Two-Dimensional scheme for convection-diffusion with linear production
Journal
Numerical Heat Transfer, Part B: Fundamentals
Journal Volume
37
Journal Issue
3
Pages
365-377
Date Issued
2000
Author(s)
Abstract
In this article we consider the scalar transport governed by the convection-diffusion equation with linear production in two dimensions. The underlying idea in the development of a steady discretization scheme is to incorporate the analytical solution, obtained within a one-dimensional context, into the formulation. The method adopted here features exponential character in the weighted coefficients of the matrix equation, which generates a scheme with high accuracy. The analysis is followed by extending this discretization scheme to solve the convection-diffusion-production equation with a source term. In this article we present an analytical validation study of the method applied to two classes of model equations. Having verified that the method applies equally well for a transport scalar in either case with constant or variable flow velocity, we employ the one-dimensional scheme in the predictor and corrector steps to obtain the two-dimensional solution in an alternating direction-implicit fashion. The result obtained for the test considered in this article follows the trend of analytic data. © 2000, Taylor & Francis Group, LLC. All rights reserved.
Type
journal article