STABILITY ANALYSIS OF FINITE-DIFFERENCE SCHEMES FOR 2-DIMENSIONAL ADVECTION DIFFUSION-PROBLEMS

This paper develops a stability analysis of second-order, two- and three-time-level difference schemes for the 2D linear diffusion-convection model problem. The corresponding 1D schemes have been extensively analysed in two previous papers by the same author. Most of these 2D schemes obviously generalize 1D schemes, i.e. their stencil only uses the nearest points and defines 'product difference schemes'; however, the stability results are not always the exact generalization of the 1D stability properties. Moreover, the 1D non-viscous MFTCS scheme may only be generalized if one uses a nine-point scheme. Numerical experiments for different values of the cell Reynolds number allow a comparison to be made between the theoretical and numerical stability limits.