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A comparison of numerical methods for solving the advection equation 2


, : A comparison of numerical methods for solving the advection equation 2. Atmospheric Environment 19(4): 571-586

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.

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