scholarly journals A Two-Dimensional Solution of the Advection–Diffusion Equation with Dry Deposition to the Ground

2008 ◽  
Vol 47 (8) ◽  
pp. 2096-2104 ◽  
Author(s):  
Tiziano Tirabassi ◽  
Daniela Buske ◽  
Davidson M. Moreira ◽  
Marco T. Vilhena
Keyword(s):  
Diffusion Equation ◽  
Dry Deposition ◽  
Exact Analytical Solution ◽  
Turbulent Dispersion ◽  
Diffusion Experiment ◽  
Dimensional Solution ◽  
Atmospheric Diffusion ◽  
Eddy Diffusivities ◽  
Advection Diffusion Equation ◽  
Nonzero Flux

Abstract A mathematical scheme is developed to simulate the vertical turbulent dispersion of air pollution that is absorbed or deposited to the ground. The scheme is an exact analytical solution of the atmospheric diffusion equation, without any restriction to the vertical profile of wind speed and eddy diffusivities, and taking into account the dry deposition by a boundary condition of a nonzero flux to the ground. The performances of the solution, with a proper parameterization of the vertical profiles of the wind and eddy diffusivities, were evaluated against the dataset from the Hanford (Washington) diffusion experiment, in which two tracers (one depositing and one nondepositing) were released simultaneously. In addition, the solution derived in this work is compared with four different models, with deposition at the ground, found in the literature.

scholarly journals Different Numerical Inversion Algorithms of the Laplace Transform for the Solution of the Advection-Diffusion Equation with Non-local Closure in Air Pollution Modeling

2018 ◽  
Vol 19 (1) ◽  
pp. 43
Author(s):  
Camila Pinto Da Costa ◽  
Karine Rui ◽  
Léslie Darien Pérez-Fernández
Keyword(s):  
Diffusion Equation ◽  
Laplace Transform ◽  
Inverse Laplace Transform ◽  
Numerical Inversion ◽  
Dimensional Solution ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Local Closure ◽  
Non Local ◽  
Pollution Modeling

In this paper, a three-dimensional solution of the steady-state advection-diffusion equation is obtained applying the Generalized Integral Advection Diffusion Multilayer Technique (GIADMT), considering non-local closure for turbulent flow. Two different parameterizations were considering for the countergradient term and different methods of numerical inversion for inverse Laplace transform. The results were compared with the experimental data of Copenhagen experiment by an evaluation of statistical indices to analyse the solution of the equation through the methods of numerical inversion. Differents parameterizations for the vertical turbulent eddy diffusivity and wind profile were utilized. The results show a good agreement with the experiment and the methods of numerical inversion for inverse Laplace transform show same efficacy.  

scholarly journals A Numerical Solution to Fractional Diffusion Equation for Force-Free Case

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
O. Tasbozan ◽  
A. Esen ◽  
N. M. Yagmurlu ◽  
Y. Ucar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Exact Analytical Solution ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Spline Functions ◽  
B Spline ◽  
Numerical Examples ◽  
Free Case

A collocation finite element method for solving fractional diffusion equation for force-free case is considered. In this paper, we develop an approximation method based on collocation finite elements by cubic B-spline functions to solve fractional diffusion equation for force-free case formulated with Riemann-Liouville operator. Some numerical examples of interest are provided to show the accuracy of the method. A comparison between exact analytical solution and a numerical one has been made.

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