Simulation of granular flows over natural terrain using Godunov Smooth Particle Hydrodynamics
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Smooth Particles Hydrodynamics (SPH) is a fully Lagrangian numerical method of obtaining approximate solutions to fluid dynamic problems. It was introduced by Lucy and Gingold & Monaghan independently. Since then it has found applications in a wide variety of applications. SPH presents some distinct advantages over classical grid based methods. Since the method is a Lagrangian calculation, advection is treated exactly, there are no geometrical restrictions on the domain and new physics can be easily incorporated in the system. Another advantage, which makes it particularly attractive to this work is, easy treatment of free boundaries in surface flows with artificial constructions. This allows us to solve fully three-dimensional systems as opposed to grid based methods where depth averaging is used. The deeper insights needed into such flows reliable hazard analysis cannot be obtained without accounting for full three-dimensinal physics. The original SPH formulation given by Lucy and Gingold & Monaghan provided good solutions for some astrophysical problems, but did not conserve momentum and energy. The later papers by Monaghan proposed improved algorithms that were conservative. These equations however, still could not resolve strong shocks with desirable accuracy. Inutsuka reformulated SPH equations to include a Riemann solver. Field variables are projected on to a density weighted interface, and a polynomial reconstruction is used to setup a Riemann problem between each pair of particles. An approximate Riemann solver is then used to compute the value of pressure. Partition of unity preserving methods are used to interpolate field variables and calculate derivatives. Traditional way of enforcing the boundary conditions failed produce good results. This required us to improve the treatment of boundary conditions. New methods to enforce essential and natural boundary conditions were developed to this end. We believe these methods will be equally successful, when using classical SPH. The objective of this thesis is to use the Inutsuka framework to solve equations that describe granular flow. The numerical results are be compared against laboratory experiments. Ultimate goal of the project is to provide geology community with an alternative tool to conduct numerical simulations of large scale geophysical mass flows.