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On the use of random walk models with spatially variable diffusivity


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Hunter, JA, Craig, PD and Phillips, HE 1993 , 'On the use of random walk models with spatially variable diffusivity' , Journal of Computational Physics, vol. 106, no. 2 , pp. 366-376 , doi: 10.1016/S0021-9991(83)71114-9.

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The random walk technique is commonly used to model diffusion in
the environment. For a constant diffusivity K and model time-step dt.
the random step should be chosen from a distribution with variance
2Kdt. However, if K varies spatially, this choice of step leads to the
accumulation of particles in regions of low diffusivity. This problem
may be overcome either by the incorporation of an apparent advection
velocity, or by transforming to a coordinate system in which the
diffusivity is constant. The latter technique requires no immediate
approximations, is applicable to any reasonable diffusivity field and is
therefore the preferred approach. In this case, as with constant K, the
random step should be chosen from a normal distribution, for reasons
of both theoretical accuracy and computational efficiency. Three
important aspects of model design are discussed: the selection of the
random number generator, the time step and the total number of

Item Type: Article
Authors/Creators:Hunter, JA and Craig, PD and Phillips, HE
Keywords: diffusivity eddy random walk
Journal or Publication Title: Journal of Computational Physics
ISSN: 0021-9991
DOI / ID Number: 10.1016/S0021-9991(83)71114-9
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