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One-dimensional linear advection–diffusion equation: Analytical and finite element solutions

Mojtabi, Abdelkader and Deville, Michel One-dimensional linear advection–diffusion equation: Analytical and finite element solutions. (2015) Computers and Fluids, 107. 189-195. ISSN 0045-7930

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Official URL: http://dx.doi.org/10.1016/j.compfluid.2014.11.006


In this paper, a time dependent one-dimensional linear advection–diffusion equation with Dirichlet homogeneous boundary conditions and an initial sine function is solved analytically by separation of variables and numerically by the finite element method. It is observed that when the advection becomes dominant, the analytical solution becomes ill-behaved and harder to evaluate. Therefore another approach is designed where the solution is decomposed in a simple wave solution and a viscous perturbation. It is shown that an exponential layer builds up close to the downstream boundary. Discussion and comparison of both solutions are carried out extensively offering the numericist a new test model for the numerical integration of the Navier–Stokes equation

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at : http://www.sciencedirect.com/science/article/pii/S0045793014004289
HAL Id:hal-01331727
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole Polytechnique Fédérale de Lausanne - EPFL (SWITZERLAND)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Laboratory name:
Deposited On:14 Jun 2016 12:15

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