Multiscale modelling of complex fluids: A mathematical initiation

Claude Le Bris; Tony Lelièvre

doi:10.1007/978-3-540-88857-4_2

Multiscale modelling of complex fluids: A mathematical initiation

Research output: Contribution to journal › Conference article › peer-review

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.

Original language	English
Pages (from-to)	49-137
Number of pages	89
Journal	Lecture Notes in Computational Science and Engineering
Volume	66 LNCSE
DOIs	https://doi.org/10.1007/978-3-540-88857-4_2
Publication status	Published - 1 Jan 2009

Keywords

Complex fluids
Couette flow
Fokker-Planck equation
Hookean and FENE dumbbell models
Multiscale modelling
Non-Newtonian flows
Oldroyd-B model
Polymer flow
Stochastic differential equation

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10.1007/978-3-540-88857-4_2

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title = "Multiscale modelling of complex fluids: A mathematical initiation",

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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AU - Lelièvre, Tony

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N2 - 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.

AB - 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.

KW - Complex fluids

KW - Couette flow

KW - Fokker-Planck equation

KW - Hookean and FENE dumbbell models

KW - Multiscale modelling

KW - Non-Newtonian flows

KW - Oldroyd-B model

KW - Polymer flow

KW - Stochastic differential equation

UR - https://www.scopus.com/pages/publications/78651588311

U2 - 10.1007/978-3-540-88857-4_2

DO - 10.1007/978-3-540-88857-4_2

M3 - Conference article

AN - SCOPUS:78651588311

SN - 1439-7358

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SP - 49

EP - 137

JO - Lecture Notes in Computational Science and Engineering

JF - Lecture Notes in Computational Science and Engineering

ER -

Multiscale modelling of complex fluids: A mathematical initiation

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Keywords

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