Differential Quadrature Method for Linear Long Wave Propagation in Open Channels

Kaya, Birol; Arisoy, Yalçìn

doi:10.5772/6855

Cited by 6 publications

(3 citation statements)

References 44 publications

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“…Robati and Barani [25] considered water surface profile in an underground canal using DQM model. They concluded that DQM has the ability to simulate the water surface profile and the results are very close to the real water surface profile.…”

Section: Introductionmentioning

confidence: 99%

Solute Transport In Two Layered Porous Media (Separated Diagonally) Using Suitable DQM Scheme

Ghamariadyan¹,

Meraji²,

Ghaheri³

2016

IOSR

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In this research, we presented Differential Quadrature Method for solving groundwater flow and advection-dispersion equations in two layered porous media which the layers are separated diagonally. This method was applied to five cases and the results are compared with Modflow and Mt3d solutions. Also, The effect of various parameters on transport process are discussed in all cases. The DQM results show a good agreement with Modflow and Mt3d results regarding selecting fewer grid points. In applying the DQM, the needed mesh size is much smaller than the traditional approaches which reduces computational time and needed less computer storage capacity.

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Section: Introductionmentioning

confidence: 99%

Solute Transport In Two Layered Porous Media (Separated Diagonally) Using Suitable DQM Scheme

Ghamariadyan¹,

Meraji²,

Ghaheri³

2016

IOSR

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“…Differential quadrature method has also been used in different fields of fluid mechanics . In hydraulic and free surface water flow fields, the work completed by Kaya et al to solve a flood propagation problem in open channel, Kaya and Arisoy to solve the Saint‐Venant equations for linear long wave propagation in open channels, Hashemi et al to modeling long waves in shallow water and tidal and surge using incremental DQM, and Hashemi et al to solve the Saint‐Venant equations for numerical simulation of unsteady open channel flow can be pointed out.…”

Section: Introductionmentioning

confidence: 99%

An efficient algorithm based on the differential quadrature method for solving Navier–Stokes equations

Meraji

Ghaheri

Malekzadeh

2012

Numerical Methods in Fluids

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SUMMARYIn this paper, an approach to improve the application of the differential quadrature method for the solution of Navier–Stokes equations is presented. In using the conventional differential quadrature method for solving Navier–Stokes equations, difficulties such as boundary conditions' implementation, generation of an ill conditioned set of linear equations, large memory storage requirement to store data, and matrix coefficients, are usually encountered. Also, the solution of the generated set of equations takes a long running time and needs high computational efforts. An approach based on the point pressure–velocity iteration method, which is a variant of the Newton–Raphson relaxation technique, is presented to overcome these problems without losing accuracy. To verify its performance, four cases of two‐dimensional flows in single and staggered double lid‐driven cavity and flows past backward facing step and square cylinder, which have been often solved by researchers as benchmark solution, are simulated for different Reynolds numbers. The results are compared with existing solutions in the open literature. Very good agreement with low computational efforts of the approach is shown. It has been concluded that the method can be applied easily and is very time efficient. Copyright © 2012 John Wiley & Sons, Ltd.

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“…After the DQM was introduced by Bellman et al [12], it has been successfully employed in finding the solutions of many problems in applied sciences [13][14][15][16][17][18][19][20][21][22][23][24]. Recent comparative studies show that the DQM provides highly accurate and efficient solutions of the differential equations taking a noticeably small number of grid points.…”

Section: Introductionmentioning

confidence: 99%

Differential Quadrature Solutions of the Generalized Burgers–Fisher Equation with a Strong Stability Preserving High-Order Time Integration

Sarı

2011

MCA

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Numerical solutions of the generalized Burgers-Fisher equation are presented based on a polynomial-based differential quadrature method with minimal computational effort. To achieve this, a combination of a polynomial-based differential quadrature method in space and a third-order strong stability preserving Runge-Kutta scheme in time have been used. The proposed technique successfully worked to give reliable results in the form of numerical approximation converging very rapidly. The computed results have been compared with the exact solution to show the required accuracy of the method. The approximate solutions to the nonlinear equations were obtained. The approach is seen to be a very reliable alternative to the rival techniques for realistic problems.

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Differential Quadrature Method for Linear Long Wave Propagation in Open Channels

Cited by 6 publications

References 44 publications

Solute Transport In Two Layered Porous Media (Separated Diagonally) Using Suitable DQM Scheme

Solute Transport In Two Layered Porous Media (Separated Diagonally) Using Suitable DQM Scheme

An efficient algorithm based on the differential quadrature method for solving Navier–Stokes equations

Differential Quadrature Solutions of the Generalized Burgers–Fisher Equation with a Strong Stability Preserving High-Order Time Integration

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