Simulation of free-surface flows and development of an improved particle method

Date
2017-02
Authors
Xu, Tibing
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Publisher
Faculty of Graduate Studies and Research, University of Regina
Abstract

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.

Description
A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Environmental Systems Engineering, University of Regina. xv, 201 p.
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