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Numerical Solution of Advection Diffusion Equation Using Semi-Discretization Scheme
Department of Mathematics, Jahangirnagar University, Savar, Bangladesh
Department of Mathematics, Patuakhali Science & Technology University, Dumki Upazila, Bangladesh
Department of Mathematics, Jahangirnagar University, Savar, Bangladesh
- 1 Department of Mathematics, Jahangirnagar University, Savar, Bangladesh
- 2 Department of Mathematics, Patuakhali Science & Technology University, Dumki Upazila, Bangladesh
- 3 Department of Mathematics, Jahangirnagar University, Savar, Bangladesh
Applied Mathematics·Volume 12 (2021)·Pages 1236–1247·Published 8 December 2021·DOI10.4236/am.2021.1212079
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Abstract
Numerical diffusion and oscillatory behavior characteristics are averted applying numerical solutions of advection-diffusion equation are themselves immensely sophisticated. In this paper, two numerical methods have been used to solve the advection diffusion equation. We use an explicit finite difference scheme for the advection diffusion equation and semi-discretization on the spatial variable for advection-diffusion equation yields a system of ordinary differential equations solved by Euler’s method. Numerical assessment has been executed with specified initial and boundary conditions, for which the exact solution is known. We compare the solutions of the advection diffusion equation as well as error analysis for both schemes.
KeywordsAdvection Diffusion EquationFinite Difference SchemeSemi-DiscretizationRate of ConvergenceError Analysis
- Mojtabi, M.D.A. (2015) One-Dimensional Linear Advection–Diffusion Equation: Analytical and Finite Element Solutions. Computers and Fluids, Elsevier, 189-195.
- Ahmed, S. (2012) A Numerical Algorithm for Solving Advection-Diffusion Equation with Constant and Variable Coefficients. The Open Numerical Methods Journal, 4, 1-7.
- Dehghan, M. (2005) On the Numerical Solution of the One Dimensional Convection-Diffusion Equation. Hindawi Publishing Corporation, 61-74.
- Appadu, A.R. (2013) Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes. Hindawi Publishing Corporation Journal of Applied Mathematics, 2013, Article ID: 734374.
- Bahar, E. and Gurarslan, G. (2017) Numerical Solution of Advection-Diffusion Equation Using Operator Splitting Method. International Journal of Engineering & Applied Sciences, 9, 76-88.
- Azad, T.M.A.K. and Andallah, L.S. (2016) Stability Analysis of Finite Difference Schemes for an Advection Diffusion Equation. Bangladesh Journal of Scientific Research, 29, 143-151.
- Chen-Charpentier, B.M. and Kojouharov, H.V. (2013) Unconditionally Positivity Presentation Scheme for Advection Diffussion Reaction Equation. Mathematical and Computer Modelling, 57, 1277-1285.
- Willem, H. and Amsterdam, C.W.I. (2000) Numerical Solution of Advection-Diffusion-Reaction Equations. Lecture Notes, Thomas Stieltjes Institute, 2000.
- Olsen-Kettle, D.L. (2011) In Numerical Solution of Partial Differential Equations. https://www.researchgate.net/publication/296672444_Numerical_solution_of_partial_differential_equations_and_code
- Socolofsky, S.A. and Jirka, G.H. (2002) Environmental Fluid Mechanics Part I: Mass Transfer and Diffusion, Germany: Universit at Karlsruhe, 76128-Karlsruhe, Institut fur Hydromechanik. 2nd Edition, Germany, 2002.
- Mathews, J.H. and Kurtis, K. (2004) Fink, Book: Numerical Methods Using Matlab. 4th Edition, Prentice Hall, Hoboken.
- Burden, R.L. and Faires, J.D. (2010) Numerical Analysis. 9th Edition, 20 Channel Center Street Boston, 2010.