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Séminaire Ilya Peshkov

9 novembre 2015

A unified flow theory for viscous fluids

Ilya Peshkov, Open and Experimental Center for Heavy Oil (CHLOE), Pau, France

Jeudi 26 novembre à 12 h 00 , salle Castex Rez de Chaussée

Abstract :

A unified continuum flow theory is discussed. Such a theory covers all the
spectrum of viscous flows ranging from non-equilibrium gas dynamics to the
flows of Newtonian and non-Newtonian fluids. In order to make this
possible, one has to abandon the conventional flow dependent point of view
on the modeling of fluid motion and explicitly describe the very essence of
any fluid flow, i.e. the process of fluid particle (fluid parcel)
rearrangements, in the mathematical model. In turn, in order to describe
the process of fluid particle rearrangement, a temporal microphysics-based
characteristic is introduced. It is an average time which a given fluid
particle spends inside of the « cage » composed of its neighbors before to
escape. The more viscous a fluid is, the bigger this time, i.e. the longer
fluid parcels stay in contact with each other. A remarkable feature of the
proposed approach is that it is free of the conventional but
phenomenological viscosity coefficient.

The model is formulated as a system of first order PDEs of hyperbolic type
with stiff algebraic source terms. It is therefore suitable for modeling of
wave propagation phenomena and to be resolved by advanced high accuracy
Godunov-type numerical methods. Potential applications of the model to
turbulence modeling (boundary layer), combustion, sound propagation, and
multi-fluid flow modeling are discussed. Eventually, results of the
extensive validation of the proposed hyperbolic model against the classical
Navier-Stokes-Fourier theory are presented. For this comparison, several
standard benchmark test problems (e.g. First Stokes problem, Blasius
boundary layer, flow around circular cylinder, compressible shear layer,
viscous shock, etc.) were solved with a high order Godunov-type numerical

This is a joined work with Evgeniy Romesnki from the Sobolev Institute of
Mathematics, Novosibirsk, Russia and with Michael Dumbser and Olindo
Zanotti from University of Trento, Italy.

( séminaire OTE/Interface)