Time-line cubic spline interpolation scheme for solution of advection equation

In this paper a new numerical scheme for solution of pure advection process has been proposed. The proposed scheme is based on backward characteristic s method and it employs cubic spline interpolation method to interpolate th e dependent variable at the foot of concentration characteristic in the tim e-line. For Courant numbers of 1, 1/2, 1/3, 1/4 etc., the computed results are identical to those obtained by the exact solution. For others Courant n umbers also, the proposed scheme performs well. The scheme has been extende d for solution of two-dimensional advection equation. The one-dimensional a dvection-diffusion equation is solved using the proposed scheme for advecti on component and Crank-Nicholson scheme for diffusion component. The comput ed pollutant concentration is comparable to the observed concentration. (C) 2001 Elsevier Science Ltd. All rights reserved.