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 characteristics method and it employs cubic spline interpolation method to interpolate the dependent variable at the foot of concentration characteristic in the time-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 numbers also, the proposed scheme performs well. The scheme has been extended for solution of two-dimensional advection equation. The one-dimensional advection-diffusion equation is solved using the proposed scheme for advection component and Crank-Nicholson scheme for diffusion component. The computed pollutant concentration is comparable to the observed concentration. (C) 2001 Elsevier Science Ltd. All rights reserved.