Download or read book An Adaptive Well Balanced Positivity Preserving Central Upwind Scheme for the Shallow Water Equations Over Quadtree Grids written by Seyed Mohammad Ali Ghazizadeh Fard and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Shallow water equations are widely used to model water flows in the field of hydrodynamics and civil engineering. They are complex, and except for some simplified cases, no analytical solution exists for them. Therefore, the partial differential equations of the shallow water system have been the subject of various numerical analyses and studies in past decades. In this study, we construct a stable and robust finite volume scheme for the shallow water equations over quadtree grids. Quadtree grids are two-dimensional semi-structured Cartesian grids that have different applications in several fields of engineering, such as computational fluid dynamics. Quadtree grids refine or coarsen where it is required in the computational domain, which gives the advantage of reducing the computational cost in some problems. Numerical schemes on quadtree grids have different properties. An accurate and robust numerical scheme is able to provide a balance between the flux and source terms, preserve the positivity of the water height and water surface, and is capable of regenerating the grid with respect to different conditions of the problem and computed solution. The proposed scheme uses a piecewise constant approximation and employs a high-order Runge-Kutta method to be able to make the solution high-order in space and time. Hence, in this thesis, we develop an adaptive well-balanced positivity preserving scheme for the shallow water system over quadtree grids utilizing different techniques. We demonstrate the formulations of the proposed scheme over one of the different configurations of quadtree cells. Six numerical benchmark tests confirm the ability of the scheme to accurately solve the problems and to capture small perturbations. Furthermore, we extend the proposed scheme to the coupled variable density shallow water flows and establish an extended method where we focus on eliminating nonphysical oscillations, as well as well-balanced, positivity preserving, and adaptivity properties of the scheme. Four different numerical benchmark tests show that the proposed extension of the scheme is accurate, stable, and robust.
Download or read book River Flow 2016 written by George Constantinescu and published by CRC Press. This book was released on 2016-06-22 with total page 3703 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding and being able to predict fluvial processes is one of the biggest challenges for hydraulics and environmental engineers, hydrologists and other scientists interested in preserving and restoring the diverse functions of rivers. The interactions among flow, turbulence, vegetation, macroinvertebrates and other organisms, as well as the transport and retention of particulate matter, have important consequences on the ecological health of rivers. Managing rivers in an ecologically friendly way is a major component of sustainable engineering design, maintenance and restoration of ecological habitats. To address these challenges, a major focus of River Flow 2016 was to highlight the latest advances in experimental, computational and theoretical approaches that can be used to deepen our understanding and capacity to predict flow and the associated fluid-driven ecological processes, anthropogenic influences, sediment transport and morphodynamic processes. River Flow 2016 was organized under the auspices of the Committee for Fluvial Hydraulics of the International Association for Hydro-Environment Engineering and Research (IAHR). Since its first edition in 2002, the River Flow conference series has become the main international event focusing on river hydrodynamics, sediment transport, river engineering and restoration. Some of the highlights of the 8th International Conference on Fluvial Hydraulics were to focus on inter-disciplinary research involving, among others, ecological and biological aspects relevant to river flows and processes and to emphasize broader themes dealing with river sustainability. River Flow 2016 contains the contributions presented during the regular sessions covering the main conference themes and the special sessions focusing on specific hot topics of river flow research, and will be of interest to academics interested in hydraulics, hydrology and environmental engineering.
Download or read book Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids written by Nasa Technical Reports Server (Ntrs) and published by BiblioGov. This book was released on 2013-08 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes. Our starting point is the recent central scheme of Kurganov and Petrova (KP) for approximating solutions of conservation laws on triangular meshes. In order to extend this scheme from systems of conservation laws to systems of balance laws one has to find an appropriate discretization of the source terms. We first show that for general triangulations there is no discretization of the source terms that corresponds to a well-balanced form of the KP scheme. We then derive a new variant of a central scheme that can be balanced on triangular meshes. We note in passing that it is straightforward to extend the KP scheme to general unstructured conformal meshes. This extension allows us to recover our previous well-balanced scheme on Cartesian grids. We conclude with several simulations, verifying the second-order accuracy of our scheme as well as its well-balanced properties.
Download or read book Advances in Hydroinformatics written by Philippe Gourbesville and published by Springer. This book was released on 2018-02-26 with total page 1205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers a collection of extended papers based on presentations given during the SimHydro 2017 conference, held in Sophia Antipolis, Nice, France on June 14–16, 2017. It focuses on how to choose the right model in applied hydraulics and considers various aspects, including the modeling and simulation of fast hydraulic transients, 3D modeling, uncertainties and multiphase flows. The book explores both limitations and performance of current models and presents the latest developments in new numerical schemes, high-performance computing, multiphysics and multiscale methods, and better interaction with field or scale model data. It gathers the lastest theoretical and innovative developments in the modeling field and presents some of the most advance applications on various water related topics like uncertainties, flood simulation and complex hydraulic applications. Given its breadth of coverage, it addresses the needs and interests of practitioners, stakeholders, researchers and engineers alike.
Download or read book Well Balanced Central Scheme for the Two dimensional Shallow Water Equations written by Sarah Tarek Khankan and published by . This book was released on 2010 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: We aim to develop a new class of well-balanced non-oscillatory second-order accurate central schemes for the approximating solution of general two-dimensional hyperbolic systems, and in particular to approximate the solution of shallow water equation systems (SWE) on Cartesian grids. The base scheme evolves the numerical solution on a unique Cartesian grid and avoids the resolution of the Riemann problems arising at the cell interfaces thanks to a layer of ghost staggered cells implicitly used while updating the solution. --The system of shallow water equations represents a good mathematical model for the hydrodynamics of coastal oceans, simulation of flows in channels and rivers, study of large-scale waves and vertically averaged regimes in the atmosphere and ocean. Here h denotes the water depth, (u, v) represents the flow velocity, g is the gravitational constant, and b is the function that models the water bed topography. b vanishes in the case of a flat riverbed and the resulting system becomes a hyperbolic system. Most numerical schemes fail to maintain the steady state constraint of shallow water equation problems and generate numerical (nonphysical) waves and storms. In this project, we shall investigate several approaches that could be coupled with our numerical base scheme in order to ensure, when necessary, the steady state condition of SWE systems.
Download or read book A Block Structured Adaptive Solution to the Shallow Water Equations written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: An adaptive mesh refinement algorithm for shallow water equations is presented. The algorithm uses upwind scheme that is Godunov type and which approximately solves the Riemann problem using Roe's technique. A highly accurate solution is achieved by using the adaptive mesh refinement technique of Berger and Oliger for mesh refinement algorithm. The numerical method is second-order accurate and approximately max-min preserving by using van Leer limited-slope technique. One-dimensional nesting algorithm has been implemented successfully. Numerical results on a test problem verify the second order accuracy of the algorithm. The nested grid results yield the equivalent solution to that of the corresponding fine grid solution.
Download or read book A Well balanced Stable GRP Scheme for Shallow Water Equations for Adaptive Unstructured Triangular Meshes written by and published by . This book was released on 2013 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Godunov Methods written by E.F. Toro and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Solution of the Shallow Water Equations of Quadtree Grids written by Sergio Cruz León and published by . This book was released on 1997 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Upwind Scheme for the 2D Shallow Water Equations with Applications written by P. Brufau and published by . This book was released on 1998 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Upwind Schemes for the Two dimensional Shallow Water Equations with Variable Depth Using Unstructured Meshes written by A. Bermùdez and published by . This book was released on 1995 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Study of Well balanced Finite Volume Methods and Refinement Indicators for the Shallow Water Equations written by Sudi Mungkasi and published by . This book was released on 2012 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis studies solutions to the shallow water equations analytically and numerically. The study is separated into three parts. The first part is about well-balanced finite volume methods to solve steady and unsteady state problems. A method is said to be well-balanced if it preserves an unperturbed steady state at the discrete level. We implement hydrostatic reconstructions for the well-balanced methods with respect to the steady state of a lake at rest. Four combinations of quantity reconstructions are tested. Our results indicate an appropriate combination of quantity reconstructions for dealing with steady and unsteady state problems. The second part presents some new analytical solutions to debris avalanche problems and reviews the implicit Carrier-Greenspan periodic solution for flows on a sloping beach. The analytical solutions to debris avalanche problems are derived using characteristics and a variable transformation technique. The analytical solutions are used as benchmarks to test the performance of numerical solutions. For the Carrier-Greenspan periodic solution, we show that the linear approximation of the Carrier-Greenspan periodic solution may result in large errors in some cases. If an explicit approximation of the Carrier-Greenspan periodic solution is needed, higher order approximations should be considered. We propose second order approximations of the Carrier-Greenspan periodic solution and present a way to get higher order approximations. The third part discusses refinement indicators used in adaptive finite volume methods to detect smooth and nonsmooth regions. In the adaptive finite volume methods, smooth regions are coarsened to reduce the computational costs and nonsmooth regions are refined to get more accurate solutions. We consider the numerical entropy production and weak local residuals as refinement indicators. Regarding the numerical entropy production, our work is the first to implement the numerical entropy production as a refinement indicator into adaptive finite volume methods used to solve the shallow water equations. Regarding weak local residuals, we propose formulations to compute weak local residuals on nonuniform meshes. Our numerical experiments show that both the numerical entropy production and weak local residuals are successful as refinement indicators.
Download or read book Towards Efficient Techniques for Solutions of the Shallow Water Equations written by Owen Thomas DeGennaro-Ransom and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Research was conducted in order to develop more efficient solution techniques for the Shallow Water Equations (SWE) for naturally occurring free-surface flows in natural and engineered channels. Methods relating to numerical solution of the two-dimensional equations utilizing graphical processing units (GPU) as the main computational device and combined one-and two-dimensional schemes are presented and tested. Different numerical methods were investigated for inclusion to the model. General requirements for the proposed schemes included the ability to be solved using a finite-difference conservative solution algorithm on a fixed rectangular grid and the ability to both withstand and provide reasonable approximation of shocks and bores within the solution domain. Two such schemes were investigated that met initial criteria: A graphical processing unit (GPU) implementation of the well established MacCormack method, and a selectively under-relaxed implicit method. Both methods included the addition of a TVD (total variation diminishing) term to help maintain stability around high gradient flow areas.The implicit method incorporates an algorithm for selectively under-relaxing the iterative process to maintain stability in the presence of shock interfaces. The value of the Courant number and the frequency at which the TVD term was incorporated were constantly updated during the computation to achieve optimal speed of execution while maintaining stability. The method was tested against published results from experiments and from computations employing alternative algorithms and the results obtained demonstrate both the economy and accuracy of the proposed algorithm. The MacCormack-based scheme was chosen for both optimizing procedure attempts. Methodology was tested that allowed for one and two-dimensional TVD-MacCormack equation coupling, reducing grid-size dependency for the solution domain, while permitting simultaneous calculation of both one and two dimensional domains, and the explicit, finite-difference formulation of the solution methodology was well suited for inclusion into simultaneous GPU calculation. Cell alignment and cell-neighbor management is shifted from matrix to array form, which allows for a new framework, optimally constructed for inclusion of the dimensionally coupled solution scheme. The code contains adaptive time-stepping, based on maximum local Courant number, and special wetting/drying schemes to maximize stability while maintaining accuracy. The method was tested against published results, showing it's effectiveness in minimizing computational resources while comparing well with experimentally derived results. The coupled code is tempered for insertion into a parallel computing array. Ultimately, while dimensional coupling provided a slight optimization in terms of computational efficiency, the dimensional interface methodology and limited domain types the solution technique was constructed for restrict it to a specific-use tool. The extension of the MacCormack method to GPU processing ultimately proved more useful, showing speed increases of 4-40 times depending on the domains geomorphological characteristics.
Download or read book An Adaptively refined Quadtree Grid Method for Incompressible Flows written by Stuart Scott Ochs and published by . This book was released on 1998 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study presents an adaptively-refined quadtree grid method used in conjunction with a pressure-based flow solution algorithm for the incompressible Navier-Stokes equations. The quadtree grid, which is composed of quadrilateral cells that can be successively subdivided into four quadrants, is examined, and the quadtree data structure, and its advantages when used in the numerical solution of the Navier-Stokes equations, is discussed. Several strategies for solution adaptive grid refinement, which is used to resolve high-gradient flow regions, are then presented. Two different flow solution methods, the uni-dimensional power-law method and the upwind method, both based on a cell-centered, finite-volume technique, are studied. These methods solve the governing equations for the primitive variables on a colocated grid using the SIMPLE algorithm.
Download or read book Parallel Simulation of the Shallow Water Equations on Structured Dynamically Adaptive Triangular Grids written by Csaba Attila Vigh and published by . This book was released on 2012 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multidimensional Upwind Schemes for the Shallow Water Equations written by H. Paillère and published by . This book was released on 1998 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Improved Treatment of Source Terms in Upwind Schemes for the Shallow Water Equations in Channels with Irregular Geometry written by María Elena Vázquez-Cendón and published by . This book was released on 1999 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
