Concentrations of chemical species transported in random environments need to be statistically characterized by probability density functions (PDF). Solutions to evolution equations for the one-point one-time PDF are usually based on systems of computational particles described by Ito equations.

We establish consistency conditions relating the concentration statistics to that of the Ito process and the solution of its associated Fokker-Planck equation to that of the PDF equation. In this frame, we propose a new numerical method which approximates PDFs by particle densities obtained with a global random walk (GRW) algorithm.

The GRW-PDF approach is illustrated for a problem of contaminant transport in groundwater.


N. Suciu
Tiberiu Popoviciu Institute of Numerical Analysis

L. Schüler

S. Attinger

C. Vamoș
Tiberiu Popoviciu Institute of Numerical Analysis

P. Knabner


PDF methods; mixing; random walk; porous media

Cite this paper as:

N. Suciu, L. Schüler, S. Attinger, C. Vamoş, P. Knabner, Consistency issues in PDF methods, Analele Stiint. Univ. Ovidius C.- Mat., , 23 (2015) 3, 187-208,
doi: 10.1515/auom-2015-0055




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