Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation
Document Type
Article
Publication Date
1-1-2019
Abstract
In the present article, the advection-diffusion equation (ADE) having a nonlinear type source/sink term with initial and boundary conditions is solved using finite difference method (FDM). The solution of solute concentration is calculated numerically and also presented graphically for conservative and nonconservative cases. The emphasis is given for the stability analysis, which is an important aspect of the proposed mathematical model. The accuracy and efficiency of the proposed method are validated by comparing the results obtained with existing analytical solutions for a conservative system. The novelty of the article is to show the damping nature of the solution profile due to the presence of the nonlinear reaction term for different particular cases in less computational time by using the reliable and efficient finite difference method. © 2019 by ASME.
Keywords
advection-diffusion equation, finite difference, groundwater contamination, nonlinear reaction term, solute transport system
Divisions
MathematicalSciences
Publication Title
Journal of Computational and Nonlinear Dynamics
Volume
14
Issue
4
Publisher
American Society of Mechanical Engineers