Computation of some unsteady flows over porous semi-infinite flat surface

Abstract

Finite difference solutions of an one-dimensional unsteady convection-diffusion problem on semi-infinite interval is considered. An artificial boundary is introduced to make the computational domain finite. On the artificial boundary an exact boundary condition is applied to reduce the original problem to an initial-boundary value problem. A finite difference scheme is derived by the method of reduction of order. It is proved that the finite difference scheme is convergent in energy norm of order 2 in space and order 3/2 in time. Numerical experiments confirm the theoretical results and show the efficiency of the constructed scheme. © Springer-Verlag Berlin Heidelberg 2006.