Application of the locally analytic differencing scheme to some test problems for the convection-diffusion equation

The locally analytic differencing (LOAD) scheme of Wong and Raithby (1979) is applied to solve a variety of 1D and 2D convection-diffusion problems. The results are compared with those obtained with the exponential differencing (ED) scheme of Spalding (1972). The LOAD scheme is significantly more accurate at grid Peclet numbers 5 or greater, the errors in the solution obtained with the LOAD scheme can be one to two orders of magnitude less than the errors obtained with the ED scheme on the same grid. For a prescribed accuracy, the LOAD scheme requires far fewer grid points (computer memory) and much less computer time (cost). For 2D problems, the cross-wind (false) diffusion in the LOAD scheme is much less than in the ED scheme. The LOAD scheme is easy to implement: the discretization coefficients remain the same as in the ED scheme, and only the term corresponding to the source term receives some additional correction. This correction term is presented. Existing compter programs based on the ED scheme can be easily modified to incorporate the LOAD scheme. 18 references