Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation
We present a cumulative density function (CDF) method for the probabilistic analysis of $$d$$-dimensional advection-dominated reactive transport in heterogeneous media. We employ a probabilistic approach in which epistemic uncertainty on the spatial heterogeneity of Darcy-scale transport coefficients is modeled in terms of random fields with given correlation structures. Our proposed CDF method employs a modified Large-Eddy-Diffusivity (LED) approach to close and localize the nonlocal equations governing the one-point PDF and CDF of the concentration field, resulting in a $(d + 1)$ dimensional PDE. Compared to the classsical LED localization, the proposed modified LED localization explicitly accounts for the mean-field advective dynamics over the phase space of the PDF and CDF. To illustrate the accuracy of the proposed closure, we apply our CDF method to one-dimensional single-species reactive transport with uncertain, heterogeneous advection velocities and reaction rates modeled as random fields.
- Research Organization:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC05-76RL01830
- OSTI ID:
- 1427894
- Report Number(s):
- PNNL-SA-123069; KJ0401000
- Journal Information:
- SIAM/ASA Journal on Uncertainty Quantification, Vol. 6, Issue 1; ISSN 2166-2525
- Publisher:
- SIAM
- Country of Publication:
- United States
- Language:
- English
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