A comparison of numerical methods applied to non‐linear adsorption columns

Abstract

Abstract Eight numerical schemes (first‐order upstream finite difference, MacCormack, explicit Taylor–Galerkin, random choice, flux‐corrected transport, ENO, TVD, and Euler–Lagrange methods) are compared on the basis of their computational efficiency for one‐dimensional non‐linear convection–diffusion problems. For the ideal chromatographic equation for which an exact solution exists, errors plotted against computational times show that the best methods are the random choice, Euler–Lagrange and flux‐corrected MacCormack methods. Even when significant diffusion is added to the model, steep gradients are possible because of non‐linearities. In such an instance, the random choice and flux‐corrected transport methods give the best performance. One can now tackle more complicated problems and refer to this comparative study in order to choose an adequate numerical method which will provide sufficiently accurate results at a reasonable cost.