Lattice Boltzmann Methods For Shallow Water Flows

The lattice Boltzmann method (LBM) is a modern numerical technique, very efficient, flexible to simulate different flows within complex/varying geome tries. It is evolved from the lattice gas automata (LGA) in order to overcome the difficulties with the LGA. The core equation in the LBM turns out to be a special discrete form of the continuum Boltzmann equation, leading it to be self-explanatory in statistical physics. The method describes the micro scopic picture of particles movement in an extremely simplified way, and on the macroscopic level it gives a correct average description of a fluid. The av eraged particle velocities behave in time and space just as the flow velocities in a physical fluid, showing a direct link between discrete microscopic and continuum macroscopic phenomena. In contrast to the traditional computational fluid dynamics (CFD) based on a direct solution of flow equations, the lattice Boltzmann method provides an indirect way for solution of the flow equations. The method is characterized by simple calculation, parallel process and easy implementation of boundary conditions. It is these features that make the lattice Boltzmann method a very promising computational method in different areas. In recent years, it receives extensive attentions and becomes a very potential research area in computational fluid dynamics. However, most published books are limited to the lattice Boltzmann methods for the Navier-Stokes equations. On the other hand, shallow water flows exist in many practical situations such as tidal flows, waves, open channel flows and dam-break flows.

The lattice Boltzmann method (LBM) proposed about decades ago has been developed and applied to simulate various complex fluids. It has become an alternative powerful method for computational fluid dynamics (CFD). Although most research on the LBM focuses on the Navier-Stokes equations, the method has also been developed to solve other flow equations such as the shallow water equations. In this thesis, the lattice Boltzmann models for the shallow water equations and solute transport equation have been improved and applied to different flows and environmental problems, including solute transport and morphological evolution. In this work, both the single-relaxation-time and multiple-relaxation-time models are used for shallow water equations (named LABSWE and LABSWEMRT, respectively), and the large eddy simulation is incorporated into the LABSWE (named LABSWETM) for turbulent flow. The capability of the LABSWETM was firstly tested by applying it to simulate free surface flows in rectangular basins with different length -width ratios, in which the characteristics of the asymmetrical flows were studied in details. The LABSWEMRT was then used to simulate the one- and two-dimensional shallow water flows over discontinuous beds. The weighted centred scheme for force term, together with the bed height for a bed slope, was incorporated into the model to improve the simulation of water flows over a discontinuous bed. The resistance stress was also included to investigate the effect of the local head loss caused by flows over a step. Thirdly, the LABSWEMRT was extended to simulate a moving body in shallow water. In order to deal with the moving boundaries, three different schemes with second-order accuracy were tested and compared for treating curved boundaries. An additional momentum term was added to reflect the interaction between the following fluid and the solid, and a refilled method was proposed to treat the wetted nodes moving out from the solid nodes. Fourthly, both LABSWE and LABSWEMRT were used to investigate solute transport in shallow water. The flows are solved using LABSWE and LABSWEMRT, and the advection-diffusion equation for solute transport was solved with a LBM-BGK model based on the D2Q5 lattice. Three cases: open channel flow with a side discharge, shallow recirculation flow and flow in a harbour, were simulated to verify the methods. In addition, the performance of LABSWEMRT and LABSWE were compared, and the results showed that the LABSWMRT has better stability and can be used for flow with high Reynolds number. Finally, the lattice Boltzmann method was used with the Euler-WENO scheme to simulate morphological evolution in shallow water. The flow fields were solved by the LABSWEMRT with the improved scheme for the force term, and the fifth order Euler-WENO scheme was used to solve the morphological equation to predict the morphological evolution caused by the bed-load transport.

Programming has become a significant part of connecting theoretical development and scientific application computation. Fluid dynamics provide an important asset in experimentation and theoretical analysis. Analysis and Applications of Lattice Boltzmann Simulations provides emerging research on the efficient and standard implementations of simulation methods on current and upcoming parallel architectures. While highlighting topics such as hardware accelerators, numerical analysis, and sparse geometries, this publication explores the techniques of specific simulators as well as the multiple extensions and various uses. This book is a vital resource for engineers, professionals, researchers, academics, and students seeking current research on computational fluid dynamics, high-performance computing, and numerical and flow simulations.

This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a variety of hardware platforms, including multi-core processors, clusters, and graphics processing units. Students and scientists learning and using the LB method will appreciate the wealth of clearly presented and structured information in this volume.

Here is a basic introduction to Lattice Boltzmann models that emphasizes intuition and simplistic conceptualization of processes, while avoiding the complex mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those whose interest is in model application over detailed mathematics will find this a powerful 'quick start' guide. Example simulations, exercises, and computer codes are included.

This edited review book on Godunov methods contains 97 articles, all of which were presented at the international conference on Godunov Methods: Theory and Applications, held at Oxford in October 1999, to commemo rate the 70th birthday of the Russian mathematician Sergei K. Godunov. The meeting enjoyed the participation of 140 scientists from 20 countries; one of the participants commented: everyone is here, meaning that virtu ally everybody who had made a significant contribution to the general area of numerical methods for hyperbolic conservation laws, along the lines first proposed by Godunov in the fifties, was present at the meeting. Sadly, there were important absentees, who due to personal circumstance could not at tend this very exciting gathering. The central theme o{ the meeting, and of this book, was numerical methods for hyperbolic conservation laws fol lowing Godunov's key ideas contained in his celebrated paper of 1959. But Godunov's contributions to science are not restricted to Godunov's method.

This book constitutes the refereed proceedings of the 8th International Conference, VISIGRAPP 2013 consisting of the Joint Conferences on Computer Vision (VISAPP), the International Conference on Computer Graphics, GRAPP 2013, and the International Conference on Information Visualization IVAPP 2013, held in Barcelona, Spain, in February 2013. The 15 revised full papers presented were carefully reviewed and selected from 445 submissions. The papers are organized in topical sections on theory and applications in computer vision, image analysis, computer graphics, and information visualization.

With the amazing advances of scientific research, Hydrodynamics - Theory and Application presents the engineering applications of hydrodynamics from many countries around the world. A wide range of topics are covered in this book, including the theoretical, experimental, and numerical investigations on various subjects related to hydrodynamic problems. The book consists of twelve chapters, each of which is edited separately and deals with a specific topic. The book is intended to be a useful reference to the readers who are working in this field.