M. Cassol, S. Wortmann, M.T. Vilhena, H.F. de Campos Velho (2007): Analytic Two-Dimensional Transient Atmospheric Pollutant Dispersion Simulation by Double GITT, Integral Methods in Science and Engineering (Edited by C. Constanda and S. Potapenko), Birkhauser, Boston, Chapter 5, pp. 37-46, ISBN 978-0-8176-4670-7, 304 p.

Abstract: An analytical solution of a transient two-dimensional atmospheric pollutant dispersion problem is presented. This solution is obtained by double GITT (Generalized Integral Transform Technique) applied for both space variables, and using the Laplace transform for time integration. The problem is mathematically represented by a transient diffusive-advective equation, in which the turbulent component (Reynolds average on the deviations) is parameterized considering a first order closure scheme, based on the Taylor statistical theory on turbulence.

The standard GITT employs a series expansion, and the associated Sturm-Liouville problem. From orthogonality property of the eigen-functions, the problem is transformed into a system of ordinary differential equations (ODE). The ODE system is solved by Laplace transform.

The use of the GITT for both space variables, and taking into acount an user prescribed accuracy, allows an automatic control of the truncation order of the expansion – another criteria for determining the number of terms in the truncated series is time processing. Actually, the number of the terms for the truncated series defines the order of the system matrix.

Numerical results are compared with experimental data obtained from the Copenhagen experiment (1978-79), as well as other methods presented in the literature.