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

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

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

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

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

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

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

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 )

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

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

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

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

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.:

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

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 )

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

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

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 )

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 )

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 )

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 )

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 )

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 )

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 )

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 )

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 )

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 )

Continuum mechanics in moving domains –

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

Ph.D. Thesis

Continuum mechanics in moving domains –

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

Ph.D. Thesis

Continuum mechanics in moving domains –

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

Ph.D. Thesis

Continuum mechanics in moving domains –

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

Ph.D. Thesis

Continuum mechanics in moving domains –

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

Ph.D. Thesis

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

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

Continuum mechanics in moving domains –

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

Ph.D. Thesis