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Transported Probability and Mass Density Function (PDF/MDF) Methods for Uncertainty Assessment and Multi-Scale Problems

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Numerical Analysis of Multiscale Problems

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 83))

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Abstract

For the simulation of fluid flows, probability and mass density function (PDF/MDF) methods have advantageous properties compared to moment-based approaches or purely deterministic methods and are applicable in different fields. For example, PDF and MDF methods are used for the quantification of uncertainty in turbulent or subsurface flows, and the simulation of multi-phase flows or rarefied fluids. In this chapter, differences of these methods compared to other solution techniques are discussed and illustrated by application examples. Moreover, the theory behind PDF and MDF methods is outlined. Finally, a PDF method for uncertainty quantification in subsurface flows and an MDF method for the simulation of rarefied fluid flows are discussed in more details.

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Authors and Affiliations

  1. Institute of Fluid Dynamics, ETH Zurich, Zurich, Switzerland

    Patrick Jenny & Daniel W. Meyer

Authors
  1. Patrick Jenny
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  2. Daniel W. Meyer
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Corresponding author

Correspondence to Patrick Jenny .

Editor information

Editors and Affiliations

  1. , Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom

    Ivan G. Graham

  2. , Applied & Computational Mathematics, California Institute of Technology, Pasadena, 91125, California, USA

    Thomas Y. Hou

  3. , Department of Mathematics, University of Sussex, Brighton, BN1 9QH, United Kingdom

    Omar Lakkis

  4. , Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom

    Robert Scheichl

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Jenny, P., Meyer, D.W. (2012). Transported Probability and Mass Density Function (PDF/MDF) Methods for Uncertainty Assessment and Multi-Scale Problems. In: Graham, I., Hou, T., Lakkis, O., Scheichl, R. (eds) Numerical Analysis of Multiscale Problems. Lecture Notes in Computational Science and Engineering, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22061-6_2

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