Nonlinear Fluid-Structure Interaction:

a Partitioned Approach and

its Application through Component Technology

Christophe Kassiotis

Advisors: A. Ibrahimbegovic, Hermann G. Matthies and D. Duhamel

December 1, 2010 | EDF R&D, Chatou

Nonlinear Fluid-Structure Interaction:a Partitioned Approach and

its Application through Component Technology

Christophe Kassiotis

November 20, 2009

Introduction

Fluid Structure Interaction

Nearly every structure is surrounded by fluids

Countless applications

Among important issues: extreme winds or tsunami impacts on coasts

2 / 45

Introduction

Fluid Structure Interaction

Nearly every structure is surrounded by fluids

Countless applications

Among important issues: extreme winds or tsunami impacts on coasts

Wind action (Eurocode I, P 2.4)

Elementary geometry: Aref

F = prefCeCzCdAref

2 / 45

Introduction

Fluid Structure Interaction

Nearly every structure is surrounded by fluids

Countless applications

Among important issues: extreme winds or tsunami impacts on coasts

Wind action (Eurocode I, P 2.4)

Elementary geometry: Aref

Simplified Force actions:prefCeCz

F = prefCeCzCdAref

2 / 45

Introduction

Fluid Structure Interaction

Nearly every structure is surrounded by fluids

Countless applications

Among important issues: extreme winds or tsunami impacts on coasts

Wind action (Eurocode I, P 2.4)

Elementary geometry: Aref

Simplified Force actions:prefCeCz

Simplified Interactionwind / structure : Cd

Only the structure point of view

F = prefCeCzCdAref

2 / 45

Introduction

Fluid Structure Interaction

Nearly every structure is surrounded by fluids

Countless applications

Among important issues: extreme winds or tsunami impacts on coasts

Tsunami modeling

Generation

Source: CMLA-Cachan [Dutykh, 09]

2 / 45

Introduction

Fluid Structure Interaction

Nearly every structure is surrounded by fluids

Countless applications

Among important issues: extreme winds or tsunami impacts on coasts

Tsunami modeling

Generation

Propagation

[Kassiotis, 07]

2 / 45

Introduction

Fluid Structure Interaction

Nearly every structure is surrounded by fluids

Countless applications

Among important issues: extreme winds or tsunami impacts on coasts

Tsunami modeling

Generation

Propagation

Run-up

Source: FBI (American Samoa office),Samoa, September 2009

2 / 45

Introduction

Fluid Structure Interaction

Nearly every structure is surrounded by fluids

Countless applications

Among important issues: extreme winds or tsunami impacts on coasts

Tsunami modeling

Generation

Propagation

Run-up

Run-up key issues

Amplitude of the flood

Resistance of buildings Source: FBI (American Samoa office),Samoa, September 2009

2 / 45

Introduction

Goals

Coupled problem ⇒ Coupling approach

Structures and fluids are two different scientific topics:

Different formulations: Lagrangian or EulerianDifferent discretization methods: FE or FVDifferent softwares

3 / 45

Introduction

Goals

Coupled problem ⇒ Coupling approach

Structures and fluids are two different scientific topics:

Different formulations: Lagrangian or EulerianDifferent discretization methods: FE or FVDifferent softwares

Monolithical approach is not a natural choice

Monolithical approach in FSI:

Finite Element based [Walhorn 02, Hubner et al 04]

Finite Volume based [Mehl 08]

3 / 45

Introduction

Goals

Coupled problem ⇒ Coupling approach

Structures and fluids are two different scientific topics:

Different formulations: Lagrangian or EulerianDifferent discretization methods: FE or FVDifferent softwares

Monolithical approach is not a natural choice

Specifications

Partitioned approaches

Reach 3D computations

Re-use dedicated and well-known codes for fluids and structures

Structures: non-linear behaviors (cracking, reinforced concrete. . . )Fluids: incompressibility, free surface flows, sloshing waves

3 / 45

Introduction

Goals

Coupled problem ⇒ Coupling approach

Structures and fluids are two different scientific topics:

Different formulations: Lagrangian or EulerianDifferent discretization methods: FE or FVDifferent softwares

Monolithical approach is not a natural choice

Specifications

Partitioned approaches

Reach 3D computations

Re-use dedicated and well-known codes for fluids and structures

Structures: non-linear behaviors (cracking, reinforced concrete. . . )Fluids: incompressibility, free surface flows, sloshing waves

Software component technology

3 / 45

Introduction

Approaches to solve FSI coupled problems

Coupling Methods

PartitionedMonolithical

4 / 45

Introduction

Approaches to solve FSI coupled problems

Coupling Methods

PartitionedMonolithical

Partitioned Approach

Introducing interfaceunknowns

Advantages:

Independant subsystemDifferent discretizationand integration schemes

Drawbacks

More unknownsStability? Convergence?

[Park & Felippa 77, Wall 99, Matthie &

Steindorf 04, Vergnault 09, Gerbeau &

Vidrascu 03, Fernandez et al 07, Deparis

& Quateroni, 06]

4 / 45

Introduction

Approaches to solve FSI coupled problems

Coupling Methods

PartitionedMonolithical

Algebraic Differential

PenaltyLagrangeMultipliers

Algebraic Approach

Minimization under analgebraic constraint(interface)

Applied to acoustic fluids

Advantages

Genericity andparallelizationLarge coupling windows

Drawbacks

Computational costData transfer

[Park, Felippa, Ohayon, 04]

4 / 45

Introduction

Approaches to solve FSI coupled problems

Coupling Methods

PartitionedMonolithical

Algebraic Differential

PenaltyLagrangeMultipliers

Implicit Explicit

Differential approach – DFMT

Direct Force-MotionTransfer [Ross & Felippa 09]

Advantages

SimplicityData exchangeFew computationsoutside existing codes

Drawbacks

Smaller couplingwindowsConditional stability

[Peric & Dettmer 03-07, Wall et al

99-09, Steindorf 04. . . ]

4 / 45

Introduction

Outline

1 Fluid structure interaction frameworkStructure and fluid subproblemsExplicit and implicit coupling algorithms for FSIConvergence and stability of coupling algorithms

2 Software implementation and validationComponent architecture copsLid driven-cavity with a flexible bottomOscillating appendix in a flow

3 Applications: 3D computations and interaction with free surface flowsThree dimensional computing and parallelingSolving free surface flowsExamples: free-surface flows impacting structures

5 / 45

Fluid structure interaction framework

Outline

1 Fluid structure interaction frameworkStructure and fluid subproblemsExplicit and implicit coupling algorithms for FSIConvergence and stability of coupling algorithms

2 Software implementation and validationComponent architecture copsLid driven-cavity with a flexible bottomOscillating appendix in a flow

3 Applications: 3D computations and interaction with free surface flowsThree dimensional computing and parallelingSolving free surface flowsExamples: free-surface flows impacting structures

6 / 45

Fluid structure interaction framework Structure and fluid subproblems

Structure and fluid subproblemsContinuum mechanics equations

Ωf

ΩsΓ

t = t0

Ωf

ΩsΓ

t

Equilibrium equation:

Structure (Lagrangian): ρ∂2t u −∇ · σ − f = 0 in Ωs

Fluid (Eulerian) in Ωf :

Equilibrium: ρ∂tv + v · ∇v −∇ · σ − f = 0

Incompressibility : ∇ · v = 0

7 / 45

Fluid structure interaction framework Structure and fluid subproblems

Structure and fluid subproblemsContinuum mechanics equations

Ωf

ΩsΓ

t = t0

Ωf

ΩsΓ

t

Equilibrium equation:

Structure (Lagrangian): ρ∂2t u −∇ · σ − f = 0 in Ωs

Fluid (ALE) in Ωf (t) :

Equilibrium: ρ∂tv + (v−∂tu) · ∇v −∇ · σ − f = 0

Incompressibility : ∇ · v = 0

Fluid domain motion: u = Ext(u|Γ )

7 / 45

Fluid structure interaction framework Structure and fluid subproblems

Structure and fluid subproblemsContinuum mechanics equations

Ωf

ΩsΓ

t = t0

Ωf

ΩsΓ

t

Equilibrium equation:

Structure (Lagrangian): ρ∂2t u −∇ · σ − f = 0 in Ωs

Fluid (ALE) in Ωf (t) :

Equilibrium: ρ∂tv + (v−∂tu) · ∇v −∇ · σ − f = 0

Incompressibility : ∇ · v = 0

Fluid domain motion: u = Ext(u|Γ )

How to solve each of this subproblems?

7 / 45

Fluid structure interaction framework Structure and fluid subproblems

Structure and fluid subproblems

Ωs

∂Ωs,D

∂Ωs ,Nλ

b

u

Structure discretization

Weak formulation

8 / 45

Fluid structure interaction framework Structure and fluid subproblems

Structure and fluid subproblems

Ωs

∂Ωs,D

∂Ωs ,Nλ

b

u

Structure discretization

Weak formulation

Finite Element Method [Zienkewicz, Taylor]

Continuous elementwise polynomial functions

8 / 45

Fluid structure interaction framework Structure and fluid subproblems

Structure and fluid subproblems

Ωs

∂Ωs,D

∂Ωs ,Nλ

b

u

Structure discretization

Weak formulation

Finite Element Method [Zienkewicz, Taylor]

Continuous elementwise polynomial functions

Poincare-Steklov operator: S−1s : λ −→ u [Simone, Deparis, Quateroni, 03]

8 / 45

Fluid structure interaction framework Structure and fluid subproblems

Structure and fluid subproblems

Ωs

∂Ωs,D

∂Ωs ,Nλ

b

u

Structure discretization

Weak formulation

Finite Element Method [Zienkewicz, Taylor]

Continuous elementwise polynomial functions

Poincare-Steklov operator: S−1s : λ −→ u [Simone, Deparis, Quateroni, 03]

Fluid discretization

Weak formulation

8 / 45

Fluid structure interaction framework Structure and fluid subproblems

Structure and fluid subproblems

Ωs

∂Ωs,D

∂Ωs ,Nλ

b

u

Structure discretization

Weak formulation

Finite Element Method [Zienkewicz, Taylor]

Continuous elementwise polynomial functions

Poincare-Steklov operator: S−1s : λ −→ u [Simone, Deparis, Quateroni, 03]

Fluid discretization

Weak formulation

FEM or Finite Volume Method [Ferziger, Peric]

Discontinous elementwise constant functions

8 / 45

Fluid structure interaction framework Structure and fluid subproblems

Structure and fluid subproblems

Ωs

∂Ωs,D

∂Ωs ,Nλ

b

u

Structure discretization

Weak formulation

Finite Element Method [Zienkewicz, Taylor]

Continuous elementwise polynomial functions

Poincare-Steklov operator: S−1s : λ −→ u [Simone, Deparis, Quateroni, 03]

tFluid discretization

Weak formulation

FEM or Finite Volume Method [Ferziger, Peric]

Discontinous elementwise constant functions

Steklov-Poincare operator: Sf : u −→ λ = pn + νf D(v)n

8 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

Coupling equation

Steklov-Poincare operators

Solid: Ss : u → λ = σns

Fluid: Sf : u → λ = σnf

Defined on Γ × [0,T ]

Can be computed with existing tools

Require (non-linear) computation onthe whole domain Ωs and Ωf

9 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

Coupling equation

Steklov-Poincare operators

Solid: Ss : u → λ = σns

Fluid: Sf : u → λ = σnf

Defined on Γ × [0,T ]

Can be computed with existing tools

Require (non-linear) computation onthe whole domain Ωs and Ωf

Interface equations

Displacement continuity: uf = us = u

Stress equilibrium: σns + σnf = 0

9 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

Coupling equation

Steklov-Poincare operators

Solid: Ss : u → λ = σns

Fluid: Sf : u → λ = σnf

Defined on Γ × [0,T ]

Can be computed with existing tools

Require (non-linear) computation onthe whole domain Ωs and Ωf

Interface equations

Displacement continuity: uf = us = u

Stress equilibrium: Ss(u) + Sf (u) = 0

9 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

Coupling equation

Steklov-Poincare operators

Solid: Ss : u → λ = σns

Fluid: Sf : u → λ = σnf

Defined on Γ × [0,T ]

Can be computed with existing tools

Require (non-linear) computation onthe whole domain Ωs and Ωf

Interface equations

Displacement continuity: uf = us = u

Stress equilibrium: Ss(u) + Sf (u) = 0

Solve FSI coupled problem:

Find roots of equation: u − S−1s (−Sf (u)) = 0

Find fix-points of equation: u = S−1s (−Sf (u))

9 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

Coupling equation

Steklov-Poincare operators

Solid: Ss : u → λ = σns

Fluid: Sf : u → λ = σnf

Defined on Γ × [0,T ]

Can be computed with existing tools

Require (non-linear) computation onthe whole domain Ωs and Ωf

Interface equations

Displacement continuity: uf = us = u

Stress equilibrium: Ss(u) + Sf (u) = 0

Solve FSI coupled problem:

Find roots of equation: u − S−1s (−Sf (u)) = 0

Find fix-points of equation: u = S−1s (−Sf (u))

9 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

DFMT coupling algorithms – Explicit

b

b

λ

uex u

−Sf

Ss

10 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

DFMT coupling algorithms – Explicit

b

b

λ

uex u

−Sf

Ss

λex −Sf (uex)

10 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

DFMT coupling algorithms – Explicit

b

b

λ

uex u

−Sf

Ss

λex −Sf (uex)

10 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

DFMT coupling algorithms – Explicit

b

b

λ

uex u

−Sf

Ss

λex

b

uN

10 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

DFMT coupling algorithms – Explicit

b

b

λ

uex u

−Sf

Ss

λex

b

uN

λN+1 −Sf (uN)

10 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

DFMT coupling algorithms – Explicit

eN+1

b

b

λ

uex u

−Sf

Ss

λex

b

uN

λN+1 −Sf (uN)

S−1s (λN+1)

uN+1

b

Spurious numerical energy at the interface

10 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

DFMT coupling algorithms – Explicit

b

b

λ

uex u

−Sf

Ss

λex

b

uNPuN

b

P

Spurious numerical energy at the interface

Cheap predictor computed at the interface

10 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

DFMT coupling algorithms – Explicit

eN+1

b

b

λ

uex u

−Sf

Ss

λex

b

uN

λN+1

uN+1

bPuN

b

P

Spurious numerical energy at the interface

Cheap predictor computed at the interface

Function of window size, subproblem time integration schemes andpredictors [Piperno & Farhat 99-03]

10 / 45

Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI

DFMT coupling algorithms – Implicit Block-Gauß-Seidel

e(k)

u(k−2)N+1 u

(k−1)N+1 u

(k)N+1 u

(k+1)N+1

uex u

b

b

λ

λ(k−1)N+1

λ(k)N+1

λ(k+1)N+1

−Sf

Ssr(k) = Ss−1

(

−Sf

(

u(k)))

− u(k)

Iterations of the explicit coupling strategyPredictor can be used to reduce the number of iterationNo information used for search direction (subproblem tangent terms)

Stability of the coupling algorithm ?11 / 45

Fluid structure interaction framework Convergence and stability of coupling algorithms

Stability of the coupling algorithm (DFMT-BGS)

Stability proof

Criterion: [Arnold, 01; Steindorf, 04] Compressible flow

∥

∥

∥Ms

−1Mf

∥

∥

∥≤ 1

Ms structure mass matrix

Mf fluid mass matrix

12 / 45

Fluid structure interaction framework Convergence and stability of coupling algorithms

Stability of the coupling algorithm (DFMT-BGS)

Stability proof

Criterion: [Arnold, 01; Steindorf, 04] Incompressible flow

∥

∥

∥M⋆

s−1

Mf

∥

∥

∥≤ 1

“Added Mass”effect [Le Tallec 01, Causin et al. 05, Forster et al. 07] :

No explicit couplingDifficulty to make DFMT-BGS algorithm converge

Ms structure mass matrix

Mf fluid mass matrix

M⋆

s = Ms (1 −F (Mf ,Bf ))

Bf fluid gradient matrix (associated to pressure)

12 / 45

Fluid structure interaction framework Convergence and stability of coupling algorithms

Stability of the coupling algorithm (DFMT-BGS)

Stability proof

Criterion: [Arnold, 01; Steindorf, 04] Incompressible flow

∥

∥

∥M⋆

s−1

Mf

∥

∥

∥≤ 1

“Added Mass”effect [Le Tallec 01, Causin et al. 05, Forster et al. 07] :

When the criterion is not fulfilled ?

Re-ordering [Arnold, 01]

Relaxation: Aitken, steepest descent [Kuttler et al. 08]

Preconditioning [Quateroni et al. 04]

Other algorithm: (In)-Exact Block-Newton [Matthies 06, Dettmer &

Peric, Gerbeau 03, Fernandez 07]

12 / 45

Fluid structure interaction framework Convergence and stability of coupling algorithms

Relaxation strategy

G(u) = S−1s (−Sf (u))

u(k+1) = u(k) + ω r(k)

I(u)

u

u

b

u(0)

b uex

b

u(1)

13 / 45

Fluid structure interaction framework Convergence and stability of coupling algorithms

Relaxation strategy

G(u) = S−1s (−Sf (u))

u(k+1) = u(k) + ω r(k)

I(u)

u

u

b

u(0)

b uex

b

u(1) u(2)

b

No relaxation

13 / 45

Fluid structure interaction framework Convergence and stability of coupling algorithms

Relaxation strategy

G(u) = S−1s (−Sf (u))

u(k+1) = u(k) + ω r(k)

I(u)

u

u

b

u(0)

b uex

b

u(1)

b

0.2r(2)

u(2)

b

No relaxation

Fixed relaxation (used in pressure-velocity coupling)

13 / 45

Fluid structure interaction framework Convergence and stability of coupling algorithms

Relaxation strategy

G(u) = S−1s (−Sf (u))

u(k+1) = u(k) + ω r(k)

I(u)

u

u

b

u(0)

b uex

b

u(1)

b

b

u(2)

b

No relaxation

Fixed relaxation (used in pressure-velocity coupling)

Aitken’s relaxation (secant) [Kuttler & Wall, 08]

13 / 45

Fluid structure interaction framework Convergence and stability of coupling algorithms

Relaxation strategy

G(u) = S−1s (−Sf (u))

u(k+1) = u(k) + ω r(k)

I(u)

u

u

b

u(0)

b uex

b

u(1)

b

b

b

u(2)

b

No relaxation

Fixed relaxation (used in pressure-velocity coupling)

Aitken’s relaxation (secant) [Kuttler & Wall, 08]

Steepest descent (tangent)

13 / 45

Fluid structure interaction framework Convergence and stability of coupling algorithms

First summaryPartitioned procedure for FSI

Fluid, structure and interface

Structure: FEM discretized Lagrangian formulation

Fluid: FVM discretized ALE formulation

Interface: primal variable continuity and dual variable equilibrium

14 / 45

Fluid structure interaction framework Convergence and stability of coupling algorithms

First summaryPartitioned procedure for FSI

Fluid, structure and interface

Structure: FEM discretized Lagrangian formulation

Fluid: FVM discretized ALE formulation

Interface: primal variable continuity and dual variable equilibrium

Partitioned strategy for FSI

Use of Steklov-Poincare operators based on existing discretization

Direct Force-Motion Transfer (DFMT) algorithms

Block Gauss–Seidel (BGS) solver

14 / 45

Fluid structure interaction framework Convergence and stability of coupling algorithms

First summaryPartitioned procedure for FSI

Fluid, structure and interface

Structure: FEM discretized Lagrangian formulation

Fluid: FVM discretized ALE formulation

Interface: primal variable continuity and dual variable equilibrium

Partitioned strategy for FSI

Use of Steklov-Poincare operators based on existing discretization

Direct Force-Motion Transfer (DFMT) algorithms

Block Gauss–Seidel (BGS) solver

Stability criterion for coupling incompressible flows and structures

Conditional stability improved by dynamic relaxation

14 / 45

Fluid structure interaction framework Convergence and stability of coupling algorithms

First summaryPartitioned procedure for FSI

Fluid, structure and interface

Structure: FEM discretized Lagrangian formulation

Fluid: FVM discretized ALE formulation

Interface: primal variable continuity and dual variable equilibrium

Partitioned strategy for FSI

Use of Steklov-Poincare operators based on existing discretization

Direct Force-Motion Transfer (DFMT) algorithms

Block Gauss–Seidel (BGS) solver

Stability criterion for coupling incompressible flows and structures

Conditional stability improved by dynamic relaxation

Partitioned approach implementation and use of component technology

14 / 45

Software implementation and validation

Outline

1 Fluid structure interaction frameworkStructure and fluid subproblemsExplicit and implicit coupling algorithms for FSIConvergence and stability of coupling algorithms

2 Software implementation and validationComponent architecture copsLid driven-cavity with a flexible bottomOscillating appendix in a flow

3 Applications: 3D computations and interaction with free surface flowsThree dimensional computing and parallelingSolving free surface flowsExamples: free-surface flows impacting structures

15 / 45

Software implementation and validation Component architecture cops

Programming context for partitionned solution procedure

u

λ

Solidcomputation

Fluidcomputation

FSI software implementation

Data exchange between fluid and structure computations

16 / 45

Software implementation and validation Component architecture cops

Programming context for partitionned solution procedure

u

λ Control

Solidcomputation

Fluidcomputation

FSI software implementation

Data exchange between fluid and structure computations

Implementation of a master code

16 / 45

Software implementation and validation Component architecture cops

Programming context for partitionned solution procedure

u

λ Control

Interpolator

Solidcomputation

Fluidcomputation

FSI software implementation

Data exchange between fluid and structure computations

Implementation of a master code

Non matching meshes handled by the Interpolator

16 / 45

Software implementation and validation Component architecture cops

Programming context for partitionned solution procedure

u

λ Control

Interpolator

FEAP OpenFOAM

FSI software implementation

Data exchange between fluid and structure computations

Implementation of a master code

Non matching meshes handled by the Interpolator

Re-using existing fluid and structure codes

16 / 45

Software implementation and validation Component architecture cops

Programming context for partitionned solution procedure

u

λ Control

Interpolator

FEAP OpenFOAM

FSI software implementation

Data exchange between fluid and structure computations

Implementation of a master code

Non matching meshes handled by the Interpolator

Re-using existing fluid and structure codes

Minimum requirement: a communication protocol

16 / 45

Software implementation and validation Component architecture cops

Programming context for partitionned solution procedure

Middleware

u

λ Control

Interpolator

FEAP OpenFOAM

Middleware – Software component technology

“Between” software and hardware

Computer science community [Mac Ilroy 68, Szyperski & Meeserschmitt 98]

Each software: a component

Generalization of OOP to software: encapsuled / interface

Middleware in charge of communication and data types

16 / 45

Software implementation and validation Component architecture cops

Programming context for partitionned solution procedure

Middleware

u

λ Control

Interpolator

FEAP OpenFOAM

Middleware – for scientific computing

Available middleware: Corba, Java-RMI, MS.net . . .

Communication Template Library (CTL): C++ [Niekamp, 02]

16 / 45

Software implementation and validation Component architecture cops

Programming context for partitionned solution procedure

Middleware

u

λ Control

Interpolator

FEAP OpenFOAM

Middleware – for scientific computing

Available middleware: Corba, Java-RMI, MS.net . . .

Communication Template Library (CTL): C++ [Niekamp, 02]

Scientific computing: requires good performances [Niekamp, 05]

16 / 45

Software implementation and validation Component architecture cops

Programming context for partitionned solution procedure

Middleware

u

λ Control

Interpolator

FEAP OpenFOAM

Middleware – for scientific computing

Available middleware: Corba, Java-RMI, MS.net . . .

Communication Template Library (CTL): C++ [Niekamp, 02]

Scientific computing: requires good performances [Niekamp, 05]

Salome platform (EDF R&D)

16 / 45

Software implementation and validation Component architecture cops

Programming context for partitionned solution procedure

Middleware: CTL

u

λ Control

Interpolator

FEAP OpenFOAM

Middleware – for scientific computing

Available middleware: Corba, Java-RMI, MS.net . . .

Communication Template Library (CTL): C++ [Niekamp, 02]

Scientific computing: requires good performances [Niekamp, 05]

Salome platform (EDF R&D)

Software development made by non-programmers

16 / 45

Software implementation and validation Component architecture cops

Components implementation and use

Middleware: CTL

u

λ

FEAP OpenFOAM

coFeap

Interpolator

Control

Structure component: coFeap [Kassiotis & Hautefeuille 08]

Interface definition simu.ci

17 / 45

Software implementation and validation Component architecture cops

Components implementation and use

Middleware: CTL

u

λ

FEAP OpenFOAM

coXXX

AbaqusCastem,Aster

Interpolator

Control

Structure component: coFeap [Kassiotis & Hautefeuille 08]

Interface definition simu.ci (Genericity)

17 / 45

Software implementation and validation Component architecture cops

Components implementation and use

Middleware: CTL

u

λ

FEAP OpenFOAM

coFeap

Interpolator

Control

Structure component: coFeap [Kassiotis & Hautefeuille 08]

Interface definition simu.ci (Genericity)

Methods declaration

#define CTL_Method6 void , set_load ,

(const array <scalar1 >/*value*/), 1

Methods implementation in Fortran

17 / 45

Software implementation and validation Component architecture cops

Components implementation and use

Middleware: CTL

u

λ

FEAP OpenFOAM

coFeap

Interpolator

Control

Structure component: coFeap [Kassiotis & Hautefeuille 08]

Compilation gives:

A library: call like a lib, thread (asynchronous calls)An executable: remote call with tcp, pipe, MPI...

Use: Multiscale [Hautefeuille 09] , EFEM [Benkemoun 09]

Stochastic [Krosche 09] , Thermomechanics [Kassiotis 06] , Masstransfer [De Sa 08] . . .

17 / 45

Software implementation and validation Component architecture cops

Components implementation and use

Middleware: CTL

u

λ

FEAP OpenFOAM

coFeap ofoam

Interpolator

Control

Fluid component: ofoam [Krosche 07, Kassiotis 09]

Interface definition can be derivated from simu.ci: CFDsimu.ci

Methods declaration

#define CTL_Method2 void , get ,

( const string /*name*/, array <real8 > /*v*/ ) const , 2

Methods implementation in C++

17 / 45

Software implementation and validation Component architecture cops

Components implementation and use

Middleware: CTL

u

λ

FEAP OpenFOAM

coFeap ofoam

InterpolatorInterpolator

Control

Interpolation component: Interpolator [Jurgens 09]

C++ component

Interpolation with radial basis functions [Beckert & Wendland 01]

Full matrices

Solve: coupled with the Lapack library

17 / 45

Software implementation and validation Component architecture cops

Components implementation and use

Middleware: CTL

u

λ

FEAP OpenFOAM

coFeap ofoam

InterpolatorInterpolator

Controlcops

COupling COmponents by a Partitioned Strategy: cops

Coupling components as templates

Implementation of DFMT coupling algorithm

Explicit coupling: collocated and non-collocated

Implicit coupling: BGS

Predictors (order 0 to 2), fixed and dynamic Aitken’s relaxation

17 / 45

Software implementation and validation Lid driven-cavity with a flexible bottom

Lid-driven cavity with a flexible bottomProblem parameters

Fluid problem

Material properties:ρf = 1kg .m−3, νf = 0.01m · s−2.

Boundary conditions:

only ∇p requiredv · ex = 1 − cos (2πt/Tchar)

Accurate discretization when Re ≤ 300

18 / 45

Software implementation and validation Lid driven-cavity with a flexible bottom

Lid-driven cavity with a flexible bottomProblem parameters

Fluid problem

Material properties:ρf = 1kg .m−3, νf = 0.01m · s−2.

Boundary conditions:

only ∇p requiredv · ex = 1 − cos (2πt/Tchar)

Accurate discretization when Re ≤ 300

Modification for the FSI case

Structure problem: ρs = 500kg · m−3, Es = 250Pa and νs = 0

18 / 45

Software implementation and validation Lid driven-cavity with a flexible bottom

Lid-driven cavity with a flexible bottomProblem parameters

Fluid problem

Material properties:ρf = 1kg .m−3, νf = 0.01m · s−2.

Boundary conditions:

only ∇p requiredv · ex = 1 − cos (2πt/Tchar)

Accurate discretization when Re ≤ 300

Modification for the FSI case

Structure problem: ρs = 500kg · m−3, Es = 250Pa and νs = 0

No incompressibility dilemma [Wall et al. 98, Gerbeau & Vidrascu 03]

Pressure fix (different from [Bathe & Zhang 09] )

18 / 45

Software implementation and validation Lid driven-cavity with a flexible bottom

Lid-driven cavity with a flexible bottomResults

Discretization

Fluid: 32x32 cells.

Structure: 16 quadratic elements.

Time step: ∆t = 0.1s.

19 / 45

Software implementation and validation Lid driven-cavity with a flexible bottom

Lid-driven cavity with a flexible bottomResults

Discretization

Fluid: 32x32 cells.

Structure: 16 quadratic elements.

Time step: ∆t = 0.1s.

Perfect benchmark for FSI

Mesh simplicity

Computational time: TCPUs = 2.95× 10−3s and TCPU

f = 1.08× 10−1s

Harmonic solution quickly reached

19 / 45

Software implementation and validation Lid driven-cavity with a flexible bottom

Lid-driven cavity with a flexible bottomExplicit results

b

0.0

0.1

0.2

0 1 2 3 4 5

Displa

cem

ent

(m)

O(1)O(∆t)O(∆t2)

Time (s)

Influence of numerical parameters

Order of predictor

Time step size

Time integration of the fluid problem

Non-collocated schemes

20 / 45

Software implementation and validation Lid driven-cavity with a flexible bottom

Lid-driven cavity with a flexible bottomExplicit results

b

0.0

0.1

0.2

0 1 2 3 4 5

Displa

cem

ent

(m)

O(1)O(∆t)O(∆t2)

Time (s)

Added mass effect

no explicit coupling whenincompressible flowinteracts with structure

Influence of numerical parameters

Order of predictor

Time step size

Time integration of the fluid problem

Non-collocated schemes

20 / 45

Software implementation and validation Lid driven-cavity with a flexible bottom

Lid-driven cavity with a flexible bottomImplicit results

b

Numerical parameters

Interface residual:‖r(k)N ‖2 ≤ 1 × 10−7

All converged computations: same results

0.0

0.1

0.2

0 20 40 60 80 100

Displa

cem

ent

(m)

Time (s)

FEMs+FVMf DFMT-BGS

21 / 45

Software implementation and validation Lid driven-cavity with a flexible bottom

Lid-driven cavity with a flexible bottomImplicit results

b

Numerical parameters

Interface residual:‖r(k)N ‖2 ≤ 1 × 10−7

All converged computations: same results

Results with other methods [Gerbeau &

Vidrascu 03, Wall & Mok 99]

0.0

0.1

0.2

0 20 40 60 80 100

Displa

cem

ent

(m)

Time (s)

FEMs+FVMf DFMT-BGSFEMs+SFEMf DFMT-BN

FEMs+SFEMf DFMT-BGS

21 / 45

Software implementation and validation Lid driven-cavity with a flexible bottom

Lid-driven cavity with a flexible bottomImplicit results – Aitken’s relaxation

0

10

20

30

0 20 40 60 80 100

Iter

atio

n–

(k)

Time (s)

ω = 0.25Aitken

22 / 45

Software implementation and validation Lid driven-cavity with a flexible bottom

Lid-driven cavity with a flexible bottomImplicit results – Aitken’s relaxation

0

10

20

30

0 20 40 60 80 100

Iter

atio

n–

(k)

Time (s)

ω = 0.25Aitken

-8

-7

-6

-5

-4

-3

-2

0 10 20 30

Res

(log

10‖r(k

)39‖

2)

Iteration number – (k)

ω = 0.25Aitken

22 / 45

Software implementation and validation Lid driven-cavity with a flexible bottom

Lid-driven cavity with a flexible bottomImplicit results – Predictors

0

10

20

30

0 20 40 60 80 100

Iter

atio

n–

(k)

Time (s)

O(1)O(∆t)O(∆t2)

-8

-7

-6

-5

-4

-3

-2

0 10 20 30

Res

(log

10‖r(k

)39‖

2)

Iteration number – (k)

O(1)O(∆t)O(∆t2)

23 / 45

Software implementation and validation Lid driven-cavity with a flexible bottom

Lid-driven cavity with a flexible bottomImplicit results – Predictors

0

0.2

0.4

0.6

0.8

1

0 5 10 15

Rel

axat

ion

(ω(k

)39

)

Iteration number – (k)

Aitken and predictor O(∆1)Aitken and predictor O(∆t)

Aitken and predictor O(∆t2)Fixed relaxation ω = 0.25

-8

-7

-6

-5

-4

-3

-2

0 10 20 30

Res

(log

10‖r(k

)39‖

2)

Iteration number – (k)

O(1)O(∆t)O(∆t2)

23 / 45

Software implementation and validation Oscillating appendix in a flow

Oscillating appendixProblem presentation

x

y

12.01.0

1.0 6.0

0.06

5.5 14.0

slip: v · n = 0

outflow p = 0

ρs , Es , νs

v = vf

ρf , νf

slip: v · n = 0

Implicit/Explicit coupling

24 / 45

Software implementation and validation Oscillating appendix in a flow

Oscillating appendixResults

25 / 45

Software implementation and validation Oscillating appendix in a flow

Oscillating appendixComputation results

-1.500

-1.000

-0.500

0.000

0.500

1.000

1.500

0 2 4 6 8 10 12 14

Displa

cem

ent

(m)

Time (s)

Comparison with other works (Maximum amplitude motion)

FEMs+FVMf DFMT-BGS

FEMs+SFEMf DFMT-BGS [Wall & Ramm 99]

FEMs+SFEMf DFMT-BN [Steindorf & Matthies 02]

FEMs+SFEMf Monolithical [Dettmer & Peric 07]

26 / 45

Software implementation and validation Oscillating appendix in a flow

Second summaryFrom a partitioned solution procedure to a component architecture

Software implementation

Suited for partitioned strategy with high performance data transfers

Middleware CTL simplifies communication

Component technology: re-use of existing codes

27 / 45

Software implementation and validation Oscillating appendix in a flow

Second summaryFrom a partitioned solution procedure to a component architecture

Software implementation

Suited for partitioned strategy with high performance data transfers

Middleware CTL simplifies communication

Component technology: re-use of existing codes

Validation and comparison with other strategies

Full definition of an adapted benchmark to validate FSIimplementation

Implicit coupling required for incompressible flows interacting withstructures required

Behavior of DMFT-BGS with dynamic relaxation validated

Comparison with other approaches gives similar qualitatives results

27 / 45

Software implementation and validation Oscillating appendix in a flow

Second summaryFrom a partitioned solution procedure to a component architecture

Software implementation

Suited for partitioned strategy with high performance data transfers

Middleware CTL simplifies communication

Component technology: re-use of existing codes

Validation and comparison with other strategies

Full definition of an adapted benchmark to validate FSIimplementation

Implicit coupling required for incompressible flows interacting withstructures required

Behavior of DMFT-BGS with dynamic relaxation validated

Comparison with other approaches gives similar qualitatives results

Advantages of re-using: efficient solvers and advanced models

27 / 45

Applications

Outline

1 Fluid structure interaction frameworkStructure and fluid subproblemsExplicit and implicit coupling algorithms for FSIConvergence and stability of coupling algorithms

2 Software implementation and validationComponent architecture copsLid driven-cavity with a flexible bottomOscillating appendix in a flow

3 Applications: 3D computations and interaction with free surface flowsThree dimensional computing and parallelingSolving free surface flowsExamples: free-surface flows impacting structures

28 / 45

Applications Three dimensional computing and paralleling

Performances and paralleling

Middleware: CTL

u

λ

FEAP OpenFOAM

coFeap ofoam

InterpolatorInterpolator

Controlcops

Lid-cavity TCPU: Structure 3%, Fluid 96% and Interpolation 1%.

29 / 45

Applications Three dimensional computing and paralleling

Performances and paralleling

Middleware: CTL

u

λ

FEAP OpenFOAM

coFeap ofoam

InterpolatorInterpolator

Controlcops ofoam

ofoam

ofoam

ofoam

Lid-cavity TCPU: Structure 3%, Fluid 96% and Interpolation 1%.

A parallel version of ofoam

Based on OpenFOAM inner paralleling (MPI)

Derive a parallel interface CFDsimu.pi from standard interface

Group of workers instantiation and communication handled by CTL

Call parallel version transparent for client

29 / 45

Applications Three dimensional computing and paralleling

Performances and paralleling

1

2

4

8

16

32

1 2 4 8 16 32 64

Spee

d-u

p(χ

)

Processor Number (N)

rs

rs

rs

rs

rs

rsrs

29 / 45

Applications Three dimensional computing and paralleling

Three-dimensional“flag” in the windProblem parameters

5.01.0

4.010.0

5.01.0

5.0

3.0

4.0

3.0

b

b

b

inflow

outflow

slip

ABC

Numerical parameters

Implicit DFMT-BGS coupling

Interface: ‖r(k)N ‖2 ≤ 1 × 10−7

Discretization: 150 × 103 or 1.2 × 106 d-o-f, 6 × 103 time step

Paralleling of the fluid sub-problem

30 / 45

Applications Three dimensional computing and paralleling

Three-dimensional“flag” in the windProblem parameters

5.01.0

4.010.0

5.01.0

5.0

3.0

4.0

3.0

b

b

b

inflow

outflow

slip

ABC

Numerical parameters

Implicit DFMT-BGS coupling

Interface: ‖r(k)N ‖2 ≤ 1 × 10−7

Discretization: 150 × 103 or 1.2 × 106 d-o-f, 6 × 103 time step

Paralleling of the fluid sub-problem

30 / 45

Applications Three dimensional computing and paralleling

Three-dimensional“flag” in the windComputation results

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 1 2 3 4 5 6

Displa

cem

ent

(dy

incm

)

Time (s)

ABC

First flexion mode

31 / 45

Applications Three dimensional computing and paralleling

Three-dimensional“flag” in the windComputation results

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 1 2 3 4 5 6

Displa

cem

ent

(dy

incm

)

Time (s)

C

FEMs+SFEMf DFMT-BGS

First flexion mode

Different from the torsional mode observed [von Scheven, 09]

Complex flow, different structure model, sensitivity to initialcondition. . .

31 / 45

Applications Three dimensional computing and paralleling

Outline

1 Fluid structure interaction frameworkStructure and fluid subproblemsExplicit and implicit coupling algorithms for FSIConvergence and stability of coupling algorithms

2 Software implementation and validationComponent architecture copsLid driven-cavity with a flexible bottomOscillating appendix in a flow

3 Applications: 3D computations and interaction with free surface flowsThree dimensional computing and parallelingSolving free surface flowsExamples: free-surface flows impacting structures

32 / 45

Applications Solving free surface flows

Structure and free surface flow subproblemsContinuum mechanics equations

Ωf

ΩsΓ

⇒

Ωf Ωs

Γ

Problem equations:

Structure (Lagrangian): ρ∂2t u −∇ · σ − f = 0 dans Ωs

Fluid (ALE) in Ωf :

Equilibrium: ρ∂tv + (v−∂tu) · ∇v −∇ · σ − f = 0

Incompressibility : ∇ · v = 0

Fluid domain motion: u = Ext(u|Γ )

33 / 45

Applications Solving free surface flows

Structure and free surface flow subproblemsContinuum mechanics equations

Ωf

ΩsΓ

⇒

Ωf Ωs

Γ

Problem equations:

Structure (Lagrangian): ρ∂2t u −∇ · σ − f = 0 dans Ωs

Fluid (ALE) in Ωf (t) :

Equilibrium: ρ∂tv + (v−∂tu) · ∇v −∇ · σ − f = σκδΓ n + ρg

Incompressibility : ∇ · v = 0

Fluid domain motion: u = Ext(u|Γ )Characteristic function: ∂tι + (v − ∂tu) · ∇ι = 0 and normal n = ∇ι

33 / 45

Applications Solving free surface flows

Structure and fluid subproblemsDiscretization

bbbb

b

b

b b

b

bb

b

bb

b

b

bb

b

b

b

b

b

b

bb b bbbbbbb 1.0

0.8

0.4

0.9

0.5

0.3

0.4

0.0

0.0

1 2 3 4

Discretization strategies

1 Moving grid method: PFEM [Idelsohn 04]

2 Meshless method: SPH [Monhagan 88, Fries 05]

3 Tracking surface method: Surface fitted method [Ferziger & Peric 96]

4 Tracking volume method: V.O.F. [Ghidaglia 01, Rusche 02, Duthyk 08]

34 / 45

Applications Free-surface flows

Two-dimensional dam-break problemProblem parameters

292

146 140 12 286

80

73

Ωf ,1ρf ,1, µf ,1

Ωf ,2

ρf ,2, µf ,2

ρs , Es , νs

Ωs

g

Structure neo-Hookean Es = 1 × 106Pa, νs = 0, ρs = 2500kg · m−3.

Fluid ρf ,1 = 1 × 103kg .m−3, νf ,1 = 1 × 106m.s−1,ρf ,2 = 1kg .m−3, νf ,2 = 1 × 105m.s−1.

35 / 45

Applications Free-surface flows

Two-dimensional dam-break problemResults

t = 0.1s t = 0.2s t = 0.3s

t = 0.4s t = 0.5s t = 0.6s

36 / 45

Applications Free-surface flows

Two-dimensional dam-break problemComputation results

0

5

10

15

20

25

0 0.2 0.4 0.6 0.8 1

Iter

atio

nnum

ber

Time (s)

fine meshcoarse mesh

t = 0.2s t = 0.4s t = 0.6s

37 / 45

Applications Free-surface flows

Two-dimensional dam-break problemComputation results

-2-1012345

0 0.2 0.4 0.6 0.8 1

Displa

cem

ent(c

m)

Time (s)

fine meshcoarse mesh[Walhorn, 05]

bbbbbbbb

bbbbbb

bbbbbbbbbb

bbbbbbbb

bbbbbbbb

bbbbbbbb

bbbbbb

bbbbbbbbbbbbbbbbbbb b b b b b b bb

bbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbb bbbbbbb b b b bb b

b bb b b bb bb b b bb b b b b b bb b b b b b b b b b b b bb b bb bbbbbbbbbbbbbbbb bb bbbbbbbb b b b b bb bb

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

bbbbbbbb

bbbbbb bb bb b b b

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bb b b bb

bbbbbbb

b

[Baudille, 06]

b b b b b b b b bb bbbbbbbbbbbbbbbbb bbbbbbbbbbbb bbbbbbbbbbbbb

bbbbbbbbb bbbbbbbbbbbbb

bbb bbbbbbbbbbbbbbb

bb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bb

bbbbbbbbbb bbbbbbbbbbb bbbbbbbbbbbbb bbbbbbb bbbb bb bb b b b b b b b b b bb bb bb bb bb bb bb bbbb bb bb bbbb bb bb bb bb bb bb bb bb bbb bb bb bb bb bb b b bb bb bb b b b bb b bb b b b b b b bb b b b b b b b b b b b b b b b b b bb bb

bbbb bbbbb bbbbb bbbbbbbbbbbbb bbbbbbbb b bb b b b b b b b b b b b b bb b b

bb b bb b bb b b b

b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b

b

t = 0.2s t = 0.4s t = 0.6s

38 / 45

Applications Free-surface flows

Three-dimensional dam-break problemProblem parameters

g

Ωf ,1

Ωf ,2

Ωs

146140

12286

146

292

146

8080

292

292Parameters

Free-outflow boundaries

Discretization:

64 × 103 or 526 × 103 d-o-f1 × 105 time step

Multigrid solver for the fluid part

Interface: ‖r(k)N ‖2 ≤ 1 × 10−6

Structure neo-Hookean Es = 1 × 106Pa, νs = 0, ρs = 2500kg · m−3.

Fluid ρf ,1 = 1 × 103kg .m−3, νf ,1 = 1 × 106m.s−1,ρf ,2 = 1kg .m−3, νf ,2 = 1 × 105m.s−1.

39 / 45

Applications Free-surface flows

Three-dimensional dam-break problemResults

Isosurface ι = 0.5

40 / 45

Applications Free-surface flows

Three-dimensional dam-break problemResults

Free-surface representation

ι = 0.01 ι = 0.50 ι = 0.99

Visualization of a qualitative free-surface

Water mass is conserved

40 / 45

Applications Free-surface flows

Three-dimensional dam-break problemComputation results

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Iter

atio

n(k

)

Time (s)

41 / 45

Applications Free-surface flows

Three-dimensional dam-break problemComputation results

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Iter

atio

n(k

)

Time (s)

-1

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Displa

cem

ent(c

m)

Time (s)

coarse meshfine mesh

41 / 45

Applications Free-surface flows

Coupling with concrete civil engineering structures

Localization limiters / Crack representation

Smeared crack model [Hidelborg et al 77]

Cohesive zone model [Barenblatt, 62]

Non-local approach [Pijaudier-Cabot and Bazant, 87]

EFEM [Wells & Sluys, 00] / XFEM [Moes et al, 99]

42 / 45

Applications Free-surface flows

Coupling with concrete civil engineering structures

Localization limiters / Crack representation

Smeared crack model [Hidelborg et al 77]

Cohesive zone model [Barenblatt, 62]

Non-local approach [Pijaudier-Cabot and Bazant, 87]

EFEM [Wells & Sluys, 00] / XFEM [Moes et al, 99]

Lattice truss model [Benkemoun et al 09]

42 / 45

Applications Free-surface flows

Coupling with concrete civil engineering structures

Localization limiters / Crack representation

Smeared crack model [Hidelborg et al 77]

Cohesive zone model [Barenblatt, 62]

Non-local approach [Pijaudier-Cabot and Bazant, 87]

EFEM [Wells & Sluys, 00] / XFEM [Moes et al, 99]

Lattice truss model [Benkemoun et al 09]

Crack opening ⇒ softening response

Force control: open question

42 / 45

Conclusion

Conclusions and OutlooksSoftware implementation

cops component based implementation

Flexible implementation

Use of the middleware CTL

Re-use existing code and libraries: FEAP, OpenFOAM

Development of components: coFeap, ofoam, cops

Parallel features for fluid subproblems (bottleneck) allows to reach 3D

Transfer operation handled independently: Interpolator

43 / 45

Conclusion

Conclusions and OutlooksSoftware implementation

cops component based implementation

Flexible implementation

Use of the middleware CTL

Re-use existing code and libraries: FEAP, OpenFOAM

Development of components: coFeap, ofoam, cops

Parallel features for fluid subproblems (bottleneck) allows to reach 3D

Transfer operation handled independently: Interpolator

Outlooks

Transfer operator based on compact support radial basis functions

Parallel features for the solid subproblem

Coupling with other softwares (e.g. conuwata for wave propagation,other fluid and structure solvers)

43 / 45

Conclusion

Conclusions and OutlooksCoupling algorithm for FSI

DFMT-BGS with Aitken’s relaxation

easy implementation and cheap computation outside existing codes

coupling incompressible fluid and structure

efficiency of Aitken’s relaxation

44 / 45

Conclusion

Conclusions and OutlooksCoupling algorithm for FSI

DFMT-BGS with Aitken’s relaxation

easy implementation and cheap computation outside existing codes

coupling incompressible fluid and structure

efficiency of Aitken’s relaxation

Outlooks

automatic choice for time step size

decrease iteration number: better approximation of the tangent terms(still partitioned)

expensive first iterations: model reduction

44 / 45

Conclusion

Conclusions and OutlooksModels and discretization

Advantages of component technology and software re-use

Popular FEM and FVM for fluid and structure part

Efficient to use already developed models

Free surface flow computations

VOF: selection of an appropriate model in ofoam

Suitable for sloshing waves

Full representation of the two-phase flow (water and air)

45 / 45

Conclusion

Conclusions and OutlooksModels and discretization

Advantages of component technology and software re-use

Popular FEM and FVM for fluid and structure part

Efficient to use already developed models

Outlooks

Fluid:turbulence, non-newtonian flows, different representation (wave

propagation and sloshing)

Structure:more advance models, multi-scale representation of the structure

(MuSCAd), concrete structures

Use FSI to model cement based material at small scales

45 / 45