, from physical principles, and will help researchers, students, and engineers to understand how the method should be used and why it works well.