Fluid structure interaction framework Structure and fluid subproblems Structure and fluid subproblems Structure discretization λ ∂Ω s , N Weak formulation Ω s Finite Element Method [Zienkewicz, Taylor] b Continuous elementwise polynomial functions ∂Ω s , D u S − 1 Poincar´ e-Steklov operator: : λ − → u [Simone, Deparis, Quateroni, 03] s Fluid discretization Weak formulation 8 / 45
Fluid structure interaction framework Structure and fluid subproblems Structure and fluid subproblems Structure discretization λ ∂Ω s , N Weak formulation Ω s Finite Element Method [Zienkewicz, Taylor] b Continuous elementwise polynomial functions ∂Ω s , D u S − 1 Poincar´ e-Steklov operator: : λ − → u [Simone, Deparis, Quateroni, 03] s Fluid discretization Weak formulation FEM or Finite Volume Method [Ferziger, Peri´ c] Discontinous elementwise constant functions 8 / 45
Fluid structure interaction framework Structure and fluid subproblems Structure and fluid subproblems Structure discretization λ ∂Ω s , N Weak formulation Ω s Finite Element Method [Zienkewicz, Taylor] b Continuous elementwise polynomial functions ∂Ω s , D u S − 1 Poincar´ e-Steklov operator: : λ − → u [Simone, Deparis, Quateroni, 03] s t Fluid discretization Weak formulation FEM or Finite Volume Method [Ferziger, Peri´ c] Discontinous elementwise constant functions Steklov-Poincar´ e operator: S f : u − → λ = p n + ν f D ( v ) n 8 / 45
Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI Coupling equation Steklov-Poincar´ e operators Defined on Γ × [0 , T ] Solid: S s : u → λ = σ n s Can be computed with existing tools Fluid: S f : u → λ = σ n f Require (non-linear) computation on the whole domain Ω s and Ω f 9 / 45
Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI Coupling equation Steklov-Poincar´ e operators Defined on Γ × [0 , T ] Solid: S s : u → λ = σ n s Can be computed with existing tools Fluid: S f : u → λ = σ n f Require (non-linear) computation on the whole domain Ω s and Ω f Interface equations Displacement continuity: u f = u s = u Stress equilibrium: σ n s + σ n f = 0 9 / 45
Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI Coupling equation Steklov-Poincar´ e operators Defined on Γ × [0 , T ] Solid: S s : u → λ = σ n s Can be computed with existing tools Fluid: S f : u → λ = σ n f Require (non-linear) computation on the whole domain Ω s and Ω f Interface equations Displacement continuity: u f = u s = u Stress equilibrium: S s ( u ) + S f ( u ) = 0 9 / 45
Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI Coupling equation Steklov-Poincar´ e operators Defined on Γ × [0 , T ] Solid: S s : u → λ = σ n s Can be computed with existing tools Fluid: S f : u → λ = σ n f Require (non-linear) computation on the whole domain Ω s and Ω f Interface equations Displacement continuity: u f = u s = u Stress equilibrium: S s ( u ) + S f ( u ) = 0 Solve FSI coupled problem: u − S − 1 Find roots of equation: ( −S f ( u )) = 0 s u = S − 1 Find fix-points of equation: ( −S f ( u )) s 9 / 45
Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI Coupling equation Steklov-Poincar´ e operators Defined on Γ × [0 , T ] Solid: S s : u → λ = σ n s Can be computed with existing tools Fluid: S f : u → λ = σ n f Require (non-linear) computation on the whole domain Ω s and Ω f Interface equations Displacement continuity: u f = u s = u Stress equilibrium: S s ( u ) + S f ( u ) = 0 Solve FSI coupled problem: u − S − 1 Find roots of equation: ( −S f ( u )) = 0 s u = S − 1 Find fix-points of equation: ( −S f ( u )) s 9 / 45
b b Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI DFMT coupling algorithms – Explicit λ −S f S s u ex u 10 / 45
b b Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI DFMT coupling algorithms – Explicit λ −S f ( u ex ) λ ex −S f S s u ex u 10 / 45
b b Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI DFMT coupling algorithms – Explicit λ −S f ( u ex ) λ ex −S f S s u ex u 10 / 45
b b b Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI DFMT coupling algorithms – Explicit λ λ ex −S f S s u N u ex u 10 / 45
b b b Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI DFMT coupling algorithms – Explicit λ λ ex −S f S s −S f ( u N ) λ N +1 u N u ex u 10 / 45
b b b b Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI DFMT coupling algorithms – Explicit λ λ ex −S f S s −S f ( u N ) λ N +1 e N +1 S − 1 ( λ N +1 ) s u N u N +1 u ex u Spurious numerical energy at the interface 10 / 45
b b b b Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI DFMT coupling algorithms – Explicit λ λ ex −S f S s P P u N u N u ex u Spurious numerical energy at the interface Cheap predictor computed at the interface 10 / 45
b b b b b Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI DFMT coupling algorithms – Explicit λ λ ex −S f λ N +1 S s e N +1 P P u N u N u N +1 u ex u Spurious numerical energy at the interface Cheap predictor computed at the interface Function of window size, subproblem time integration schemes and predictors [Piperno & Farhat 99-03] 10 / 45
b b Fluid structure interaction framework Explicit and implicit coupling algorithms for FSI DFMT coupling algorithms – Implicit Block-Gauß-Seidel λ −S f r ( k ) = S s − 1 � λ ( k +1) � u ( k ) �� − u ( k ) S s −S f N +1 λ ( k ) N +1 e ( k ) λ ( k − 1) N +1 u ( k − 2) u ( k − 1) u ( k ) N +1 u ( k +1) u ex u N +1 N +1 N +1 Iterations of the explicit coupling strategy Predictor can be used to reduce the number of iteration No 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 � − 1 M f � � M s � ≤ 1 � � M s structure mass matrix M f 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: Incompressible flow [Arnold, 01; Steindorf, 04] � − 1 M f � � M ⋆ � ≤ 1 � � s “Added Mass”effect [Le Tallec 01, Causin et al. 05, Forster et al. 07] : No explicit coupling Difficulty to make DFMT-BGS algorithm converge M s structure mass matrix M f fluid mass matrix M ⋆ s = M s ( 1 − F ( M f , B f )) B f 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: Incompressible flow [Arnold, 01; Steindorf, 04] � − 1 M f � � M ⋆ � ≤ 1 � � s “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 [K¨ uttler et al. 08] Preconditioning [Quateroni et al. 04] Other algorithm: (In)-Exact Block-Newton [Matthies 06, Dettmer & Peri´ c, Gerbeau 03, Fern´ andez 07] 12 / 45
b b Fluid structure interaction framework Convergence and stability of coupling algorithms Relaxation strategy u u ( k +1) = u ( k ) + ω r ( k ) I ( u ) G ( u ) = S − 1 ( −S f ( u )) s b u ex u (1) u (0) u 13 / 45
b b b Fluid structure interaction framework Convergence and stability of coupling algorithms Relaxation strategy u u ( k +1) = u ( k ) + ω r ( k ) I ( u ) G ( u ) = S − 1 ( −S f ( u )) s b u ex u (1) u (2) u (0) u No relaxation 13 / 45
b b b b Fluid structure interaction framework Convergence and stability of coupling algorithms Relaxation strategy u u ( k +1) = u ( k ) + ω r ( k ) I ( u ) 0 . 2 r (2) G ( u ) = S − 1 ( −S f ( u )) s b u ex u (1) u (2) u (0) u No relaxation Fixed relaxation (used in pressure-velocity coupling) 13 / 45
b b b b b Fluid structure interaction framework Convergence and stability of coupling algorithms Relaxation strategy u u ( k +1) = u ( k ) + ω r ( k ) I ( u ) G ( u ) = S − 1 ( −S f ( u )) s b u ex u (1) u (2) u (0) u No relaxation Fixed relaxation (used in pressure-velocity coupling) Aitken’s relaxation (secant) [K¨ uttler & Wall, 08] 13 / 45
b b b b b b Fluid structure interaction framework Convergence and stability of coupling algorithms Relaxation strategy u u ( k +1) = u ( k ) + ω r ( k ) I ( u ) G ( u ) = S − 1 ( −S f ( u )) s b u ex u (1) u (2) u (0) u No relaxation Fixed relaxation (used in pressure-velocity coupling) Aitken’s relaxation (secant) [K¨ uttler & Wall, 08] Steepest descent (tangent) 13 / 45
Fluid structure interaction framework Convergence and stability of coupling algorithms First summary Partitioned 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 summary Partitioned 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-Poincar´ e 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 summary Partitioned 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-Poincar´ e 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 summary Partitioned 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-Poincar´ e 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 Fluid structure interaction framework 1 Structure and fluid subproblems Explicit and implicit coupling algorithms for FSI Convergence and stability of coupling algorithms Software implementation and validation 2 Component architecture cops Lid driven-cavity with a flexible bottom Oscillating appendix in a flow Applications: 3D computations and interaction with free surface flows 3 Three dimensional computing and paralleling Solving free surface flows Examples: free-surface flows impacting structures 15 / 45
Software implementation and validation Component architecture cops Programming context for partitionned solution procedure λ u Solid Fluid computation computation 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 λ Control u Solid Fluid computation computation 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 λ Control u Solid Fluid computation computation Interpolator 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 λ Control u OpenFOAM FEAP Interpolator 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 λ Control u OpenFOAM FEAP Interpolator 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 λ Control u OpenFOAM FEAP Interpolator 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 λ Control u OpenFOAM FEAP Interpolator 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 λ Control u OpenFOAM FEAP Interpolator 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 λ Control u OpenFOAM FEAP Interpolator 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] e platform (´ Salom´ EDF R&D) 16 / 45
Software implementation and validation Component architecture cops Programming context for partitionned solution procedure Middleware: CTL λ Control u OpenFOAM FEAP Interpolator 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] e platform (´ Salom´ EDF R&D) Software development made by non-programmers 16 / 45
Software implementation and validation Component architecture cops Components implementation and use Middleware: CTL coFeap λ Control u OpenFOAM FEAP Interpolator 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 coXXX λ Control u OpenFOAM FEAP Abaqus Castem,Aster Interpolator 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 coFeap λ Control u OpenFOAM FEAP Interpolator 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 coFeap λ Control u OpenFOAM FEAP Interpolator 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] , Mass transfer [De Sa 08] . . . 17 / 45
Software implementation and validation Component architecture cops Components implementation and use Middleware: CTL coFeap λ Control ofoam u OpenFOAM FEAP Interpolator 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 coFeap λ Control ofoam u OpenFOAM FEAP Interpolator Interpolator Interpolation component: Interpolator [J¨ urgens 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 co ps coFeap λ Control ofoam u OpenFOAM FEAP Interpolator Interpolator COupling COmponents by a Partitioned Strategy: co ps 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 bottom Problem parameters Fluid problem Material properties: ρ f = 1 kg . m − 3 , ν f = 0 . 01 m · s − 2 . Boundary conditions: only ∇ p required v · e x = 1 − cos (2 π t / T char ) Accurate discretization when R e ≤ 300 18 / 45
Software implementation and validation Lid driven-cavity with a flexible bottom Lid-driven cavity with a flexible bottom Problem parameters Fluid problem Material properties: ρ f = 1 kg . m − 3 , ν f = 0 . 01 m · s − 2 . Boundary conditions: only ∇ p required v · e x = 1 − cos (2 π t / T char ) Accurate discretization when R e ≤ 300 Modification for the FSI case ρ s = 500 kg · m − 3 , E s = 250 Pa and ν s = 0 Structure problem: 18 / 45
Software implementation and validation Lid driven-cavity with a flexible bottom Lid-driven cavity with a flexible bottom Problem parameters Fluid problem Material properties: ρ f = 1 kg . m − 3 , ν f = 0 . 01 m · s − 2 . Boundary conditions: only ∇ p required v · e x = 1 − cos (2 π t / T char ) Accurate discretization when R e ≤ 300 Modification for the FSI case ρ s = 500 kg · m − 3 , E s = 250 Pa and ν s = 0 Structure problem: 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 bottom Results Discretization Fluid: 32 x 32 cells. Structure: 16 quadratic elements. Time step: ∆ t = 0 . 1 s . 19 / 45
Software implementation and validation Lid driven-cavity with a flexible bottom Lid-driven cavity with a flexible bottom Results Discretization Fluid: 32 x 32 cells. Structure: 16 quadratic elements. Time step: ∆ t = 0 . 1 s . Perfect benchmark for FSI Mesh simplicity Computational time: T CPU = 2 . 95 × 10 − 3 s and T CPU = 1 . 08 × 10 − 1 s s f Harmonic solution quickly reached 19 / 45
b Software implementation and validation Lid driven-cavity with a flexible bottom Lid-driven cavity with a flexible bottom Explicit results Displacement ( m ) O (1) 0.2 O (∆ t ) O (∆ t 2 ) 0.1 0.0 0 1 2 3 4 5 Time ( s ) Influence of numerical parameters Order of predictor Time step size Time integration of the fluid problem Non-collocated schemes 20 / 45
b Software implementation and validation Lid driven-cavity with a flexible bottom Lid-driven cavity with a flexible bottom Explicit results Displacement ( m ) O (1) 0.2 O (∆ t ) O (∆ t 2 ) 0.1 0.0 0 1 2 3 4 5 Time ( s ) Added mass effect Influence of numerical parameters no explicit coupling when Order of predictor incompressible flow Time step size interacts with structure Time integration of the fluid problem Non-collocated schemes 20 / 45
b Software implementation and validation Lid driven-cavity with a flexible bottom Lid-driven cavity with a flexible bottom Implicit results Numerical parameters Interface residual: � r ( k ) N � 2 ≤ 1 × 10 − 7 All converged computations: same results Displacement ( m ) 0.2 0.1 FEM s +FVM f DFMT-BGS 0.0 0 20 40 60 80 100 Time ( s ) 21 / 45
b Software implementation and validation Lid driven-cavity with a flexible bottom Lid-driven cavity with a flexible bottom Implicit results 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] Displacement ( m ) 0.2 0.1 FEM s +FVM f DFMT-BGS FEM s +SFEM f DFMT-BN FEM s +SFEM f DFMT-BGS 0.0 0 20 40 60 80 100 Time ( s ) 21 / 45
Software implementation and validation Lid driven-cavity with a flexible bottom Lid-driven cavity with a flexible bottom Implicit results – Aitken’s relaxation 30 Iteration – ( k ) 20 10 ω = 0 . 25 Aitken 0 0 20 40 60 80 100 Time ( s ) 22 / 45
Software implementation and validation Lid driven-cavity with a flexible bottom Lid-driven cavity with a flexible bottom Implicit results – Aitken’s relaxation 30 Iteration – ( k ) 20 10 ω = 0 . 25 Aitken 0 0 20 40 60 80 100 Time ( s ) -2 ω = 0 . 25 39 � 2 ) Aitken -3 Res (log 10 � r ( k ) -4 -5 -6 -7 -8 0 10 20 30 Iteration number – ( k ) 22 / 45
Software implementation and validation Lid driven-cavity with a flexible bottom Lid-driven cavity with a flexible bottom Implicit results – Predictors O (1) O (∆ t ) 30 Iteration – ( k ) O (∆ t 2 ) 20 10 0 0 20 40 60 80 100 Time ( s ) -2 O (1) 39 � 2 ) O (∆ t ) -3 O (∆ t 2 ) Res (log 10 � r ( k ) -4 -5 -6 -7 -8 0 10 20 30 Iteration number – ( k ) 23 / 45
Software implementation and validation Lid driven-cavity with a flexible bottom Lid-driven cavity with a flexible bottom Implicit results – Predictors 1 Aitken and predictor O (∆1) 39 ) Aitken and predictor O (∆ t ) Relaxation ( ω ( k ) Aitken and predictor O (∆ t 2 ) 0.8 Fixed relaxation ω = 0 . 25 0.6 0.4 0.2 0 0 5 10 15 Iteration number – ( k ) -2 O (1) 39 � 2 ) O (∆ t ) -3 O (∆ t 2 ) Res (log 10 � r ( k ) -4 -5 -6 -7 -8 0 10 20 30 Iteration number – ( k ) 23 / 45
Software implementation and validation Oscillating appendix in a flow Oscillating appendix Problem presentation 5 . 5 14 . 0 slip: v · n = 0 ρ f , ν f ρ s , E s , ν s 12 . 0 0 . 06 1 . 0 1 . 0 6 . 0 outflow p = 0 y v = v f x slip: v · n = 0 Implicit/Explicit coupling 24 / 45
Software implementation and validation Oscillating appendix in a flow Oscillating appendix Results 25 / 45
Software implementation and validation Oscillating appendix in a flow Oscillating appendix Computation results 1.500 Displacement ( m ) 1.000 0.500 0.000 -0.500 -1.000 -1.500 0 2 4 6 8 10 12 14 Time ( s ) Comparison with other works (Maximum amplitude motion) FEM s +FVM f DFMT-BGS FEM s +SFEM f DFMT-BGS [Wall & Ramm 99] FEM s +SFEM f DFMT-BN [Steindorf & Matthies 02] FEM s +SFEM f Monolithical [Dettmer & Peri´ c 07] 26 / 45
Software implementation and validation Oscillating appendix in a flow Second summary From 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 summary From 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 FSI implementation Implicit coupling required for incompressible flows interacting with structures 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 summary From 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 FSI implementation Implicit coupling required for incompressible flows interacting with structures 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 Fluid structure interaction framework 1 Structure and fluid subproblems Explicit and implicit coupling algorithms for FSI Convergence and stability of coupling algorithms Software implementation and validation 2 Component architecture cops Lid driven-cavity with a flexible bottom Oscillating appendix in a flow Applications: 3D computations and interaction with free surface flows 3 Three dimensional computing and paralleling Solving free surface flows Examples: free-surface flows impacting structures 28 / 45
Applications Three dimensional computing and paralleling Performances and paralleling Middleware: CTL co ps coFeap λ Control ofoam u OpenFOAM FEAP Interpolator Interpolator Lid-cavity T CPU : Structure 3%, Fluid 96% and Interpolation 1%. 29 / 45
Applications Three dimensional computing and paralleling Performances and paralleling Middleware: CTL co ps ofoam coFeap λ Control ofoam u ofoam OpenFOAM FEAP ofoam Interpolator Interpolator ofoam Lid-cavity T CPU : 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
rs rs rs rs rs rs rs Applications Three dimensional computing and paralleling Performances and paralleling 32 16 Speed-up ( χ ) 8 4 2 1 1 2 4 8 16 32 64 Processor Number ( N ) 29 / 45
b b b Applications Three dimensional computing and paralleling Three-dimensional“flag”in the wind Problem parameters outflow slip inflow 3 . 0 C B 4 . 0 A 3 . 0 10 . 0 5 . 0 1 . 0 5 . 0 1 . 04 . 0 5 . 0 Numerical parameters Implicit DFMT-BGS coupling Interface: � r ( k ) N � 2 ≤ 1 × 10 − 7 150 × 10 3 or 1 . 2 × 10 6 d-o-f, 6 × 10 3 time step Discretization: Paralleling of the fluid sub-problem 30 / 45
b b b Applications Three dimensional computing and paralleling Three-dimensional“flag”in the wind Problem parameters outflow slip inflow 3 . 0 C B 4 . 0 A 3 . 0 10 . 0 5 . 0 1 . 0 5 . 0 1 . 04 . 0 5 . 0 Numerical parameters Implicit DFMT-BGS coupling Interface: � r ( k ) N � 2 ≤ 1 × 10 − 7 150 × 10 3 or 1 . 2 × 10 6 d-o-f, 6 × 10 3 time step Discretization: Paralleling of the fluid sub-problem 30 / 45
Applications Three dimensional computing and paralleling Three-dimensional“flag”in the wind Computation results A 0.6 Displacement ( d y in cm ) B C 0.4 0.2 0 -0.2 -0.4 -0.6 0 1 2 3 4 5 6 Time ( s ) First flexion mode 31 / 45
Applications Three dimensional computing and paralleling Three-dimensional“flag”in the wind Computation results FEM s +SFEM f DFMT-BGS 0.6 Displacement ( d y in cm ) C 0.4 0.2 0 -0.2 -0.4 -0.6 0 1 2 3 4 5 6 Time ( s ) First flexion mode Different from the torsional mode observed [von Scheven, 09] Complex flow, different structure model, sensitivity to initial condition. . . 31 / 45
Recommend
More recommend
