OpenFOAM Library for Fluid Structure Interaction

Transcription

1 OpenFOAM Library for Fluid Structure Interaction 9th OpenFOAM Workshop - Zagreb, Croatia Željko Tuković, P. Cardiff, A. Karač, H. Jasak, A. Ivanković University of Zagreb Faculty of Mechanical Engineering and Naval Architecture Zeljko.Tukovic@fsb.hr June 25, 2014

2 Outline Objective Topics Present new OpenFOAM library for fluid structure interaction (FSI) simulation Present some general purpose numerical procedures implemented during FSI library development Basic components of FSI library and example of FSI solver New parallel least squares voltopoint interpolation Vertex based Gauss gradient method skewcorrected sngrad scheme Improved finite volume mesh motion solver Extended GGI interpolation

3 Previous FSI functionality icofsifoam solver Laminar flow of incompressible fluid calculated using FVM solver on dynamic mesh using PISO procedure Deformation of solid described by small-strain total Lagrangian formulation and calculated using FVM solver Weak coupling between fluid and solid newicofsifoam (icofsielasticnonlinulsolidfoam) solver PISO dynamic mesh FVM solver for laminar flow of incompressible fluid Large-strain updated Lagrangian FVM solver for deformation of elastic solid Strong coupling between fluid and solid Coupling schemes: fixed relaxation, Aitken, (IQN-ILS) Enabled parallel calculations

4 Concept of new FSI library Using object oriented approach, it is enabled selection of fluid flow solvers, stress analysis solvers and fsi coupling schemes. In such a way, it is facilitated addition of new solvers and coupling schemes. All this is achieved by introducing following classes: 1 class flowmodel 2 class stressmodel 3 class fluidstructureinterface

5 Basic components of FSI library Abstract base class flowmodel class flowmodel : public IOdictionary {... //- Face zone viscous force (N/m2) virtual tmp<vectorfield> facezoneviscousforce ( const label zoneid, const label patchid ) const = 0; //- Face zone pressure force (N/m2) virtual tmp<scalarfield> facezonepressureforce ( const label zoneid, const label patchid ) const = 0; }; //- Evolve the stress model virtual bool evolve() = 0;

6 Basic components of FSI library Currently implemented flow models icoflow Equivalent to icodymfoam solver without ddtphicorr consistenticoflow Equivalent to icodymfoam solver with consistent ddtphicorr; Tukovic, Jasak, C&F, pisoflow Equivalent to pisofoam solver with dynamic mesh

7 Basic components of FSI library Abstract base class stressmodel class stressmodel : public IOdictionary {... //- Face zone point displacement increment virtual tmp<vectorfield> 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 model virtual bool evolve() = 0;

8 Basic components of FSI library Currently implemented stress models unstotallagrangianstress Large strain elastic stress analysis solver based on total Lagrangian displacement formulation unsincrtotallagrangianstress Large strain elastic stress analysis solver based on total Lagrangian displacement increment formulation New family of stress analysis solvers (uns-solvers) is introduced which is based on vertex based Gauss gradient calculation method and least squares voltopoint interpolation

9 Basic components of FSI library class fluidstructureinterface Extended GGI interpolation Allows face and point zone-to-zone interpolation for non-conformal meshes at fsi interface Coupling schemes Fixed relaxation Aitken dynamic relaxation IQN-ILS (implemented by J. Degroote, UGent) Setting boundary conditions for fluid mesh motion and handling fluid global interface face zone

10 Example of FSI solver partitioned strongly coupled FSI FVM solver fluidstructureinterface fsi(mesh, stressmesh); for (runtime++;!runtime.end(); runtime++) { fsi.initializefields(); fsi.updateinterpolator(); scalar residualnorm = 0; do { fsi.outercorr()++; fsi.updatedisplacement(); // Using selected coupling scheme fsi.movefluidmesh(); fsi.flow().evolve(); fsi.updateforce(); // Face ggi interpolation fsi.stress().evolve(); } residualnorm = fsi.updateresidual(); // Point ggi interpolation } while ( (residualnorm > fsi.outercorrtolerance()) && (fsi.outercorr() < fsi.noutercorr()) );

11 Extended GGI interpolation GGI interpolation is extended by allowing point interpolations between master and slave patches or zones Efficient point-addressing calculation using existing face-addressing i Faces searched during calculation of point i interpolation addressing

12 Backward scheme for second temporal derivative Backward temporal discretization scheme was available only for first temporal derivative In order to allow unified temporal discretization for fluid and solid, backward discretization scheme is implemented for second temporal derivative [ t ( )] [m] φ = 3( ) φ [m] 4( φ t P t t P ( ) [m] φ = 3φ[m] t P ) [m 1] P 2 t P 4φ[m 1] P 2 t +φ [m 2] P + ( ) φ [m 2] t P

13 voltopoint interpolation Calculation of mesh point values from cell-centre values is needed in following cases: Cell-centred FVM mesh motion solver Cell-centred FVM updated Lagrangian stress analysis solvers Cell-centred FVM FSI solver Standard approach to calculate mesh point values in OpenFOAM is simple inverse distance weighted interpolation New approach proposed by Philip Cardiff: least squares method with linear interpolation function

14 Parallel least-squares voltopoint interpolation PROC-1 i ik ij PROC-2 WLS with linear fit function: φ(r i ) = φ i0 +C i (r i r i0 ) i2 i i1 r i0 = n j=1 w ijr ij n j=1 w ij i3 i4 φ i0 = n j=1 w ijφ ij n j=1 w ij Normal equations WLS C i = [ (X T WX) 1 X T W ] Φ i

15 Vertex based Gauss gradient method n f N n τ z τ d f c S τ f e L e m e j P i r P y S f V P Cell-centre gradient: ( φ) P = 1 n τ φ τ S τ V P Volume of polyhedral cell: V P = 1 n τ r τ S τ 3 τ τ x

16 Vertex based Gauss gradient method Why we need tangential face-centre gradient in stress analysis? Traction vector for linear-elastic body t = (2µ+λ)n u (µ+λ)n u t +µ t u n +λntr( t u t ) t = (I nn) the tangential gradient operator

17 Vertex based Gauss gradient method n f N n τ z τ d f c S τ f e L e m e j P i r P S f Tangential face-centre gradient: ( t φ) f = 1 m e φ e L e S f e y V P x

18 skewcorrected sngrad scheme P k fp f P N k fn n f d fn N k fp = (I n f n f ) (r f r P ) k fn = (I n f n f ) (r N r f ) d fn = n f (r N r P ) Normal derivative at face-centre calculated with skewness and non-orthogonal correction: n f ( φ) f = φ N φ P d fn + k fn ( φ) N k fp ( φ) P d fn,

19 Improved FVM mesh motion solver Laplace mesh motion equation with variable diffusivity is discretized using cell-centred FVM with skewcorrected sngrad scheme and voltopoint interpolation of displacement is performed using new least-squares method

20 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) p sigmaeq e+4 2e+4 3e+4 4e e U sigmaeq sigmaeq e+03 p

21 Conclusions New FSI OpenFOAM library is developed and made available to OpenFOAM community through foam-extend-3.1/extend-bazaar Using object oriented approach it is enabled easy extension of the library by adding new solvers and coupling schemes Future work will be oriented toward development of monolithic fsi approach