2D Shallow Water Model for Dam Break and Column Interactions

Dam break causes disastrous effects on the surrounding area, especially at the downstream, therefore, there is a need for accurate and timely predictions of dam break propagation to prevent both property damage and loss of life. This study aimed to determine the movement of dam-break flow in the downstream area by solving the Shallow Water Equations (SWE) or Saint Venant Equations which are based on the conservation of mass and momentum derived from Navier Stokes equation. The model was generated using a finite difference scheme which is the most common and simplest method for dam-break modeling while Forward Time Central Space (FTCS) numerical scheme was applied to simulate two-dimensional SWE. Moreover, the accuracy of the numerical model was checked by comparing its results with the analytic results of one-dimensional cases and a relatively small value of error was found in comparison to the analytic models as indicated with the RMSE values close to 0. The numerical to the two-dimensional models were also compared to a simple dam break in a flume and dam break with column interactions and the wave propagation in both cases was observed to become very close at a certain time.  The model, however, used numerical filter (Hansen) to reduce the oscillations or numerical instability. The simulation and analysis, therefore, showed the ability of the numerical scheme of FTCS to resolve both cases of the simple dam break and dam break with column interactions in the Two-dimensional Shallow Water.

Modelling the Eddy Pattern in the harbour of Zeebrugge

Hydrodynamic

A New Parallel Framework of SPH-SWE for Dam Break Simulation Based on OpenMP

Due to its Lagrangian nature, Smoothed Particle Hydrodynamics (SPH) has been used to solve a variety of fluid-dynamic processes with highly nonlinear deformation such as debris flows, wave breaking and impact, multi-phase mixing processes, jet impact, flooding and tsunami inundation, and fluid–structure interactions. In this study, the SPH method is applied to solve the two-dimensional Shallow Water Equations (SWEs), and the solution proposed was validated against two open-source case studies of a 2-D dry-bed dam break with particle splitting and a 2-D dam break with a rectangular obstacle downstream. In addition to the improvement and optimization of the existing algorithm, the CPU-OpenMP parallel computing was also implemented, and it was proven that the CPU-OpenMP parallel computing enhanced the performance for solving the SPH-SWE model, after testing it against three large sets of particles involved in the computational process. The free surface and velocities of the experimental flows were simulated accurately by the numerical model proposed, showing the ability of the SPH model to predict the behavior of debris flows induced by dam-breaks. This validation of the model is crucial to confirm its use in predicting landslides’ behavior in field case studies so that it will be possible to reduce the damage that they cause. All the changes made in the SPH-SWEs method are made open-source in this paper so that more researchers can benefit from the results of this research and understand the characteristics and advantages of the solution proposed

SWE-SPHysics Simulation of Dam Break Flows at South-Gate Gorges Reservoir

This paper applied a Smoothed Particle Hydrodynamics (SPH) approach to solve Shallow Water Equations (SWEs) to study practical dam-break flows. The computational program is based on the open source code SWE-SPHysics, where a Monotone Upstream-centered Scheme for Conservation Laws (MUSCL) reconstruction method is used to improve the Riemann solution with Lax-Friedrichs flux. A virtual boundary particle method is applied to treat the solid boundary. The model is first tested on two benchmark collapses of water columns with the existence of downstream obstacle. Subsequently the model is applied to forecast a prototype dam-break flood, which might occur in South-Gate Gorges Reservoir area of Qinghai Province, China. It shows that the SWE-SPH modeling approach could provide a promising simulation tool for practical dam-break flows in engineering scale

Advances in Modelling and Numerical Simulation of Sediment Transport in Shallow Water Flows

A class of novel models for sediment transport, for which multilayer fluid models are combined with a multi-sediment method, is developed and analysed. Turbulent effects in both water flow and sediment transport are also accounted for in the presented models. The aim of this thesis is to advance fast and accurate techniques that overcome some of the assumptions limiting current sediment transport models of this type. To the best knowledge of the author, this is the first time a two-dimensional multilayer model has been used for modelling and simulation of sediment transport. Sediment transport methods using the Shallow Water Equations (SWEs) are reviewed and some of the limiting assumptions are highlighted. Fast methods for modelling sediment transport with multiple sediments are developed in both one space dimension (1D) and two space dimensions (2D). A new formulation for multilayer SWEs is expanded in 1D and 2D to also include sediment transport. Turbulence modelling with the well-established k-epsilon$ model is also evolved to deal with a multilayer formulation. Each development is tested by itself to quantify its effects and then combined with all the other developments to create the final model. Two second-order accurate solvers are in this thesis: namely a Roe-type solver and a novel Eulerian-Lagrangian formulation. The latter is favoured and is used to solve the complete model, including turbulence and multiple sediment types. This creates a fast and easy-to-implement method that can handle complex flows and irregular bed topographies. The methods are compared to other shallow water systems along with Navier-Stokes results and data obtained from experiments performed in the Department of Engineering at Durham University. Overall, this thesis provides interesting and highly applicable results that add a new avenue of applications to sediment transport in shallow water flows

Shallow Water Moment models for bedload transport problems

In this work a simple but accurate shallow model for bedload sediment transport is proposed. The model is based on applying the moment approach to the Shallow Water Exner model, making it possible to recover the vertical structure of the flow. This approach allows us to obtain a better approximation of the fluid velocity close to the bottom, which is the relevant velocity for the sediment transport. A general Shallow Water Exner moment model allowing for polynomial velocity profiles of arbitrary order is obtained. A regularization ensures hyperbolicity and easy computation of the eigenvalues. The system is solved by means of an adapted IFCP scheme proposed here. The improvement of this IFCP type scheme is based on the approximation of the eigenvalue associated to the sediment transport. Numerical tests are presented which deal with large and short time scales. The proposed model allows to obtain the vertical structure of the fluid, which results in a better description on the bedload transport of the sediment layer

Robust finite volume schemes for 2D shallow water models. Application to flood plain dynamics

This study proposes original combinations of higher order Godunov type finite volume schemes and time discretization schemes for the 2d shallow water equations, leading to fully second-order accuracy with well-balanced property. Also accuracy, positiveness and stability properties in presence of dynamic wet/dry fronts is demonstrated. The test cases are the classical ones plus extra new ones representing the geophysical flow features and difficulties

A hybrid stabilization technique for simulating water wave - Structure interaction by incompressible Smoothed Particle Hydrodynamics (ISPH) method

The Smoothed Particle Hydrodynamics (SPH) method is emerging as a potential tool for studying water wave related problems, especially for violent free surface flow and large deformation problems. The incompressible SPH (ISPH) computations have been found not to be able to maintain the stability in certain situations and there exist some spurious oscillations in the pressure time history, which is similar to the weakly compressible SPH (WCSPH). One main cause of this problem is related to the non-uniform and clustered distribution of the moving particles. In order to improve the model performance, the paper proposed an efficient hybrid numerical technique aiming to correct the ill particle distributions. The correction approach is realized through the combination of particle shifting and pressure gradient improvement. The advantages of the proposed hybrid technique in improving ISPH calculations are demonstrated through several applications that include solitary wave impact on a slope or overtopping a seawall, and regular wave slamming on the subface of open-piled structure