Assessment of the unified analytical solution of the steady-state atmospheric diffusion equation for stable conditions

Abstract

In this work, the performance of a unified formal analytical solution for the simulation of atmospheric diffusion problems under stable conditions is evaluated. The eigenquantities required by the formal analytical solution are obtained by solving numerically the associated eigenvalue problem based on a newly developed algorithm capable of being used in high orders and without missing eigenvalues. The performance of the formal analytical solution is evaluated by comparing the converged predicted results against the observed values in the stable runs of the Prairie Grass experiment as well as the simulated results available in the literature. It was found that the developed algorithm was efficient and that the convergence rate depends on the stability condition and the considered parametrizations for wind speed and turbulence. The comparisons among predicted and observed concentrations showed a good agreement and indicate that the considered dispersion formulations are appropriate to simulate dispersion under slightly to moderate atmospheric stable conditions.

Hybrid integral transforms for flow development in ducts partially filled with porous media

“…Direct analytical solution to equation (2.15a-e) is unlikely to be obtainable in terms of known functions. Therefore, the GITT itself was used to solve this eigenvalue problem, even though other methodologies can be found elsewhere [40], making use of a simpler auxiliary problem, in a similar procedure already applied in previous work on the single domain formulation with integral transforms [33][34][35][36][37][38]. In order to employ the GITT procedure in solving equation (2.15a), the classical biharmonic eigenvalue problem was selected in the following form:…”