Numerical solution of advection-diffusion equation using finite difference schemes

  • LS Andallah Department of Mathematics, Jahangirnagar University, Savar, Dhaka-1342, Bangladesh
  • MR Khatun Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalgonj-8100
Keywords: Advection-Diffusion Equation; Explicit scheme; Crank-Nicolson scheme; Relative error; Rate of convergence


This paper presents numerical simulation of one-dimensional advection-diffusion equation. We study the analytical solution of advection diffusion equation as an initial value problem in infinite space and realize the qualitative behavior of the solution in terms of advection and diffusion co-efficient. We obtain the numerical solution of this equation by using explicit centered difference scheme and Crank-Nicolson scheme for prescribed initial and boundary data. We implement the numerical scheme by developing a computer programming code and present the stability analysis of Crank-Nicolson scheme for ADE. For the validity test, we perform error estimation of the numerical scheme and presented the numerical features of rate of convergence graphically. The qualitative behavior of the ADE for different choice of the advection and diffusion co-efficient is verified. Finally, we estimate the pollutant in a river at different times and different points by using these numerical scheme.

Bangladesh J. Sci. Ind. Res.55(1), 15-22, 2020


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How to Cite
Andallah, L., & Khatun, M. (2020). Numerical solution of advection-diffusion equation using finite difference schemes. Bangladesh Journal of Scientific and Industrial Research, 55(1), 15-22.