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

作者：Hanert Emmanuel^*

来源：Environmental Fluid Mechanics, 2010, 10(1-2): 7-20.

DOI：10.1007/s10652-009-9145-4

• Tracer transport
• Fractional calculus
• Levy distributions
• Spectral element method

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 L,vy 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.

• 出版日期2010-4