A water quality computation in the uniform channel

Pochai, Nopparat; Tangmanee, Suwon; Crane, L. J.; Miller, John J. H.

doi:10.1080/09720502.2008.10700602

Cited by 17 publications

(16 citation statements)

References 2 publications

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“…They found the theoretical solution of the model at the end point of the domain. They also use theanalytical solution to check the accuracy of our approximate solution.In [7], they propose the Lax-Wendroff method with stability analysis to solve the two-dimensional hydrodynamic model with a rectangular domain.…”

Section: Introductionmentioning

confidence: 99%

“…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%

“…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. The term of the friction forces due to the drag of sides of the uniform reservoir is considered.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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 hydrodynamics model provides the velocity field and tidal elevation of the water. In [7][8][9][10], they used the hydrodynamics model and the advection-dispersion equation to approximate the velocity of the water current in bay, uniform reservoir, and stream, respectively. Among these numerical techniques, the finite difference methods, including both explicit and implicit schemes, are mostly used for one-dimensional domain such as in longitudinal stream systems [11,12].…”

Section: Introductionmentioning

confidence: 99%

Numerical Treatment of a Modified MacCormack Scheme in a Nondimensional Form of the Water Quality Models in a Nonuniform Flow Stream

Pochai

2014

Journal of Applied Mathematics

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Two mathematical models are used to simulate water quality in a nonuniform flow stream. The first model is the hydrodynamic model that provides the velocity field and the elevation of water. The second model is the dispersion model that provides the pollutant concentration field. Both models are formulated in one-dimensional equations. The traditional Crank-Nicolson method is also used in the hydrodynamic model. At each step, the flow velocity fields calculated from the first model are the input into the second model as the field data. A modified MacCormack method is subsequently employed in the second model. This paper proposes a simply remarkable alteration to the MacCormack method so as to make it more accurate without any significant loss of computational efficiency. The results obtained indicate that the proposed modified MacCormack scheme does improve the prediction accuracy compared to that of the traditional MacCormack method.

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“…In [10], a nondimensional form of the hydrodynamic model with variable coefficients using Lax-Wendroff method is presented. In [11], the Lax-Wendroff finite difference method is also proposed to approximate the water elevation and water flow velocity with a rectangular domain. In [12], the mathematical models and numerical methods for approximating water current and pollutant concentration level in Rama-nine reservoirs are presented.…”

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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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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A water quality computation in the uniform channel

Cited by 17 publications

References 2 publications

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

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

Numerical Treatment of a Modified MacCormack Scheme in a Nondimensional Form of the Water Quality Models in a Nonuniform Flow Stream

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

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