Simple test cases for validating a finite element unstructured grid fecal bacteria transport model
(2010) Applied Mathematical Modelling — Vol. 34, n° 10, p. 3055-3070 (2010)
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- Abstract
- This paper presents analytical test cases for tracer advection-diffusion-decay problems. The test cases are used to validate a finite element, unstructured grid fecal bacteria transport model. The test cases include the following domains: one-dimensional infinitely long river, two-dimensional half plane and two-dimensional infinitely long channel. In this work the bacteria are considered to enter the domain only through point sources. Analytical solutions are derived using either a Dirac delta function or a variable-width Gaussian function as a point source. Both analytical derivations and numerical simulations suggest that the error is maximised at the source. We present formulae for estimating the error caused by replacing a Dirac source with a Gaussian function in the numerical model. Furthermore, numerical simulations suggest that the best approximation for a Dirac source is a Gaussian whose width parameter is one third of the local mesh size. (C) 2010 Elsevier Inc. All rights reserved.
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Kärnä, T., Deleersnijder, E., & Debrauwere, A. (2010). Simple test cases for validating a finite element unstructured grid fecal bacteria transport model. Applied Mathematical Modelling, 34(10), 3055-3070. https://doi.org/10.1016/j.apm.2010.01.012 (Original work published 2010)