Analytic Solutions To A 1D Advection-Diffusion Equation And Comparison To Observations
Date
2021-12
Authors
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Publisher
University Of Ghana
Abstract
In this study, we provide two analytic solutions to a one dimensional Advection-
Diffusion Equation (ADE). The ADE is solved using a constant and an exponentially
decaying inlet boundary condition, together with a Dirichlet and Neumann outlet
conditions. The analytic solutions are shown to be simple if a combination of the
initial concentration and the transformed boundary condition result in a non-zero
singularity pole of inverse Laplace transform. The differences between the two analytic
solutions are elucidated. Additionally, to verify the analytic solutions provided,
comparisons are done with a solution to a mathematically related problem in Kim
(2020a) and an error that appears in the paper is corrected.
Moreover, the analytical solutions are compared to some observational data from
the Fena river in the Ashanti region of Ghana and the difference between the two
(analytical and observational) are clarified.
Description
MPhil. Mathematics
Keywords
1D Advection-Diffusion, Observations