HIGH-ORDER DIFFERENCE-SCHEMES FOR UNSTEADY ONE-DIMENSIONAL DIFFUSION CONVECTION PROBLEMS

For unsteady 1 D diffusion-convection problems, this paper develops an extensive analysis of two-level three-point finite difference schemes of order 2 in time and 4 in space. This general class of FDS includes several schemes independently proposed by different authors. One main objective is the identification of difference schemes yielding satisfactory numerical results for strongly convective problems (i.e., when the cell Reynolds number alpha=lambdah/2 is greater than unity). The stability and the oscillatory behaviour of the schemes are carefully studied and the analyses are completed by some numerical experiments. We outline some key points: (i) the great difficulty to obtain accurate numerical results for large values of cr, (ii) the possibility of virtually optimum schemes is essentially theoretical and requires, in practice, careful experiments; (iii) for strongly convective problems, some second-order explicit schemes are almost as efficient (and less costly) than implicit fourth-order schemes. (C) 1994 Academic Press, Inc.