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

Abstract

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.

Authors:
;
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1427894
Report Number(s):
PNNL-SA-123069
Journal ID: ISSN 2166-2525; KJ0401000
DOE Contract Number:
AC05-76RL01830
Resource Type:
Journal Article
Resource Relation:
Journal Name: SIAM/ASA Journal on Uncertainty Quantification; Journal Volume: 6; Journal Issue: 1
Country of Publication:
United States
Language:
English
Subject:
Contaminant transport; advection-reaction equation; stochastic partial differential equations; PDF methods; LED closures; stochastic advection-reaction equations

Citation Formats

Barajas-Solano, David A., and Tartakovsky, Alexandre M. Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation. United States: N. p., 2018. Web. doi:10.1137/16M1109163.
Barajas-Solano, David A., & Tartakovsky, Alexandre M. Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation. United States. doi:10.1137/16M1109163.
Barajas-Solano, David A., and Tartakovsky, Alexandre M. Mon . "Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation". United States. doi:10.1137/16M1109163.
@article{osti_1427894,
title = {Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation},
author = {Barajas-Solano, David A. and Tartakovsky, Alexandre M.},
abstractNote = {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.},
doi = {10.1137/16M1109163},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
number = 1,
volume = 6,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2018},
month = {Mon Jan 01 00:00:00 EST 2018}
}