A Numerical Algorithm for Solving Advection-Diffusion Equation with Constant and Variable Coefficients

Abstract

See, stats, and : http : / / www . researchgate . net / publication / 258687525 A - Diffusion Coefficients ARTICLE DOI : 10 . 2174 / 1876389801204010001 CITATIONS 2 DOWNLOAD 1 VIEWS 44 1 : S . G . Ahmed Zagazig 68 SEE Available : S . G . Ahmed Retrieved : 01 The Open Numerical Methods Journal , 2011 , 3 , 59 - 65 59 1876 - 3898 / 11 Abstarct : Advection - diffusion equation with constant and variable coefficients has a wide range of practical and industrial applications . Due to the importance of advection - diffusion equation the present paper , solves and analyzes these problems using a new finite difference equation as well as a numerical scheme . The developed scheme is based on a mathematical combination between Siemieniuch and Gradwell approximation for time and Dehghan ' s approximation for spatial variable . In the proposed scheme a special discretization for the spatial variable is made in such away that when applying the finite difference equation at any time level (j + 1) two nodes from both ends of the domain are left . After that the unknowns at the two nodes adjacent to the boundaries are obtained from the interpolation technique . The results are compared with some available analytical solutions and show a good agreement .