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Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Fluid-Structure Interactions – Challenges and Solution Approaches
Miriam Mehl
Technische Universität München
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Outline
Fluid-Structure Interactions
The Partitioned Approach
Surface Coupling
Coupling Strategies
Data Mapping for Non-Matching Grids
Lagrangian versus Eulerian Approaches
Conclusion
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Outline
Fluid-Structure Interactions
The Partitioned Approach
Surface Coupling
Coupling Strategies
Data Mapping for Non-Matching Grids
Lagrangian versus Eulerian Approaches
Conclusion
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Fluid-Structure Interactions
Vienna Online, 01/08/2009
Frederic Le Floch,1999 ACO Le Mans Annual
W. Wall, M. Gee, TUM, 2009
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Fluid-Structure Interactions
Characteristics:
surface-coupled problem
slightly different time scales
same spatial scale (at least for laminar flows)
non-linearities
fluid computationally more expensive
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Outline
Fluid-Structure Interactions
The Partitioned Approach
Surface Coupling
Coupling Strategies
Data Mapping for Non-Matching Grids
Lagrangian versus Eulerian Approaches
Conclusion
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Scenario 1: changing fields of application
Scenario 2: changing components (ideology-free coupling)
coupling
The Partitioned Approach
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
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
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
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
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Outline
Fluid-Structure Interactions
The Partitioned Approach
Surface Coupling
Coupling Strategies
Data Mapping for Non-Matching Grids
Lagrangian versus Eulerian Approaches
Conclusion
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Coupling Strategies
Fluid Structure
unidirectional coupling
small range of applicability
fixed and almost rigid
structures
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Coupling Strategies
Fluid Structure
staggered coupling
large range of applicability
standard approach
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Coupling Strategies
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)
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Coupling Strategies
Fluid Structure
staggered coupling
instabilities!!!
unconditionally unstable
forces
velocities/displacements
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)
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Coupling Strategies
Fluid Structure
staggered coupling
instabilities!!!
unconditionally unstable
even worse for smaller dt
in case of massless
structure!
forces
velocities/displacements
incompressible fluids
J. Degroote, J. Vierendeels, In: Fluid-Structure Interaction II,Springer, LNCSE (2010)
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Coupling Strategies
Fluid Structure
staggered coupling
instabilities!!!
unconditionally unstable
forces
velocities/displacements
Aitken underrelaxation:
stabilizing low frequencies
slowing down high
frequencies
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Coupling Strategies
Fluid Structure
forces
velocities/displacements
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
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Coupling Strategies
Fluid Structure
forces
velocities/displacements
multigrid???
unstable modes
more expensive coupling???
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Coupling Strategies
Fluid Structure
forces
velocities/displacements
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
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
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
Surface Coupling – Coupling Strategies
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Coupling Strategies
Fluid Structure
forces
velocities/displacements
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)
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Coupling Strategies
Fluid Structure
forces
velocities/displacements
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)
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Coupling Strategies
Fluid
non-staggered coupling
parallel!!!
stability?
efficiency?
Structure
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
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
Surface Coupling – Coupling Strategies
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
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
Surface Coupling – Coupling Strategies
black-box solvers!!!
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Data Mapping
non-matching grids neighbourhood relations? mapping?
without interface grid with interface grid
differences inlocations,
mesh width,discr. order
accuracy?conservation?
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Data Mapping
non-matching grids neighbourhood relations? mapping?
without interface grid with interface grid
projections(bi-)linear interpolationradial basis functions
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Data Mapping
non-matching grids neighbourhood relations? mapping?
without interface grid with interface grid
always required:neighbourhood
search
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
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
Surface Coupling – Data Mapping
Klaus Daubner
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
conservation of energy at the discrete interface
mapping forces and displacements:
mapping stresses and displacements:
Surface Coupling – Data Mapping
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)
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Surface Coupling – Data Mapping
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
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Outline
Fluid-Structure Interactions
The Partitioned Approach
Surface Coupling
Coupling Strategies
Data Mapping for Non-Matching Grids
Lagrangian versus Eulerian Approaches
Conclusion
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Lagrangian versus Eulerian Approaches
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Lagrangian versus Eulerian Approaches
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
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 ¿¿
¿ ¿¿
Lagrangian versus Eulerian Approaches
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
monolithic FE:
partitioned FE: weakly enforce boundary conditions at cell-cuts
fluideq⋅χ fstructureeq⋅χs
Janos Benk, method implemented
in Sundance
Lagrangian versus Eulerian Approaches
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
monolithic FE:
partitioned FE: weakly enforce boundary conditions at cell-cuts
fluideq⋅χ fstructureeq⋅χs
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.
Lagrangian versus Eulerian Approaches
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
monolithic FE:
partitioned FE: weakly enforce boundary conditions at cell-cuts
fluideq⋅χ fstructureeq⋅χs
Source: Janos Benk
Lagrangian versus Eulerian Approaches
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
Outline
Fluid-Structure Interactions
The Partitioned Approach
Surface Coupling
Coupling Strategies
Data Mapping for Non-Matching Grids
Lagrangian versus Eulerian Approaches
Conclusion
Technische Universität München
Miriam Mehl, ICiS Multiphysics Workshop 2011, July 31-August 6
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
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