Download or read book A Block Structured Adaptive Solution to the Shallow Water Equations written by Nitin Bhagat 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 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 An Adaptive Multiblock High order Finite volume Method for Solving the Shallow water Equations on the Sphere written by and published by . This book was released on 2015 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a high-order finite-volume approach for solving the shallow-water equations on the sphere, using multiblock grids on the cubed-sphere. This approach combines a Runge--Kutta time discretization with a fourth-order accurate spatial discretization, and includes adaptive mesh refinement and refinement in time. Results of tests show fourth-order convergence for the shallow-water equations as well as for advection in a highly deformational flow. Hierarchical adaptive mesh refinement allows solution error to be achieved that is comparable to that obtained with uniform resolution of the most refined level of the hierarchy, but with many fewer operations.

Download or read book Adaptive Multigrid Solution of the Shallow Water Equations written by Brittany L. Mitchell and published by . This book was released on 1999 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 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 Computational Algorithms for Shallow Water Equations written by Eleuterio F. Toro and published by Springer Nature. This book was released on with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Solution of the Shallow Water Equations written by David L. Whitfield and published by . This book was released on 1996 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Numerical Solution of the Shallow water Equations written by F. W. Wubs and published by . This book was released on 1988 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Adaptive Grids in Weather and Climate Modeling written by Christiane Jablonowski and published by . This book was released on 2004 with total page 572 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 Issues in Global Environment Climate and Climate Change 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 867 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Global Environment: Climate and Climate Change: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Global Environment—Climate and Climate Change. The editors have built Issues in Global Environment: Climate and Climate Change: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Global Environment—Climate and Climate Change in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Global Environment: Climate and Climate Change: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Download or read book GMD Research Series written by and published by . This book was released on 1999 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book UTBEST 3D written by Vadym Aizinger and published by . This book was released on 2005 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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: