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

A non-oscillatory numerical scheme based on a general solution of unsteady advection–diffusion equations is presented. A general solution for initial value problems of linear two-dimensional unsteady advection–diffusion equations is obtained using the spectral method. The resulting numerical scheme is explicit with respect to time, and fulfills the Patankarʹs positive coefficients condition for any advection velocity, diffusivity and temporal mesh increment. Hence the present scheme guarantees solutions free from numerical oscillations for unsteady advection–diffusion equations. Numerical experiments show good solutions.