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A comparison of three Eulerian numerical methods for fractional-order transport models

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Abstract

Tracer transport in complex systems like turbulent flows or heterogeneous porous media is now more and more regarded as a non-local process that can hardly be represented by second-order diffusion models. In this work, we consider diffusion models that assume that tracer particles follow a heavy-tail Lévy distribution, which allows for large displacements. We show that such an assumption leads to a fractional-order diffusion operator in the governing equation for tracer concentration. A comparison of three Eulerian numerical methods to discretize that equation is then performed. These consist of the finite difference, finite element and spectral element methods. We suggest that non-local methods, like the spectral element method, are better suited to transport models with fractional-order diffusion operators.

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Authors and Affiliations

  1. Department of Environmental Sciences and Land Use Planning, Université Catholique de Louvain, Place Croix du Sud 2/16, 1348, Louvain-la-Neuve, Belgium

    Emmanuel Hanert

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  1. Emmanuel Hanert
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Correspondence to Emmanuel Hanert.

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Hanert, E. A comparison of three Eulerian numerical methods for fractional-order transport models. Environ Fluid Mech 10, 7–20 (2010). https://doi.org/10.1007/s10652-009-9145-4

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  • DOI: https://doi.org/10.1007/s10652-009-9145-4

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