Solution of weighted finite difference techniques with the advection-diffusion equation using spreadsheets

Abstract

This study proposes one-dimensional advection - diffusion equation (ADE) with finite differences method (FDM) using spreadsheet simulation (ADESS). By changing only the values of weighted parameter with ADESS model, solutions are obtained for the FTSC, Upwind and Lax-Wendroff schemes. Two examples which, have the numerical and analytical solutions in literature, are solved in order to test the proposed model. Both examples are solved for three schemes. It has been determined that the Lax - Wendroff scheme is in good agreement with the analytical solution; however the results of FTSC is lower than the analytical solution and the Upwind scheme is higher than the analytical solution. Moreover, it has been obtained that the model accuracy is higher than that of the other models in literature, when the results of the ADESS model are compared with the numerical solutions. Results showed that by changing the input parameters in the ADESS model, the results of the model may easily be examined graphically. © 2008 Wiley Periodicals, Inc.