Abstract
A formal statistical discussion of the origins of the random walk and its relation to the classic advection-dispersion equation is given. At issue is the common use of Gaussian distributed steps in producing the desired dispersive effects. Shown are alternative solutions to the basic Langevin equation describing mass displacements based on non-Gaussian, white increments. In particular, the results reveal that uniform or symmetric-triangular steps can be employed without loss of generality in accuracy of the solution (over all Peclet numbers) and may yield significant savings in the computational generation of the random deviates required in the Monte Carlo procedures of the random walk method.
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Hathhorn, W.E. A second look at the method of random walks. Stochastic Hydrol Hydraul 10, 319–329 (1996). https://doi.org/10.1007/BF01581872
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DOI: https://doi.org/10.1007/BF01581872