Simulation Of Granular Flows Over Natural Terrain Using Godunov Smooth Particle Hydrodynamics

Simulation of Granular Flows Over Natural Terrain Using Godunov Smooth Particle Hydrodynamics

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, whichmakes 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 beobtained without accounting for full three-dimensinal physics. The original SPH formulation given by Lucy and Gingold & Monaghan provided good solutions forsome 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, whenusing 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.

Simulation of Free-surface Flows and Development of an Improved Particle Method

Undergoing development for decades, the mesh-free methods, both Smoothed Particle Hydrodynamics (SPH) and the Moving Particle Semi-implicit method (MPS), have become useful numerical tools for studying free-surface flows in various engineering problems. They are able to easily simulate complicated fluid interface flows. As a Lagrangian method, MPS with a weakly-compressible technique, Weakly-Compressible Moving Particle Semi-implicit method (WC-MPS), has been widely applied into handling free-surface flows in hydraulic engineering. WC-MPS has been reported to perform well in reproducing the flow structures and velocity distributions in many free-surface flows. One aspect of this study is to apply WC-MPS to simulate fishway flows and dry granular flows, numerically investigating the flows structures and velocity distributions. However, this method suffers from pressure noise and unphysical pressure fluctuations in modeling flows. Therefore, the other aspect of this study is to improve the method in calculating pressure and stabilize the simulations. In the investigation of the flows in the pool-and-weir fishway, different design parameters are examined, including the discharge, the length of the fishway pool, and the height of the weir, are considered in the investigation. Two typical flow patterns, plunging flow and skimming flow, are successfully reproduced. The free-surface profiles and velocity distribution in the two flow patterns are compared with experimental measurements. To simulate dry granular flows, the  (I) rheology model is coupled with WC-MPS to calculate the effective viscosity and shear stress. The coupled method is then employed to simulate granular column collapses caused by dry granular materials such as glass beads. During the collapses, the flowing region and static region are reproduced. Free-surface profiles and wave fronts are shown to have good agreement with experimental research in literature. The simulated velocity also compared well with the experimental data. It is found that the typical linear relation on velocity distribution exists in the flowing region. On the basis of velocity analysis, the distribution of shear stress is examined and discussed. Furthermore, an improved WC-MPS (IWC-MPS) is proposed to improve the accuracy and stabilize the pressure calculation. A new Laplacian model is derived to improve the accuracy in the method. A stabilization technique is also proposed to enhance the incompressibility and reduce pressure noise. The new Laplacian model is validated by a 2D diffusion problem and the Couette flow. It shows that the new Laplacian model is able to calculate more accurate results. The stabilization technique is validated by a water jet impinging on a rigid flat plate. The stabilization technique is able to greatly reduce the pressure noise and unphysical pressure fluctuations. In modeling a dam-breaking flow, IWC-MPS is able to achieve similar good results with other numerical methods such as AQUAgpusph and DualSPHysics. WC-MPS is useful numerical tool in handling free-surface flows such as fishway flows and dry granular flows. With the new version of it-IWC-MPS, more stabilized results can be achieved.

Application of Smoothed Particle Hydrodynamics Modelling to Turbulent Open Channel Flows Over Rough Beds