Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation

Journal Article · Mon Jan 01 04:00:00 EST 2018 · SIAM/ASA Journal on Uncertainty Quantification

DOI:https://doi.org/10.1137/16M1109163· OSTI ID:1427894

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

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 Laboratory (PNNL), Richland, WA (US)
• 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, Journal Name: SIAM/ASA Journal on Uncertainty Quantification Journal Issue: 1 Vol. 6; ISSN 2166-2525
• Publisher: SIAM
• Country of Publication: United States
• Language: English

Related Subjects

Contaminant transport
LED closures
PDF methods
advection-reaction equation
stochastic advection-reaction equations
stochastic partial differential equations