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Probability and Filtered Density Function Approaches

  • Nicolae Suciu
Chapter
Part of the Geosystems Mathematics book series (GSMA)

Abstract

Beyond mean and variance, traditionally used in stochastic approaches, the full one-point one-time concentration probability density function (PDF) is needed to estimate exceedance probabilities in assessments of groundwater contamination. By solving PDF evolution equations one avoids the cumbersome MC simulations used to obtain statistical inferences. The PDF approach is mainly useful in case of reactive transport: because reaction terms are in a closed form, there is no need to upscale them, as in case of modeling the mean behavior of species concentrations. In a filtered density function (FDF) approach, the PDF is estimated by spatial filtering. PDF/FDF equations will be formulated as Fokker–Planck equations with solutions in the Cartesian product of physical and concentration spaces. Numerical solutions will be obtained by GRW algorithms.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Nicolae Suciu
    • 1
    • 2
  1. 1.Department of MathematicsFriedrich-Alexander University of Erlangen-NürnbergErlangenGermany
  2. 2.Tiberiu Popoviciu Institute of Numerical AnalysisCluj-Napoca Branch of the Romanian AcademyCluj-NapocaRomania

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