© Copyright Cenaero 2009 – All rights reserved

EXCELLENCE IN SIMULATION TECHNOLOGIES

Development and Application of Partioned Methods for Large Scale FSI Problems

Philippe GeuzaineCFD-MP Group, Cenaero

Email: philippe.geuzaine@cenaero.be

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Sample Targeted Applications

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Unsteady Aeroelastic Response

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Four-field Formulation

Heat Transfer Fluid (ALE)

Structure Fluid Mesh

Temperature(Displacements) Force Mesh Motion

TemperatureHeat flux

DisplacementsVelocities

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Aero- & Elasto-Dynamic Data Exchange

• Interpolation across non matching interfaces (accuracy and conservation)

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Exchange With Non-Matching Interfaces

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Example of Displacement Exchange

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Data Exchange & Code Coupling

• Dynamic data communication between CSD and CFD modules

• Available tools (integration platforms) for interpolation and/or data communication– MpCCI (Fraunhofer Institute SCAI)– MDICE (CFD RC)– SimServer (EADS)– PALM (CERFACS)– CALCIUM (EDF)– SALOME (EDF/CEA)– ...

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Fluid Mesh Motion

• Spring-type analogy• No node collapse• No face penetration• Mesh recovery

(after one oscillation cycle)• Mesh shearing?

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CFD on Moving Grids

• Navier-Stokes equations on fixed grids

• Arbitrary Lagrangian Eulerian (ALE) formulation on moving grids

• The discrete geometric conservation law (DGCL) can guide the selection among the multiple accuracy preserving ALE extensions

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Additional Issues for Nonlinear FSI

• Non specific issues (CAD to mesh generation, turbulence modeling, nonlinear structural effects modeling, ...)

• Modularity & compatibility with existing tools (plug-and-play/off-the-shelf approach)

• Speed & turnaround time– Second-order accurate & robust coupled time-

integration for large time-steps– Parallel computing

• Verification & validation

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Monolithic Schemes for Coupled Systems

• Single time-integrator (system of first-order semi-discrete equations)

• Solution at the nonlinear level (single set of equations for fluid, fluid mesh and structure)– Newton type method

• Solution at the linear level (very large system)– Single approach (direct, iterative)– Partioned or staggered approach (block Jacobi, block

Gauss-Seidel)

• Appealing for accuracy and stability, but issues for software modularity

• Demonstrated usually for academic problems

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Partioned Schemes for Coupled Systems

• Collocated staggered approach

• Loosely-coupled scheme (maximize efficiency)• Strongly-coupled scheme (similar monolithic)

CSD

CFD

CFD Mesh

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Individual Time-integrator Selection

• Second-order accurate time-integrators (necessary condition to achieve second-order time-accuracy for the coupled system)

• Newmark scheme (with the equilibrium written at time level tn+1) for the CSD solver (no mass or stiffness matrices exported from the CSD solver)

• ALE version of the three-point backward difference scheme for the CFD solver (not trivially second-order time-accurate on moving meshes)

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Sample Predictors and Correctors

• Structural displacement predictor

• Aerodynamic force corrector

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Control Parameters Design

• Control parameters– Structural displacement predictor– Mesh integrator– Aerodynamic force corrector

• Preserve second-order time-accuracy of individual time-integrators (three-point backward difference and Newmark schemes)

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AGARD 445.6 Wing Configuration

• Nonlinear flow model (inviscid Argo model)• Linear structural model (SAMCEF Mecano model)• Steady & unsteady aeroelastic analyses• Flutter analysis

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CFD Meshes

22,014 points

178,938 points

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Steady Simulation

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Unsteady Simulations

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Time-Accuracy Analysis

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Unsteady Simulations with P/C

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Unsteady Simulations with Large Δt

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AGARD 445.6 Wing Flutter Analysis

• Flow conditions: 0.5 < M < 1.141 (zero incidence)• Density taken from Yates’ experiment• Pressure adjusted to produce flutter• Coupling time-step Δt = 1 ms• Flutter index definition

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Response at Mach = 0.957

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Flutter Frequency

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Flutter Index

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CAD-based Wing MDO

CAD : CATIAV5

AutomaticMesh Generation

Parallel Aeroelastic Computation

Argo + Samcef

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Optimization Workflow with Minamo

UserUserSpecifications

Approximate ModelANN, RBF, Kriging, …

OptimizationOptimizationEA, gradient-based, …

Performance Check

DATABASEDATABASE

Accurate Model Accurate Model CFD / Structure / Exp. / ...

END

ONLINE modeling

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Simulation Workflow with Argo/Samcef

Design Variables

Inviscid Aeroelastic Computation

CFD CSD

Wing Deformed Shape

Viscous Computation

CFD

Lift & dragStress, buckling,tip displacement

CAD generation& meshing

Meshing with Boundary Layers

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Wing Parameterization

Tip chord

Root chord

Span

Sweep angle

twist

Angle ofattack

3 spars

10 ribs

Stringers 1 Stringer

s 2 Stringers 3 Stringer

s 4 Stringers 5

Panels 1 Panels

2Panels

3

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Optimized Stringers and Planform

• Objective: wing mass reduction• Constraints: L/D, stress, buckling

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Future Work on Supersonic Transport

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Aerothermoelasticity Challenge at Mach 5