A numerical computation of the non-dimensional form of a non-linear hydrodynamic model in a uniform reservoir

Pochai, Nopparat

doi:10.1016/j.nahs.2009.03.005

Cited by 11 publications

(9 citation statements)

References 6 publications

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“…For the left boundary condition, we have = 0 and 1 ≤ ≤ , letting 0, = 1, , 0, = 1, , and 0, = 1, . Substituting the approximate unknown vector nodes 0, , 0, , and 0, of the left boundary into (7), (9), and (11), respectively,…”

Section: Lax-wendroff Methods For the Hydrodynamic Modelmentioning

confidence: 99%

“…In [8], the Crank-Nicolson method is used to solve the hydrodynamic model and the backward time central space (BTCS) for the dispersion model. In [9], the approximated solutions of the hydrodynamic model and advection-diffusion-reaction equation in a uniform reservoir are proposed. In [10], a nondimensional form of the hydrodynamic model with variable coefficients using Lax-Wendroff method is presented.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Simulations of Water Quality Measurement Model in an Opened-Closed Reservoir with Contaminant Removal Mechanism

Thongtha

Kasemsuwan

2018

International Journal of Differential Equations

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The mathematical simulation of water contaminant measurement is often used to assess the water quality. The monitoring point placement for water quality measurement in an opened-closed reservoir can give accurate or inaccurate assessment. In this research, the mathematical model of the approximated water quality in an opened-closed reservoir with removal mechanism system is proposed. The water quality model consists of the hydrodynamic model and the dispersion model. The hydrodynamic model is used to describe the water current in the opened-closed reservoir. The transient advection-diffusion equation with removal mechanism provides the water pollutant concentration. The water velocity from the hydrodynamic model is plugged into the dispersion model. The finite difference techniques are used to approximate the solution of the water quality model. The proposed numerical simulations give a suitable area of zonal removal mechanism placement. The proposed simulations also give the overall and specified approximated water quality for each point and time when the exit gate is opened on the different periods of time. In addition, the proposed techniques can give a suitable period of time to open the exit gate to achieve a good agreement water quality by using contaminant removal mechanism.

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Section: Lax-wendroff Methods For the Hydrodynamic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical Simulations of Water Quality Measurement Model in an Opened-Closed Reservoir with Contaminant Removal Mechanism

Thongtha

Kasemsuwan

2018

International Journal of Differential Equations

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“…Pochai et al [7] had addressed a mathematical model of water pollution by employing the finite element method. The same author(s) [8,9] implemented the finite difference method (F DM ) to the hydrodynamic model with constant coefficients in the uniform reservoir and stream. This model needs the calculation of the substance dispersion given water velocity in the channel to work properly.…”

Section: Introductionmentioning

confidence: 99%

A Solution for a Water Quality Model in a Uniform Stream Channel using New Iterative Method

Khalid¹,

Sultana²,

Zaidi³

et al. 2015

IJCA

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During the last decade, political awareness of river water quality issues has increased significantly. New environmental policies have a requirement for improved methods for the investigation and evaluation of river water quality. Moreover, the derivation and assessment of management practices is also necessary. An efficient Perturbation Iteration Algorithm for solving the water quality assessment model has been developed. The employed equation of this uniform flow model is one-dimensional Advection-DispersionReaction equation that has variable coefficients. This water quality model requires the calculation of the substance dispersion considering the water velocity in the channel. Numerical values are obtained by using the Runge-Kutta-Fehlberg fourth-fifth order method for comparison. It was discovered that Perturbation Iteration Algorithm solution gels well with the numerical solution. Two examples are included to demonstrate the efficiency, accuracy, and simplicity of the proposed method.

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“…In [3], [8], [13], [14], [15] and [16], the finite element method for solving steady and unsteady water pollution measurements are presented. The various numerical techniques to solve the uniform flow of stream water quality model are presented in [5], [11] and [12].The numerical methods to approximate the solution of the two-dimensional advection-diffusionreaction equation are proposed in [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…The hydrodynamics model provides the velocity field and tidal elevation of the water. In [4][5][6][7][8][9][10][11][12], the hydrodynamics model and advection-diffusion equation were used to approximate the velocity of the water current in a bay and a channel. In [7,16], the results from hydrodynamic model are data for the non-uniform flow of the advection-diffusion-reactione quation, which provides the pollutant concentration field.…”

Section: Introductionmentioning

confidence: 99%

A numerical treatment of a non-dimensional form of a water quality model in the Rama-nine reservoir

Klaychang

Pochai

2015

Journal of Interdisciplinary Mathematics

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The purposes of this research are to develop mathematical models and numerical methods for approximating water flow directions and pollution levels in a Rama-nine reservoir, Pathumthani, Thailand with non-uniform current. The Rama-nine reservoir is opened with two parallel canals. The pollution levels in a reservoir are assessing via data collection at the real field. It is quite complex and the results obtained tentatively deviate from one point of time and position to another. There are many research works applied a mathematical model called the dispersion model to estimate the water pollutant concentration. The approximation accuracy received is seemingly unsatisfied, especially, when the water flow is not uniformly distributed.The research begins with revising a mathematical model that combines two existing mathematical models: a non-dimensional form of hydrodynamic model and a dispersion model. The model is to make suitable to the Rama-nine reservoir.The LaxWendroff method is subsequently used in a non-dimensional form of a shallow water equation to approximate the water velocity and elevation. Next, we use the forward differences in time and backward difference in space in advection-diffusion equation. Combined the equation with the calculated velocity is thus used in the dispersion model to approximate the concentration levels of the pollutants. The result of this research showed that the proposed *concentration of the pollutants in a Rama-nine reservoir at any various time and position. The accuracy of approximation is within the units of centimeters and seconds. In addition, this research has shown that the proposed model can be applied to other water sources having non-uniformly distributed water flows.

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A numerical computation of the non-dimensional form of a non-linear hydrodynamic model in a uniform reservoir

Cited by 11 publications

References 6 publications

Numerical Simulations of Water Quality Measurement Model in an Opened-Closed Reservoir with Contaminant Removal Mechanism

Numerical Simulations of Water Quality Measurement Model in an Opened-Closed Reservoir with Contaminant Removal Mechanism

A Solution for a Water Quality Model in a Uniform Stream Channel using New Iterative Method

A numerical treatment of a non-dimensional form of a water quality model in the Rama-nine reservoir

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