integral laplace transform
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2020 ◽  
Vol 42 ◽  
pp. e11
Author(s):  
Camila Fávero ◽  
Glênio Aguiar Gonçalves ◽  
Daniela Buske ◽  
Régis Sperotto de Quadros ◽  
Viliam Cardoso da Silveira

This work presents an analytical solution for the transient three-dimensional advection-diffusion equation. This solution, obtained from a combination of the variable separation method and GILTT (Generalized Integral Laplace Transform Technique) is used to simulate the pollutant dispersion in the atmosphere. The new solution has the advantage of not requiring a numerical inversion performed in the temporal variable in works using only GILTT technique. The model was tested in low wind condition, with diffusion in transverse and longitudinal directions and stochastic speeds. Simulations were performed for the INEL experiment. The analytical character of the model makes it simple, which represents advantages in its development and implementation, as well as in the computational cost for execution.


2020 ◽  
Vol 42 ◽  
pp. e28
Author(s):  
Viliam Cardoso da Silveira ◽  
Daniela Buske ◽  
Régis Sperotto de Quadros ◽  
Glênio Aguiar Gonçalves ◽  
Guilherme Jahnecke Weymar

The aim of this work is to present a pollutants dispersion transient model in low wind conditions to simulate the behavior of the pollutants plume in the atmosphere, considering in the model the u e v horizontal wind components simulated by the LES-PALM model. The dispersion model is based in the advection-diffusion equation and represent by this methodology the wind meandering phenomenon. The Generalized Integral Laplace Transform Technique in three dimensions (3D- GILTT) solves the transient advection-diffusion equation. The data utilized to initialize the simulations are data of the low wind INEL (Idaho National Engineering Laboratory) experiment accomplished in EUA. The results show that the dispersion model reproduces the wind meandering phenomenon, in other words, the autocorrelation function of the concentration simulated over an hour presents the negative lobule, similarly to observed lobules in the u and v wind components. Therefore, the model simulates the pollutants plume in a satisfactory way and can be used to air quality regulatory applications in low wind and wind meandering conditions.


2014 ◽  
Vol 1040 ◽  
pp. 633-637 ◽  
Author(s):  
Leonid A. Igumnov ◽  
Ivan Markov ◽  
Yan Yu. Rataushko

The numerical modeling problem is solved using a direct formulation of the boundary element method. The integral Laplace transform is used, as well as time-step methods of its numerical inversion. Matrices of fundamental and singular solutions are computed with the help of a combined direct-interpolation approach. The computational results obtained are compared with the results of other authors.


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