a brief introduction to fluid- structure...
TRANSCRIPT
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A brief introduction to fluid-
structure interactions
O. Souček
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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
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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)
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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
![Page 5: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/5.jpg)
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.
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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
![Page 7: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/7.jpg)
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 – a generalized
space-time perspective
Space-time deformational gradient
![Page 8: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/8.jpg)
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 )
Referential-to-Eulerian map
Mesh
displacement
Mesh velocity
Mesh
deformation
gradient,
Jacobian
![Page 9: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/9.jpg)
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 )
Referential-to-Eulerian map – a generalized
space-time perspective
Space-time deformational gradient
![Page 10: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/10.jpg)
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-referential map
displacement
velocity
Deformation
gradient,
jacobian
![Page 11: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/11.jpg)
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-referential map
![Page 12: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/12.jpg)
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-Referential map – a
generalized space-time perspective
Space-time deformational gradient
![Page 13: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/13.jpg)
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 )
![Page 14: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/14.jpg)
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 )
Fundamental kinematic relationships
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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 )
Transport theorems
![Page 16: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/16.jpg)
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 )
Transport theorems
![Page 17: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/17.jpg)
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 )
Transport theorems for surface integrals
Transport theorems for line integrals
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Continuum mechanics in moving domains –
MASTER BALANCE EQUATIONSFrom: 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 )
Using Reynold’s t.t.:
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Continuum mechanics in moving domains –
MASTER BALANCE EQUATIONSFrom: 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 )
Rankine-Hugoniot conditions
![Page 20: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/20.jpg)
Continuum mechanics in moving domains –
MASTER BALANCE EQUATIONSFrom: 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 )
![Page 21: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/21.jpg)
Continuum mechanics in moving domains –
MASTER BALANCE EQUATIONSFrom: 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 )
may be written as
with
![Page 22: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/22.jpg)
Continuum mechanics in moving domains –
MASTER BALANCE EQUATIONSFrom: 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 )
may be written as
with
![Page 23: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/23.jpg)
Continuum mechanics in moving domains –
MASTER BALANCE EQUATIONSFrom: 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 )
![Page 24: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/24.jpg)
Continuum mechanics in moving domains –
MASTER BALANCE EQUATIONSFrom: 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 )
![Page 25: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/25.jpg)
Continuum mechanics in moving domains –
CONSERVATION LAWSFrom: 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 )
![Page 26: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/26.jpg)
Continuum mechanics in moving domains –
CONSERVATION LAWSFrom: 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 )
![Page 27: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/27.jpg)
Continuum mechanics in moving domains –
CONSERVATION LAWSFrom: 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 )
![Page 28: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/28.jpg)
Continuum mechanics in moving domains –
CONSERVATION LAWSFrom: 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 )
![Page 29: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/29.jpg)
Continuum mechanics in moving domains –
CONSERVATION LAWSFrom: 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 )
![Page 30: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/30.jpg)
Continuum mechanics in moving domains –
CONSERVATION LAWSFrom: 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 )
![Page 31: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/31.jpg)
Continuum mechanics in moving domains –
CONSERVATION LAWSFrom: 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 )
![Page 32: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/32.jpg)
Continuum mechanics in moving domains –
CONSERVATION LAWSFrom: 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 )
![Page 33: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/33.jpg)
Continuum mechanics in moving domains –
CONSERVATION LAWSFrom: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body,
Ph.D. Thesis
![Page 34: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/34.jpg)
Continuum mechanics in moving domains –
CONSERVATION LAWSFrom: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body,
Ph.D. Thesis
![Page 35: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/35.jpg)
Continuum mechanics in moving domains –
Single continuum modelFrom: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body,
Ph.D. Thesis
![Page 36: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/36.jpg)
Continuum mechanics in moving domains –
Single continuum modelFrom: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body,
Ph.D. Thesis
![Page 37: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/37.jpg)
Continuum mechanics in moving domains –
Single continuum modelFrom: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body,
Ph.D. Thesis
![Page 38: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/38.jpg)
Continuum mechanics in moving domains –
Single continuum modelFrom: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body,
Ph.D. Thesis
Lagrangian descr. In the solid partALE in the fluid part
![Page 39: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/39.jpg)
Continuum mechanics in moving domains –
Single continuum modelFrom: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body,
Ph.D. Thesis
Lagrangian descr. In the solid part ALE in the fluid part
![Page 40: A brief introduction to fluid- structure interactionsgeo.mff.cuni.cz/jednooci_slepym/os-FSI-intro.pdf · Fluid-structure interactions ... • Conflict of descriptions fluid – Eulerian](https://reader031.vdocument.in/reader031/viewer/2022030404/5a79fce67f8b9ae67b8e18e5/html5/thumbnails/40.jpg)
Continuum mechanics in moving domains –
Single continuum modelFrom: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body,
Ph.D. Thesis