A nonoscillatory numerical scheme based on a general solution of 2-D unsteady advection–di usion equations

A non-oscillatory numerical scheme based on a general solution of unsteady advection–di usion equations is presented. A general solution for initial value problems of linear two-dimensional unsteady advection–di usion equations is obtained using the spectral method. The resulting numerical scheme is explicit with respect to time, and ful lls the Patankar’s positive coe cients condition for any advection velocity, di usivity and temporal mesh increment. Hence the present scheme guarantees solutions free from numerical oscillations for unsteady advection–di usion equations. Numerical experiments show good solutions. c © 1999 Elsevier Science B.V. All rights reserved. MSC: Numerical analysis category 65; Numerical method