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

ABSTRACT In this paper, a three-dimensional solution of the steady-state dvection-diffusion equation is obtained applying the so-called generalized integral advection-diffusion multilayer technique, considered non-local closure for turbulent flow. Two different parametrizations were considered for the countergradient coefficient and three 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 indexes to analyze the solution of the equation through the methods of numerical inversion. Different parametrizations 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 almost the same accuracy.