A Flux Vector Splitting Technique for Shallow Water Equations

2003 ◽  
Author(s):  
Arturo Pacheco-Vega ◽  
J. Rafael Pacheco ◽  
Tamara Rodic´
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Hydraulic Jump ◽  
Computational Domain ◽  
Flux Vector ◽  
Governing Equations ◽  
Splitting Technique ◽  
Flux Vector Splitting ◽  
Film Flows ◽  
Upwind Finite Difference

We present a flux vector splitting (FVS) for the solution of the shallow water equations with emphasis in their application to film flows for which a hydraulic jump may exist. The governing equations and boundary conditions are transformed from the physical to the computational domain and solved in a rectangular grid. A first-order upwind finite difference scheme is used at the point of the shock while a second-order upwind differentiation is applied elsewhere. Higher-order spatial accuracy is achieved by using a MUSCL approach. Two problems, (a) one-dimensional dam break problem and (b) radial flow with jump, are investigated to show the usefulness and accuracy of the method. Results demonstrate that the method is able to predict accuratelly the hydraulic jump using shallow water theory.

Analysis of Thin Film Flows Using a Flux Vector Splitting1

2003 ◽  
Vol 125 (2) ◽  
pp. 365-374 ◽  
Author(s):  
J. Rafael Pacheco ◽  
Arturo Pacheco-Vega
Keyword(s):  
Thin Film ◽  
Shallow Water ◽  
Radial Flow ◽  
Computational Domain ◽  
Flux Vector ◽  
Thin Film Flow ◽  
Flow Problems ◽  
Shallow Water Approximation ◽  
Flux Vector Splitting ◽  
Film Flows

We propose a flux vector splitting (FVS) for the solution of film flows radially spreading on a flat surface created by an impinging jet using the shallow-water approximation. The governing equations along with the boundary conditions are transformed from the physical to the computational domain and solved in a rectangular grid. A first-order upwind finite difference scheme is used at the point of the shock while a second-order upwind differentiation is applied elsewhere. Higher-order spatial accuracy is achieved by introducing a MUSCL approach. Three thin film flow problems (1) one-dimensional dam break problem, (2) radial flow without jump, and (3) radial flow with jump, are investigated with emphasis in the prediction of hydraulic jumps. Results demonstrate that the method is useful and accurate in solving the shallow water equations for several flow conditions.

A kinetic flux vector splitting scheme for shallow water flows

2003 ◽  
Vol 26 (6) ◽  
pp. 635-647 ◽  
Author(s):  
S.Q. Zhang ◽  
M.S. Ghidaoui ◽  
W.G. Gray ◽  
N.Z. Li
Keyword(s):  
Shallow Water ◽  
Splitting Scheme ◽  
Flux Vector ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Flux Vector Splitting

High Order Well-Balanced Weighted Compact Nonlinear Schemes for Shallow Water Equations

2017 ◽  
Vol 22 (4) ◽  
pp. 1049-1068 ◽  
Author(s):  
Zhen Gao ◽  
Guanghui Hu
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
High Order ◽  
High Order Accuracy ◽  
Local Characteristic ◽  
Order Accuracy ◽  
Splitting Technique ◽  
Strong Discontinuities ◽  
Comput Phys ◽  
Fifth Order

AbstractIn this study, a numerical framework of the high order well-balanced weighted compact nonlinear (WCN) schemes is proposed for the shallow water equations based on the work in [S. Zhang, S. Jiang, C.-W Shu, J. Comput. Phys. 227 (2008) 7294-7321]. We employ a special splitting technique for the source term proposed in [Y. Xing, C.-W Shu, J. Comput. Phys. 208 (2005) 206-227] to maintain the exact C-property, which can be proved theoretically. In the meantime, the genuine high order accuracy of the numerical scheme can be observed successfully, and small perturbation of the stationary state can be resolved and evolved well. In order to capture the strong discontinuities and large gradients, the fifth-order upwind weighted nonlinear interpolations together with the fourth/sixth order cell-centered compact scheme are used to construct different WCN schemes. In addition, the local characteristic projections are considered to further restrain the potential numerical oscillations. A variety of representative one- and two-dimensional examples are tested to demonstrate the good performance of the proposed schemes.

Numerical Solution of Transient Flow in Wind Tunnels

Volume 1 ◽  
2004 ◽  
Author(s):  
A. Nouri-Borujerdi ◽  
M. Ziaei-Rad
Keyword(s):  
Atmospheric Pressure ◽  
Transient Flow ◽  
Splitting Method ◽  
Wind Tunnels ◽  
Flux Vector ◽  
Governing Equations ◽  
One Dimensional ◽  
Flux Vector Splitting ◽  
Pass Through ◽  
Good Agreement

This paper deals with design and analysis of intermittent supersonic wind tunnels. System can be constructed by allowing air at atmospheric pressure to pass through a converging-diverging nozzle, a test section and a diffuser into a vacuum tank. The governing equations of compressible fluid flow have been solved numerically using flux vector splitting method to obtain running time under which it works at the design Mach number. The formulation has been tested on the theory of quasi one-dimensional compressible flow. The numerical results are in good agreement with the results of the theory.

Solving shallow water equations with crisp and uncertain initial conditions

2018 ◽  
Vol 28 (12) ◽  
pp. 2801-2815 ◽  
Author(s):  
Perumandla Karunakar ◽  
Snehashish Chakraverty
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Triangular Fuzzy Number ◽  
Governing Equations ◽  
Content Type ◽  
Variational Iteration

Purpose This paper aims to deal with the application of variational iteration method and homotopy perturbation method (HPM) for solving one dimensional shallow water equations with crisp and fuzzy uncertain initial conditions. Design/methodology/approach Firstly, the study solved shallow water equations using variational iteration method and HPM with constant basin depth and crisp initial conditions. Further, the study considered uncertain initial conditions in terms of fuzzy numbers, which leads the governing equations to fuzzy shallow water equations. Then using cut and parametric concepts the study converts fuzzy shallow water equations to crisp form. Then, HPM has been used to solve the fuzzy shallow water equations. Findings Results obtained by both methods HPM and variational iteration method are compared graphically in crisp case. Solution of fuzzy shallow water equations by HPM are presented in the form triangular fuzzy number plots. Originality/value Shallow water equations with crisp and fuzzy initial conditions have been solved.

Purely erosional cyclic and solitary steps created by flow over a cohesive bed

2000 ◽  
Vol 419 ◽  
pp. 203-238 ◽  
Author(s):  
GARY PARKER ◽  
NORIHIRO IZUMI
Keyword(s):  
Shallow Water ◽  
Wave Height ◽  
Shallow Water Equations ◽  
Hydraulic Jump ◽  
Water Surface ◽  
Migration Speed ◽  
One Dimensional ◽  
Surface Profiles ◽  
Cohesive Bed ◽  
Cohesive Material

An erodible surface exposed to supercritical flow often devolves into a series of steps that migrate slowly upstream. Each step delineates a headcut with an associated hydraulic jump. These steps can form in a bed of cohesive material which, once eroded, is carried downstream as washload without redeposition. Here the case of purely erosional, one-dimensional periodic, or cyclic steps in cohesive material is considered. The St. Venant shallow-water equations combined with a formulation for sediment erosion are used to construct a complete theory of the erosional case. The solution allows wavelength, wave height, migration speed and bed and water surface profiles to be determined as functions of imposed parameters. The analysis also admits a solution for a solitary step, or single headcut of self-preserving form.

scholarly journals Load balancing using Hilbert space-filling curves for parallel shallow water simulations

2019 ◽  
pp. 75-87
Author(s):  
А.В. Чаплыгин ◽  
Н.А. Дианский ◽  
А.В. Гусев
Keyword(s):  
Hilbert Space ◽  
Load Balancing ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
General Circulation ◽  
Sigma Model ◽  
Ocean Model ◽  
Computational Domain ◽  
Space Filling ◽  
Space Filling Curves

Представлен метод балансировки нагрузки вычислений с использованием кривых Гильберта применительно к параллельному алгоритму решения уравнений мелкой воды. Рассматриваемая система уравнений мелкой воды возникает в сигма-модели общей циркуляции океана INMOM (Institute of Numerical Mathematics Ocean Model) при разрешении гравитационных волн и является одним из основных блоков модели. Из-за наличия в океанах островов и берегов балансировка нагрузки вычислений на процессоры является особенно актуальной задачей. В качестве одного из таких методов был выбран метод балансировки нагрузки вычислений с использованием кривых Гильберта. Продемонстрирована большая эффективность этого метода по сравнению с равномерным разбиением без балансировки нагрузки и показано, что этот метод служит хорошей альтернативой библиотеке разбиений METIS. Оптимальность реализованного разбиения для мелкой воды точно соответствует оптимальности и для трехмерной сигма-модели INMOM в силу одинакового количества вертикальных уровней во всей расчетной области. This paper presents a method of load balancing using Hilbert space-filling curves applied to a parallel algorithm for solving shallow water equations. We consider the system of shallow water equations in the form presented in the ocean general circulation sigma-model INMOM (Institute of Numerical Mathematics Ocean Model). This system of equations is one of the basic blocks of the model. Due to land points in the computational grid, the load balancing is an especially urgent task. The method of load balancing using Hilbert space-filling curves is chosen as one of such methods. The paper demonstrates the greater efficiency of this method in comparison with the uniform partitioning without load balancing. It is shown that this method is a good alternative to the METIS standard library. Moreover, the optimality of the implemented partition for the shallow water equations exactly corresponds to the optimality for the INMOM three-dimensional sigma-model due to the same number of vertical levels in the entire computational domain.

Sign in / Sign up

Export Citation Format

Share Document