<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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 Itô equations. We establish consistency conditions relating the concentration statistics to that of the Itô process and the solution of its associated Fokker-Planck equation to that of the PDF equation. In this frame, we use a recently proposed 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.</p></abstract>

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 Itô equations. We establish consistency conditions relating the concentration statistics to that of the Itô process and the solution of its associated Fokker-Planck equation to that of the PDF equation. In this frame, we use a recently proposed 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.

Consistency issues in PDF methods

Mathematics Department, Friedrich-Alexander University Erlangen-Nuremberg, Cauerstr. 11, 91058 Erlangen, Germany

Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Str. Fantanele 57, 400320 Cluj-Napoca,

Faculty for Chemistry and Earth sciences, University of Jena, Burgweg 11, 07749 Jena, Germany

Department Computational Hydrosystems, UFZ Centre for Environmental Research, Permoserstraße 15 04318 Leipzig,

Mathematics Department, Friedrich-Alexander University Erlangen-Nuremberg, Cauerstr. 11, 91058 Erlangen,

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Consistency issues in PDF methods"}

Concentrations of chemical species transported in random environments need to be statistically characterized by probability density functions (PDF). Solutions...

Consistency issues in PDF methods

Publié en ligne: 22 avr. 2017

Pages: 187 - 208

Reçu: 01 déc. 2014

Accepté: 01 févr. 2015

DOI: https://doi.org/10.1515/auom-2015-0055

Mots clés
PDF methods, mixing, random walk, porous media

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Consistency issues in PDF methods

Publié en ligne: 22 avr. 2017

Pages: 187 - 208

Reçu: 01 déc. 2014

Accepté: 01 févr. 2015

DOI: https://doi.org/10.1515/auom-2015-0055

Mots clésPDF methods, mixing, random walk, porous media

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
PDF methods, mixing, random walk, porous media