Author(s): I. Haltas

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Keywords: Stochastic transport equation; Macrodispersion coefficient; Lagrangiantrajectory

Abstract: One of the methodologies used to up-scale the transport equation to larger scales is the cumulant expansion method combined with the calculus for the time-ordered exponential and calculus for Lie operator. When the laboratory scale transport equation is scaled up to the larger scales using the cumulant expansion method a new dispersion coefficient emerges in the dispersive term of the transport equation in addition to the molecular dispersion coefficient. This velocity driven dispersion term is also called as “macrodispersion coefficient”. The macrodispersion coefficient is the integral function of the time ordered covariance of velocities, and explicitly depends on the distance from the source and on the time elapsed from the beginning of the simulation. Especially for the unsteady spatially non-stationary, non-uniform flow field, the macrodispersion coefficient is generally calculated after some approximations. Here we develop an approach to numerically calculate the macrodispersion coefficient for the most general case and with the minimum approximation possible by transforming the coefficient into a more explicit form. This approach can fill the gap between the stochastic theory and the numerical applications.

DOI:

Year: 2009