Zeljko Tukovic OFW09 P 0103

8/10/2019 Zeljko Tukovic OFW09 P 0103

1/21

OpenFOAM Library for

Fluid Structure Interaction9th OpenFOAM Workshop - Zagreb, Croatia

Zeljko Tukovic, P. Cardiff, A. Karac,H. Jasak, A. Ivankovic

University of ZagrebFaculty of Mechanical Engineering and Naval Architecture

[email protected]

June 25, 2014
http://find/http://goback/


2/21

Outline

Objective

Present new OpenFOAM library for fluid structureinteraction (FSI) simulation

Present some general purpose numerical proceduresimplemented during FSI library development

Topics

Basic components of FSI library and example of FSI solver

New parallel least squares volToPoint interpolation

Vertex based Gauss gradient methodskewCorrected snGrad scheme

Improved finite volume mesh motion solver

Extended GGI interpolation

Zeljko Tukovic, P. Cardiff, A. Karac, H. Jasak, A. Ivankovic fsiFoam
http://find/


3/21

Previous FSI functionality

icoFsiFoam solver

Laminar flow of incompressible fluid calculated usingFVM solver on dynamic mesh using PISO procedureDeformation of solid described by small-strain totalLagrangian formulation and calculated using FVM solver

Weak coupling between fluid and solidnewIcoFsiFoam (icoFsiElasticNonLinULSolidFoam) solver

PISO dynamic mesh FVM solver for laminar flow ofincompressible fluidLarge-strain updated Lagrangian FVM solver fordeformation of elastic solidStrong coupling between fluid and solidCoupling schemes: fixed relaxation, Aitken, (IQN-ILS)Enabled parallel calculations

http://find/


4/21

Concept of new FSI library

Using object oriented approach, it is enabled selection of fluidflow solvers, stress analysis solvers and fsi coupling schemes.In such a way, it is facilitated addition of new solvers andcoupling schemes.

All this is achieved by introducing following classes:

1 class flowModel

2 class stressModel

3 class fluidStructureInterface

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5/21

Basic components of FSI library

Abstract base class flowModelclass flowModel

:public IOdictionary

{...

//- Face zone viscous force (N/m2)

virtual tmp faceZoneViscousForce

(const label zoneID,const label patchID

) const = 0;

//- Face zone pressure force (N/m2)virtual tmp faceZonePressureForce

(

const label zoneID,

const label patchID) const = 0;

//- Evolve the stress modelvirtual bool evolve() = 0;

};

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6/21


Currently implemented flow models

icoFlow

Equivalent to icoDyMFoam solver without ddtPhiCorr

consistentIcoFlow

Equivalent to icoDyMFoam solver with consistentddtPhiCorr; Tukovic, Jasak, C&F, 2012.

pisoFlow

Equivalent to pisoFoam solver with dynamic mesh

http://find/


7/21


Abstract base class stressModelclass stressModel

:public IOdictionary

{...

//- Face zone point displacement increment

virtual tmp faceZonePointDisplacementIncrement

(const label zoneID

) const = 0;

//- Set traction at specified face zone

virtual void setTraction(

const label patchID,

const label zoneID,

const vectorField& faceZoneTraction) = 0 ;

//- Evolve the stress modelvirtual bool evolve() = 0;

};

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8/21


Currently implemented stress modelsunsTotalLagrangianStress

Large strain elastic stress analysis solver based on totalLagrangian displacement formulation

unsIncrTotalLagrangianStressLarge strain elastic stress analysis solver based on totalLagrangian displacement increment formulation

New family of stress analysis solvers (uns-solvers) is introducedwhich is based on vertex based Gauss gradient calculationmethod and least squares volToPoint interpolation

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9/21


class fluidStructureInterface


Allows face and point zone-to-zone interpolation fornon-conformal meshes at fsi interface

Coupling schemes

Fixed relaxationAitken dynamic relaxationIQN-ILS (implemented by J. Degroote, UGent)

Setting boundary conditions for fluid mesh motion andhandling fluid global interface face zone



10/21

Example of FSI solver

fsiFoam partitioned strongly coupled FSI FVM solverfluidStructureInterface fsi(mesh, stressMesh);

for (runTime++; !runTime.end(); runTime++){

fsi.initializeFields();

fsi.updateInterpolator();scalar residualNorm = 0;

do

{

fsi.outerCorr()++;

fsi.updateDisplacement(); // Using selected coupling schemefsi.moveFluidMesh();

fsi.flow().evolve();

fsi.updateForce(); // Face ggi interpolationfsi.stress().evolve();

residualNorm =fsi.updateResidual(); // Point ggi interpolation

}while

((residualNorm > fsi.outerCorrTolerance())

&& (fsi.outerCorr() < fsi.nOuterCorr()));

}



11/21


GGI interpolation is extended by allowing pointinterpolations between master and slave patches or zones

Efficient point-addressing calculation using existingface-addressing

i

of point i interpolation addressing

Faces searched during calculation



12/21

Backward scheme for second temporal derivative

Backward temporal discretization scheme was availableonly for first temporal derivative

In order to allow unified temporal discretization for fluidand solid, backward discretization scheme is implementedfor second temporal derivative

t

t

[m]P

=3

t

[m]P 4

t

[m1]P

+

t

[m2]P

2t

t

[m]P

=3

[m]P 4

[m1]P +

[m2]P

2t

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13/21

volToPoint interpolation

Calculation of mesh point values from cell-centre values isneeded in following cases:

Cell-centred FVM mesh motion solver

Cell-centred FVM updated Lagrangian

stress analysis solversCell-centred FVM FSI solver

Standard approach to calculate mesh point values in

OpenFOAM is simple inverse distance weighted interpolationNew approach proposed by Philip Cardiff: least squaresmethod with linear interpolation function

http://find/


14/21

Parallel least-squares volToPoint interpolation

i

i

ij

ik

PROC-2PROC-1

i3 i4

i1i2

WLS with linear fitfunction:

(ri) = i0+ Ci (ri ri0)

ri0 =n

j=1

wijrijnj=1 wij

i0 =

nj=1 wijij

n

j=1 wij

Normal equations WLS

Ci=

(XTWX)1XTWi

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15/21

Vertex based Gauss gradient method

f

c

N

df

P

VP

z

y

x

rP

Sf

j

nf

i

n

Se

meLeCell-centre gradient:

(

)P=

1

VP

nS

Volume of polyhedral cell:

VP=

1

3n rS

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16/21


Why we need tangential face-centre gradientin stress analysis?

Traction vector for linear-elastic body

t= (2 + )nu ( + )nut+ tun+ n tr (tut)

t= (I nn) the tangential gradient operator

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17/21


f

c

N

df

P

VP

z

y

x

rP

Sf

j

nf

i

n

Se

meLe

Tangential face-centre

gradient:

(t)f = 1

Sf

e

meeLe


C G
http://find/


18/21

skewCorrected snGrad scheme

kfN

kfP

f

nf

P

N

P

dfn NkfP = (I nfnf)(rf rP)

kfN = (I nfnf)(rN rf)

dfn = nf (rN rP)

Normal derivative at face-centre calculated with skewness andnon-orthogonal correction:

nf ()f =N P

dfn+kfN()N kfP()P

dfn,


I d FVM h i l
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19/21

Improved FVM mesh motion solver

Laplace mesh motion equation with variable diffusivity isdiscretized using cell-centred FVM with skewCorrected snGradscheme and volToPoint interpolation of displacement isperformed using new least-squares method


V lid i f FSI lib
http://./movies/hronTurekFvmMeshMotion.avihttp://find/http://goback/


20/21

Validation of FSI library

Z. Tukovic, P. Cardiff, A. Karac, H. Jasak and A. Ivankovic: Parallel unstructured

finite-volume method for fluid-structure interaction, manuscript in preparation (2014)

1e+4 2e+4 3e+4 4e+4

sigmaEq

42.3 4.36e+04

1 2U

0 2.17

2000 4000 6000 8000

sigmaEq

60.9 8.52e+03

-0.4 0 0.4 0.8 1.2p

-0.42 1.33

200 400 600 800

sigmaEq

31.7 901

0.02 0.04

p

0 0.0556


C l i
http://./movies/hronTurekFsi2_U_sigmaEq.avihttp://./movies/hronTurekFsi2_U_sigmaEq.avihttp://./movies/hronTurekFsi2_U_sigmaEq.avihttp://./movies/hronTurekFsi2_U_sigmaEq.avihttp://./movies/hronTurekFsi2_U_sigmaEq.avihttp://./movies/hronTurekFsi2_U_sigmaEq.avihttp://./movies/3dTube_p_sigmaEq.avihttp://./movies/3dTube_p_sigmaEq.avihttp://./movies/3dTube_p_sigmaEq.avihttp://./movies/3dTube_p_sigmaEq.avihttp://./movies/3dTube_p_sigmaEq.avihttp://./movies/3dTube_p_sigmaEq.avihttp://./movies/3dTube_p_sigmaEq.avihttp://./movies/3dTube_p_sigmaEq.avihttp://./movies/hronTurekFsi2_U_sigmaEq.avihttp://find/


21/21

Conclusions

New FSI OpenFOAM library is developed and madeavailable to OpenFOAM community throughfoam-extend-3.1/extend-bazaar

Using object oriented approach it is enabled easyextension of the library by adding new solvers andcoupling schemes

Future work will be oriented toward development of

monolithic fsi approach

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Documents

Zeljko Tukovic OFW09 P 0103