Analytic Solutions To A 1D Advection-Diffusion Equation And Comparison To Observations

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2021-12

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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.

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MPhil. Mathematics

Keywords

1D Advection-Diffusion, Observations

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