Abstract
This paper presents results of the test of methods for numerical inversion of the Laplace Transform for solving the one-dimensional advection-diffusion equation, which describes solute transport processes, focusing on the contaminant transport in a porous medium. The performance of Stehfest and Power Series Expansion methods is analyzed, for diffusion-dominated and advection-dominated transport problems under linear flow condition. Numerical results are compared to the analytical solution by means of the absolute error. Based on these results, we concluded that both methods, Stehfest and Power Series Expansion, are recommended only for diffusion-dominated cases.
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