CDF solutions of buckley-leverett equation with uncertain parameters

P. Wang, D. M. Tartakovsky, K. D. Jarman, A. M. Tartakovsky

Research output: Contribution to journalArticlepeer-review


The Buckley-Leverett (nonlinear advection) equation is often used to describe twophase flow in porous media. We develop a new probabilistic method to quantify parametric uncertainty in the Buckley-Leverett model. Our approach is based on the concept of a fine-grained cumulative density function (CDF) and provides a full statistical description of the system states. Hence, it enables one to obtain not only average system response but also the probability of rare events, which is critical for risk assessment. We obtain a closed-form, semianalytical solution for the CDF of the state variable (fluid saturation) and test it against the results from Monte Carlo simulations.

Original languageEnglish (US)
Pages (from-to)118-133
Number of pages16
JournalMultiscale Modeling and Simulation
Issue number1
StatePublished - 2013
Externally publishedYes


  • Buckley-Leverett equation
  • Cumulative density function
  • Multiphase flow
  • Oil recovery
  • Probability density function
  • Uncertainty quantification

ASJC Scopus subject areas

  • Chemistry(all)
  • Modeling and Simulation
  • Ecological Modeling
  • Physics and Astronomy(all)
  • Computer Science Applications


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