Fluid-Structure Interactions – Challenges and Solution ... · Technische Universität München...

Technische Universität München

Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6

Fluid-Structure Interactions – Challenges and Solution Approaches

Miriam Mehl




Outline

Fluid-Structure Interactions

The Partitioned Approach

Surface Coupling

Coupling Strategies

Data Mapping for Non-Matching Grids

Lagrangian versus Eulerian Approaches

Conclusion




Vienna Online, 01/08/2009

Frederic Le Floch,1999 ACO Le Mans Annual

W. Wall, M. Gee, TUM, 2009




Characteristics:

surface-coupled problem

slightly different time scales

same spatial scale (at least for laminar flows)

non-linearities

fluid computationally more expensive



Outline



Surface Coupling

Coupling Strategies



Conclusion



Scenario 1: changing fields of application

Scenario 2: changing components (ideology-free coupling)

coupling




MpCCI (Fraunhofer SCAI – Algorithms and Scientific Computing)

client-server approach

coupling of parallel codes

coupling functionality on one CPU

no central coupling numerics

http://www.mpcci.de/mpcci/technical-description/system-features.html

The Partitioned Approach – Tools



preCICE – our inhouse coupling tool library approach – P2P solver communication coupling of parallel codes

coupling functionality on one CPU

central coupling numerics

Bernhard Gatzhammer

The Partitioned Approach – Tools



Outline



Surface Coupling

Coupling Strategies



Conclusion



Surface Coupling – Coupling Strategies

Fluid Structure

unidirectional coupling

small range of applicability

fixed and almost rigid

structures




Fluid Structure

staggered coupling

large range of applicability

standard approach




Fluid Structure

staggered coupling

instabilities!!!

conditionally stable

forces

velocities/displacements

en1, i=c⋅exp iκxiμt

∣en1, i1∣≈ρ f

mdt∣en1, i∣

compressible fluids

E. H. van Brummelen, Journal of Applied Mechanics (2009)




Fluid Structure

staggered coupling

instabilities!!!

unconditionally unstable

forces


en1, i=c⋅exp iκxiμt

∣en1, i1∣=ρ f

m∣κ∣−1∣en1, i∣

incompressible fluids

E. H. van Brummelen, Journal of Applied Mechanics (2009)




Fluid Structure

staggered coupling

instabilities!!!


even worse for smaller dt

in case of massless

structure!

forces


incompressible fluids

J. Degroote, J. Vierendeels, In: Fluid-Structure Interaction II,Springer, LNCSE (2010)




Fluid Structure

staggered coupling

instabilities!!!


forces


Aitken underrelaxation:

stabilizing low frequencies

slowing down high

frequencies




Fluid Structure

forces


u si1=Ass

−1 bs−Asf u fi1

usi1, ϑ , new∣Γ fs

=1−ωi , ϑ⋅usi , ϑ

∣Γ fsωi , ϑ¿ us

i1, ϑ∣Γ fs

for all levels ϑ




Fluid Structure

forces


multigrid???

unstable modes

more expensive coupling???




Fluid Structure

forces


interface quasi-Newton

(Degroote/Vierendeels):

underrelaxation for low

frequencies

Gauss-Seidel for high

frequencies

essential: few unstable modes!

solve xdispl

=s f x

Δ rit1=−rit= Δr k k=1, , it cto be det.

⇒ Δ x it1= Δ xk k=1, , it c



algorithm runtime #iterations

constant underrelaxation 136.5 852.38

Aitken underrelaxation 8.3 50.94

IQN-ILS 3.0 16.21

IQN-ILS(2) 1.3 6.20

IQN-ILS(4) 1.0 4.60

results with preCICE

Compare:Degroote, Bruggemann,

Haeltermann, Vierendeels,Computation & Structure 86,

2008





Fluid Structure

forces


interface quasi-Newton extensions:

two-grid coupling (ECCOMAS Coupled Problems 2011, H. Bijl)

two-grid construction of sensitivities (ECCOMAS Coupled Problems 2011, J.

Degroote)

parallel computation of sensitivities (Munich Multiphysics Meeting 2001, J.

Degroote)




Fluid Structure

forces


other aspect: fitting time steps decisive for

damping of spurious modes (Vierendeels et al., FSI II, Springer, 2010)

order of convergence (van Zuijlen, Bijl, Computers & Structures 83, 2005)




Fluid

non-staggered coupling

parallel!!!

stability?

efficiency?

Structure



non-staggered coupling

equality of displacements for non-matching grids

explicit time-stepsolve interface equation exactly

LLM (compressible fluids, Ross, Park, Felippa)Mike Ross, Phd thesis, 2006




fully parallel coupling

M ff M fI

M If M II M Is

M sI M ssu f

u I

us=

f f

f If s

Block-Jacobi:

fluid: u fi1=M ff

−1 f f−M fI u Ii

interface: u Ii1=M II

−1 f I−M If u fi −M Isu s

i structure: u s

i1=M ss−1 f s−M sI u I

i

Fluid

Structure


black-box solvers!!!



Surface Coupling – Data Mapping

non-matching grids neighbourhood relations? mapping?

without interface grid with interface grid

differences inlocations,

mesh width,discr. order

accuracy?conservation?






projections(bi-)linear interpolationradial basis functions






always required:neighbourhood

search



octree-supported neighbourhood search

octree depth

time (sec)

nodes

7 0.8 203,905

9 4.9 3,288,225

11 48.2 52,662,337

13 662.8 842,687,105


Klaus Daubner



conservation of energy at the discrete interface

mapping forces and displacements:

mapping stresses and displacements:


work: {u fT f f=u s

T f s¿ f s=H fs f f , {u ¿ f=H sf us⇒H fs=H sf

T ¿¿

work: {u fT M f

mass matrix

σ f=usT M s

mass matrix

σs

¿σ s=H fsσ f , {u¿ f=H sf u s⇒H fsT M s=M f H sf ¿¿

(de Boer, van Zuijlen, Bijl, ECCOMAS CFD 2006)




projection interpolation

surface discretiszationrequired

radial basis functions (cf. A. Beckert, H. Wendland, 2001; CP-related work by H. Bijl et al.)

works for arbitrary point clouds

∑i

αi φ ∥x− x i∥p x

http://en.wikipedia.org/wiki/Radial_basis_function

Markus Brenk



Outline



Surface Coupling

Coupling Strategies



Conclusion



monolithic FE: partitioned FE: weakly enforce boundary conditions at cell-cuts

fluideq⋅χ fstructureeq⋅χs

Fluid with Dirichlet boundary (FE):

boundary integrals

from partial integration

boundary condition

enforcing

right hand

side

boundary condition

enforcing

a u , p φ , ξ standard FE

c u , p φ underbracealignl ¿¿

b u φ ,ξ underbracealignl ¿¿

¿ ¿= f φunderbracealignl ¿¿

¿b g φ ,ξ underbracealignl ¿¿

¿ ¿¿




monolithic FE:

partitioned FE: weakly enforce boundary conditions at cell-cuts


Janos Benk, method implemented

in Sundance




monolithic FE:



γ=1,000 drag lift

111x21 5.57919 0.012239

221x41 5.57935 0.010597

441x81 5.57935 0.010622

γ=10,000

111x21 5.57936 0.0120811

221x41 5.57936 0.0105961

441x81 5.57936 0.0106214

reference 5.579535 0.0106189

Reference values from:R. Becker, M. Braack, R. Rannacher, and C. Waguet. Fast and reliable solutions of the Navier-stokes equations including chemistry. Computer and Visualization in Science, 2(3), 1999.




monolithic FE:



Source: Janos Benk




Outline



Surface Coupling

Coupling Strategies



Conclusion



Conclusion

modular multiphysics simulations require partitioned approaches

current partitioned coupling not parallel!!!

methods with general applicability:

Aitken underrelaxation

interface quasi-Newton: few unstable modes

conservative and consistent mapping

modular software structure

structured grids versus unstructured grids

Eulerian versus Lagrangian grids

Fluid-Structure Interactions – Challenges and Solution ... · Technische Universität München...

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