A COMPARISON OF NUMERICAL-METHODS FOR SOLVING THE ADVECTION EQUATION-III

As a sequel to the previous studies (Atmospheric Environment 17, 11-24, 1983; Atmospheric Environment 19, 571-586, 1985), four algorithms and their variations for solving the advection equation were compared in terms of their accuracy, speed and storage requirements. The algorithms are the Smolarkiewicz methods, the higher-degree-weighting Petrov-Galerkin method, the Taylor-Galerkin method and the accurate-space-derivative method. The test problem was the rotation of a cosine-shaped hill of concentration in a two-dimensional circular velocity field at three or four different time increments. The Smolarkiewicz methods were found to be highly diffusive. The higher-degree-weighting Petrov-Galerkin method is comparable to, in accuracy and storage, but more time consuming than the chapeau-function method coupled with the Crank-Nicolson scheme. The forward-Euler Taylor-Galerkin method is even superior to the forward Euler chapeau-function method with balancing diffusion-a method recommended previously, because it has a greater range of applicable Courant number. The accurate-space-derivative method is extremely accurate but time consuming. A simple approach to remove the requirement for periodic boundary conditions was proposed which should enhance the attractiveness of the method for air quality modeling.