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Analytical and Numerical Solutions to a 1D Advection- Diffusion Equation with Exponentially Decaying Inlet Boundary Condition |
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PP: 285-295 |
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doi:10.18576/amis/200119
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Author(s) |
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Joseph K. Ansong,
Ferdinard Obeng-Forson,
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Abstract |
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| This paper presents analytic and numerical solutions to a one-dimensional advection-diffusion equation (ADE) in a bounded domain in which the inlet boundary condition is exponentially decaying. The Laplace transform technique is utilized to obtain the analytic solution and an optimal explicit scheme is used to obtain the numerical solution. One of the analytic solutions, which employs a relatively recent technique, is not continuous at the end points, while the solution derived here is continuous at the ends of the domain. The discrepancy between the two analytic solutions is explained. This paper also explains the correspondence between two different forms of the dimensionless ADE often presented in the literature, making it straightforward for comparisons of analytical and numerical solutions. |
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