Transported probability and mass density function (PDF/MDF) methods for uncertainty assessment and multi-scale problems

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.