scholarly journals Asymptotic Solution for a Water Quality Model in a Uniform Stream

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Fazle Mabood ◽  
Nopparat Pochai
Keyword(s):  
Mathematical Modeling ◽  
Water Quality ◽  
Diffusion Reaction ◽  
Order Method ◽  
Quality Model ◽  
Reaction Equation ◽  
One Dimensional ◽  
Advection Diffusion ◽  
Optimal Homotopy Asymptotic Method ◽  
Uniform Stream

We employ approximate analytical method, namely, Optimal Homotopy Asymptotic Method (OHAM), to investigate a one-dimensional steady advection-diffusion-reaction equation with variable inputs arises in the mathematical modeling of dispersion of pollutants in water is proposed. Numerical values are obtained via Runge-Kutta-Fehlberg fourth-fifth order method for comparison purpose. It was found that OHAM solution agrees well with the numerical solution. An example is included to demonstrate the efficiency, accuracy, and simplicity of the proposed method.

scholarly journals Numerical Simulation of a One-Dimensional Water-Quality Model in a Stream Using a Saulyev Technique with Quadratic Interpolated Initial-Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Pawarisa Samalerk ◽  
Nopparat Pochai
Keyword(s):  
Numerical Simulation ◽  
Water Quality ◽  
Boundary Condition ◽  
Diffusion Reaction ◽  
Quality Model ◽  
Reaction Equation ◽  
One Dimensional ◽  
Advection Diffusion ◽  
Pollutant Concentrations ◽  
The One

The one-dimensional advection-diffusion-reaction equation is a mathematical model describing transport and diffusion problems such as pollutants and suspended matter in a stream or canal. If the pollutant concentration at the discharge point is not uniform, then numerical methods and data analysis techniques were introduced. In this research, a numerical simulation of the one-dimensional water-quality model in a stream is proposed. The governing equation is advection-diffusion-reaction equation with nonuniform boundary condition functions. The approximated pollutant concentrations are obtained by a Saulyev finite difference technique. The boundary condition functions due to nonuniform pollutant concentrations at the discharge point are defined by the quadratic interpolation technique. The approximated solutions to the model are verified by a comparison with the analytical solution. The proposed numerical technique worked very well to give dependable and accurate solutions to these kinds of several real-world applications.

Time discretization versus state quantization in the simulation of a one-dimensional advection–diffusion–reaction equation

SIMULATION ◽  
2015 ◽  
Vol 92 (1) ◽  
pp. 47-61 ◽  
Author(s):  
Federico Bergero ◽  
Joaquín Fernández ◽  
Ernesto Kofman ◽  
Margarita Portapila
Keyword(s):  
Time Discretization ◽  
Diffusion Reaction ◽  
Reaction Equation ◽  
One Dimensional ◽  
Advection Diffusion

COMBINING ADJOINT STABILIZED METHODS FOR THE ADVECTION-DIFFUSION-REACTION PROBLEM

2007 ◽  
Vol 17 (02) ◽  
pp. 305-326 ◽  
Author(s):  
GUILLERMO HAUKE ◽  
GIANCARLO SANGALLI ◽  
MOHAMED H. DOWEIDAR
Keyword(s):  
Piecewise Linear ◽  
Diffusion Reaction ◽  
One Dimensional ◽  
Stabilized Methods ◽  
Advection Diffusion ◽  
Diffusive Limit ◽  
Reaction Transport ◽  
Globally Stable ◽  
Supg Method ◽  
Reaction Problem

Computational methods for the advection-diffusion-reaction transport equation are still a challenge. Although there exist globally stable methods, oscillations around sharp layers such as boundary, inner and outflow layers, are typical in multi-dimensional flows. In this paper a variational formulation that combines two types of stabilization integrals is proposed, namely an adjoint stabilization and a gradient adjoint stabilization. Two free parameters are chosen by imposing one-dimensional superconvergence. Then, when applied to multi-dimensional flows, the method presents better local stability than the present stabilized methods. Furthermore, in the advective-diffusive limit and for piecewise linear functional spaces, the method recovers the classical SUPG method.

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