A COMPARISON OF NUMERICAL-METHODS FOR SOLVING THE ADVECTION EQUATION .2.

Five algorithms and their variations for solving the advection equation were compared in terms of their accuracy, speed and storage requirements. The algorithms are a chapeau-function method including mass-lumping, Forester''s method, a method called Filtering Remedy and Methodology, a Hermite-cubic orthogonal-collocation method and a quadratic function method. The test problem was the rotation of a cosine-shaped hill of concentration in a 2-dimensional circular velocity field at 3 different time increments (or angular velocities). The forward-Euler time-integration scheme coupled with a balancing diffusion term was extensively used and was found to be superior to the Crank-Nicolson scheme in accuracy for the methods considered. Together with the results of part I (Atmospheric Environment 1983), Forester''s method applied to the chapeau-function solution appears to be the best method for solving the advention equation in air-pollution modeling. The combined method retains the peak value well, has high accuracy with little or no negative concentration region, and requires short execution time and minimal memory storage.