AN ADAPTIVE PSEUDOSPECTRAL SOLUTION FOR ATMOSPHERIC DIFFUSION-PROBLEMS

An adaptive pseudospectral method is applied to the solution of advect ion-diffusion problems arising from the turbulent dispersion of pollut ants in the atmosphere. For a localized source term specified by a fun ction with steep gradients or discontinuities, the authors show that t he associated rapidly varying functions can be smoothed out and gradua lly varied by using polynomial approximations in a transformed coordin ate system. The solutions obtained from the advection-diffusion equati on still preserve spectral accuracy, and the usual spectral oscillatio n is avoided. The authors solve both one- and two-dimensional time-dep endent advection-diffusion equations associated with both small and re latively large diffusion coefficients. The numerical solutions are com pared with exact solutions. The results show that the adaptive pseudos pectral solution for the advection-diffusion problems is very effectiv e and accurate for an imposed shock function. No numerical diffusion i s introduced. This method does not need any special treatment of nonpe riodic boundary conditions, which is otherwise generally needed in spe ctral methods. The stability of the algorithm is discussed. Examples w ith Chebyshev nodes and uniformly spaced collocation points are given.