APPLICATION OF THE LOCALLY ANALYTIC DIFFERENCING SCHEME TO SOME TEST PROBLEMS FOR THE CONVECTION-DIFFUSION EQUATION

Abstract

The locally analytic differencing (LOAD) scheme of Wong and Raithby is applied to solve a variety of one- and two-dimensional convection-diffusion problems. The results are compared with those obtained with the exponential differencing (ED) scheme of Spalding. The LOAD scheme is significantly more accurate; at grid Peclet numbers ≥ 5 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 two-dimensional 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 computer programs based on the ED scheme can be easily modified to incorporate the LOAD scheme.