A brief introduction to fluid- structure...

A brief introduction to fluid-

structure interactions

O. Souček

Fluid-structure interactions

From http://www.ihs.uni-stuttgart.de

From https://www.rocq.inria.fr/REO/spip.php?rubrique37

•Important class computational

models

•Civil engineering

•Biomechanics

•Industry

•Geophysics

•…

M. Madlik

Fluid-structure interactions

Main technical computational difficulties:

• Typically problems with changing domain

• Interaction – forces exerted by the fluid deform

the structure, affecting the motion of the fluid

• Conflict of descriptions fluid – Eulerian vs.

structure (solid) – Lagrangian

Two basic computational approaches

Interaction approach

•Fluid and solid parts are solved for iteratively, one

by one

•Main advantage – allows the use of traditional

solvers for the standard fluid and elasticity

problems, the only difficulty is implementation of

interaction (convergence)

Fluid-structure interactionsTwo basic computational approaches

Monolithic approach

•Both fluid and solid equations are

formulated and solved for together

•Advantage – unified approach,

parallelizable, allows also for unified

space-time discretization

•Disadvantage – typically very large both

linear and non-linear problems, hard to

treat numerically

Interaction approach

•Fluid and solid parts are solved for

iteratively, one by one

•Weak coupling (fluid and solid at a

time) vs. strong coupling (sub

timelevel interactions)

•Main advantage – allows the use of

traditional solvers for the standard

fluid and elasticity problems, the only

difficulty is implementation of

interaction (convergence)

•Disadvantage – slow, harder to

parallelize (sequentional

comuptation), convergence issues

Continuum mechanics in moving

domainsFrom: Guglielmo Scovazzi, Thomas J.R. Hughes Lecture notes on Continuum

Mechanics on Arbitrary Moving Domains

(http://www.cs.sandia.gov/~gscovaz/publications/CMAMD_SANDarticle.pdf )

•Eulerian (present) configuration

•Langangian configuration

•Referential configuration –

arbitrarily moving v.r.t. E. and L.

conf.

Continuum mechanics in moving domains -

KINEMATICSFrom: Guglielmo Scovazzi, Thomas J.R. Hughes Lecture notes on

Continuum Mechanics on Arbitrary Moving Domains

(http://www.cs.sandia.gov/~gscovaz/publications/CMAMD_SANDarticl

e.pdf )

Lagrangian-to-Eulerian map

displacement

velocity

Deformation

gradient,

jacobian





e.pdf )

Lagrangian-to-Eulerian map – a generalized

space-time perspective

Space-time deformational gradient





e.pdf )

Referential-to-Eulerian map

Mesh

displacement

Mesh velocity

Mesh

deformation

gradient,

Jacobian





e.pdf )

Referential-to-Eulerian map – a generalized

space-time perspective






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Lagrangian-to-referential map

displacement

velocity

Deformation

gradient,

jacobian





e.pdf )

Lagrangian-to-referential map





e.pdf )

Lagrangian-to-Referential map – a

generalized space-time perspective






e.pdf )





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Fundamental kinematic relationships





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Transport theorems





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Transport theorems for surface integrals

Transport theorems for line integrals

Continuum mechanics in moving domains –

MASTER BALANCE EQUATIONSFrom: Guglielmo Scovazzi, Thomas J.R. Hughes Lecture notes on



e.pdf )

Using Reynold’s t.t.:





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Rankine-Hugoniot conditions





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may be written as

with





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CONSERVATION LAWSFrom: Guglielmo Scovazzi, Thomas J.R. Hughes Lecture notes on



e.pdf )


CONSERVATION LAWSFrom: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body,

Ph.D. Thesis


Single continuum modelFrom: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body,

Ph.D. Thesis



Ph.D. Thesis

Lagrangian descr. In the solid partALE in the fluid part



Ph.D. Thesis

Lagrangian descr. In the solid part ALE in the fluid part



Ph.D. Thesis

A brief introduction to fluid- structure...

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