A comparison of numerical methods for solving the advection equation

Six algorithms for solving the advection equation have been compared as to their accuracy, speed and storage requirements, the purpose being to determine the suitability of the algorithms for use in photochemical grid models. The algorithms tested are a flux-correction method, a multidimensional fluxcorrection method, an orthogonal-collocation method, a second-moment method, a pseudospectral method and a chapeau-function method. For some of these, more than one variant of the method has been examined. Also, some improvements are suggested in the second-moment method. The test problem was the rotation of a hill of concentration in a two-dimensional, circular velocity field, and the methods were tested at three or four time steps (Courant numbers). The flux-correction and orthogonal-collocation methods are the least accurate and would not be good choices for photochemical models. The pseudospectral method is the most accurate, but it and the second-moment method require the longest execution time. The chapeau-function and multidimensional flux-correction methods appear the most appropriate for photochemical grid models.