An Analysis of Finite Difference and Galerkin Techniques Applied to the Simulation of Advection and Diffusion of Air Pollutants from a Line Source

Runca, E., Melli, P., & Sardei, F. (1981). An Analysis of Finite Difference and Galerkin Techniques Applied to the Simulation of Advection and Diffusion of Air Pollutants from a Line Source. IIASA Collaborative Paper. IIASA, Laxenburg, Austria: CP-81-026

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Abstract

A finite difference and a Galerkin type scheme are compared with reference to a very accurate solution describing time dependent advection and diffusion of air pollutants from a line source in an atmosphere vertically stratified and limited by an inversion layer.

The accurate solution was achieved by applying the finite difference scheme on a very refined grid with a very small time step. Grid size and time step were defined according to stability and accuracy criteria discussed in the text.

It is found that for the problem considered, the two methods can be considered equally accurate. However, the Galerkin method gives larger areas of small errors close to the source, This was assumed to be partly due to the different way the source term is taken into account by the two methods. An improvement of the accuracy of the finite difference scheme was achieved by approximating, at every step, the contribution of the source term by a Gaussian puff moving and diffusing with velocity and diffusivity of the source location, instead of utilizing a stepwise function for the numerical approximation of the delta function representing the source term.

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