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Multiscale modelling of complex fluids: A mathematical initiation.

Claude Le Bris 1 Tony Lelièvre 1
1 MICMAC - Methods and engineering of multiscale computing from atom to continuum
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : We present a general introduction to the multiscale modelling and simulation of complex fluids. The perspective is mathematical. The level is elementary. For illustration purposes, we choose the context of incompressible flows of infinitely dilute solutions of flexible polymers, only briefly mentioning some other types of complex fluids. We describe the modelling steps, compare the multiscale approach and the purely macroscopic, more traditional, approach. We also introduce the reader with the appropriate mathematical and numerical tools. A complete set of codes for the numerical simulation is provided, in the simple situation of a Couette flow. This serves as a test-bed for the numerical strategies described in a more general context throughout the text. A dedicated section of our article addresses the mathematical challenges on the front of research.
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https://hal.inria.fr/inria-00165171
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Submitted on : Friday, August 31, 2007 - 12:07:09 PM
Last modification on : Friday, November 29, 2019 - 12:42:01 PM
Long-term archiving on: : Thursday, September 23, 2010 - 3:51:33 PM

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  • HAL Id : inria-00165171, version 3

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Claude Le Bris, Tony Lelièvre. Multiscale modelling of complex fluids: A mathematical initiation.. [Research Report] RR-6275, INRIA. 2007. ⟨inria-00165171v3⟩

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