Probability and cumulative density function methods for the stochastic advection-reaction equation

David A. Barajas-Solano, Alexandre M. Tartakovsky

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)180-212
Number of pages33
JournalSIAM-ASA Journal on Uncertainty Quantification
Issue number1
StatePublished - 2018
Externally publishedYes


  • Cumulative density function method
  • LED closure
  • Probability density function method
  • Reactive transport
  • Stochastic advection-reaction equation
  • Uncertainty quantification

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'Probability and cumulative density function methods for the stochastic advection-reaction equation'. Together they form a unique fingerprint.

Cite this