Design and Analysis of Mathematical Model for the Concentration of Pollution and River Water Quality

2021 ◽  
pp. 13359-13368
Author(s):  
Rati Bajpai, Hari Om Sharan
Keyword(s):  
Water Quality ◽  
Diffusion Equation ◽  
River Water ◽  
Numerical Solutions ◽  
Water Quality Control ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Mathematical Analyses ◽  
Coupled Reaction ◽  
Concentration Levels

This paper mainly focuses on the recent advances in the mathematical models that provide the ability to predict the contaminant concentration levels of river water. The study represents an attempt for the researchers to study the problem of pollution, and we think that these mathematical analyses would provide better planning for water quality control. The model consists of a pair of coupled reaction Advection-diffusion equations for the pollutant and dissolved oxygen concentrations. Numerical solutions are obtained and some important inferences are drawn through simulation study. The Advection-Diffusion equation is characterized by the reaction term whenever it depends on concentration of the contaminants and in this case the original single Advection-diffusion equation will evolve to be a system of equations. It is no ticked that the higher are diffusion and reaeration coefficients, the faster is the river purity.

scholarly journals Comparison between two analytical solutions of advection-diffusion equation using separation technique and Hankel transform

MAUSAM ◽  
2021 ◽  
Vol 72 (4) ◽  
pp. 905-914
Author(s):  
KHALED S. M. ESSA ◽  
H. M. TAHA
Keyword(s):  
Wind Speed ◽  
Diffusion Equation ◽  
Numerical Solutions ◽  
Separation Of Variables ◽  
Eddy Diffusivity ◽  
Hankel Transform ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Information Sets ◽  
Vertical Eddy Diffusivity

On this work, contrast between two analytical and numerical solutions of the advection-diffusion equation has been completed. We  use the method of separation of variables, Hankel transform and Adomian numerical method. Also, Fourier rework, and square complement methods has been used to clear up the combination. The existing version is validated with the information sets acquired at the Egyptian Atomic Energy Authority test of radioactive Iodine-135 (I135) at Inshas in unstable conditions. On this model the wind speed and vertical eddy diffusivity are taken as characteristic of vertical height in the techniques and crosswind eddy diffusivity as function in wind speed. These values of predicted and numerical concentrations are comparing with the observed data graphically and statistically.

scholarly journals Numerical Solution of Advection-Diffusion Equation Using a Sixth-Order Compact Finite Difference Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Gurhan Gurarslan ◽  
Halil Karahan ◽  
Devrim Alkaya ◽  
Murat Sari ◽  
Mutlu Yasar
Keyword(s):  
Diffusion Equation ◽  
Numerical Solutions ◽  
Current Method ◽  
Sixth Order ◽  
Solution Approach ◽  
Compact Finite Difference Method ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Conventional Solution ◽  
Combined Technique

This study aims to produce numerical solutions of one-dimensional advection-diffusion equation using a sixth-order compact difference scheme in space and a fourth-order Runge-Kutta scheme in time. The suggested scheme here has been seen to be very accurate and a relatively flexible solution approach in solving the contaminant transport equation forPe≤5. For the solution of the present equation, the combined technique has been used instead of conventional solution techniques. The accuracy and validity of the numerical model are verified through the presented results and the literature. The computed results showed that the use of the current method in the simulation is very applicable for the solution of the advection-diffusion equation. The present technique is seen to be a very reliable alternative to existing techniques for these kinds of applications.

scholarly journals Sixth-Order Combined Compact Finite Difference Scheme for the Numerical Solution of One-Dimensional Advection-Diffusion Equation with Variable Parameters

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1027
Author(s):  
Gurhan Gurarslan
Keyword(s):  
Differential Equations ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Method Of Lines ◽  
Sixth Order ◽  
Variable Parameters ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

A high-accuracy numerical method based on a sixth-order combined compact difference scheme and the method of lines approach is proposed for the advection–diffusion transport equation with variable parameters. In this approach, the partial differential equation representing the advection-diffusion equation is converted into many ordinary differential equations. These time-dependent ordinary differential equations are then solved using an explicit fourth order Runge–Kutta method. Three test problems are studied to demonstrate the accuracy of the present methods. Numerical solutions obtained by the proposed method are compared with the analytical solutions and the available numerical solutions given in the literature. In addition to requiring less CPU time, the proposed method produces more accurate and more stable results than the numerical methods given in the literature.

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