A Mathematical Model of Water Pollution Control Using the Finite Element Method

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

doi:10.1002/pamm.200610358

Cited by 27 publications

(15 citation statements)

References 2 publications

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“…In [1][2][3], they used the hydrodynamic model and the dispersion model with the finite element method to approximate the velocity of the water current in bay, estuaries, and open reservoir, respectively. In [4], the finite element method was used for solving the water pollution levels to the optimal control of the water treatment plants to achieve minimum cost.…”

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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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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“…In our paper, a mathematical model for the dispersion of pollutants in a river is presented; the Perturbation Iteration Algorithm for assessment of the chemical oxygen demand (COD) concentration in a river is considered. 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.…”

Section: Introductionmentioning

confidence: 99%

“…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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“…For the shallow water mass transport problems that were presented in [1], the method of characteristics has been reported as being applied with success, but in real cases it presents some difficulties. In [2] and [3], the finite element method for solving the water pollution models in one-and two-dimensional water areas are presented, respectively. Most mathematical models require data concerning the velocity of the current at any point in the domain.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model of Water Pollution Control Using the Finite Element Method

Cited by 27 publications

References 2 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 computation of the non-dimensional form of a non-linear hydrodynamic model in a uniform reservoir

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