Motivations and Framework Non Linear & MultiPhysics RB Applications Conclusions References Reduced basis methods and high performance computing. Applications to non-linear multi-physics problems Christophe Prud’homme prudhomme@unistra.fr Cemosis - http://www.cemosis.fr IRMA Université de Strasbourg 15 avril 2014 C. Prud’homme RB & HPC
Motivations and Framework Non Linear & MultiPhysics RB Applications Conclusions References 1 Motivations and Framework 2 Reduced Basis for Non-Linear Problems and Extension to Multiphysics 3 Applications 4 Conclusions C. Prud’homme RB & HPC
Motivations and Framework Non Linear & MultiPhysics RB Applications Conclusions References Collaborators on the framework Non-intrusive RB • Cecile Daversin (IRMA - UdS, • Rachida Chakir (LJLL - Strasbourg and CNRS/LNCMI, UPMC, Paris) Grenoble) • Yvon Maday (LJLL - • Christophe Prud’homme (IRMA - UdS, UPMC, Paris) Strasbourg) • Alexandre Ancel (IRMA - UdS, Current Funding Strasbourg) ANR/CHORUS, • Christophe Trophime (CNRS/LNCMI, ANR/HAMM, Grenoble) FRAE/RB4FASTSIM, ANR/Vivabrain, Labex • Stephane Veys (LJK - UJF, Grenoble) IRMIA, IDEX and former collaborators : S. Vallaghe, E. Schenone. C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References Motivations and Framework C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References OPUS Heat Transfer Benchmark C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References Thermal Testcase Description y Hot air outflow Overview Γ 3 • Heat-Transfer with conduction Ω 43 and convection possibly coupled Ω 4 ( Air ) = ∪ 4 i = 1 Ω 4 i e IC with Navier-Stokes • Simple but complex enough to Γ 32 = Γ 23 Ω 2 ( IC 2 ) h IC = Ω 2 ∩ Ω 3 contain all difficulties to test the certified reduced basis x 2 Γ 1 Γ 2 h PCB Ω 42 Ω 44 • non symmetric, non e IC compliant Γ 1 • steady/unsteady Γ 31 = Γ 13 Ω 1 ( IC 1 ) h IC = Ω 1 ∩ Ω 3 • physical and geometrical parameters x 1 Ω 41 Ω 3 ( PCB ) • coupled models Γ 4 x • Testcase can be easily e PCB e a complexified Cooling air inflow (fan) C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References Thermal Testcase Description y Hot air outflow Heat transfer equation Γ 3 Ω 43 � ∂ T � ∂ t + v ·∇ T −∇· ( k i ∇ T ) = Q i , Ω 4 ( Air ) = ∪ 4 i = 1 Ω 4 i ρ C i e IC i = 1 , 2 , 3 , 4 Γ 32 = Γ 23 Ω 2 ( IC 2 ) h IC = Ω 2 ∩ Ω 3 Inputs x 2 h PCB Γ 1 Γ 2 Ω 42 Ω 44 µ = { e a ; k Ic ; D ; Q ; r } . e IC Γ 1 Γ 31 = Γ 13 Ω 1 ( IC 1 ) h IC Outputs = Ω 1 ∩ Ω 3 � 1 x 1 Ω 41 s 1 ( µ ) = T Ω 3 ( PCB ) e IC h IC Γ 4 Ω 2 x � e PCB e a s 2 ( µ ) = 1 T e a Cooling air inflow (fan) Ω 4 ∩ Γ 3 C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References Thermal Testcase Description y Hot air outflow Fluid model Γ 3 Poiseuille flow or Navier-Stokes flow Ω 43 Ω 4 ( Air ) = ∪ 4 i = 1 Ω 4 i e IC Boundary conditions • on Γ 3 ∩ Ω 3 , a zero flux Γ 32 = Γ 23 Ω 2 ( IC 2 ) h IC = Ω 2 ∩ Ω 3 • on Γ 3 ∩ Ω 4 , outflow x 2 Γ 1 Γ 2 h PCB • on Γ 4 , ( 0 ≤ x ≤ e Pcb + e a , y = 0 ) Ω 42 Ω 44 e IC temperature is set Γ 1 • Γ 1 and Γ 2 periodic Γ 31 = Γ 13 Ω 1 ( IC 1 ) h IC = Ω 1 ∩ Ω 3 • at interfaces between the ICs and x 1 Ω 41 PCB, thermal discontinuity Ω 3 ( PCB ) (conductance) Γ 4 x e PCB e a • on other internal boundaries, the continuity of the heat flux and Cooling air inflow (fan) temperature C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References Thermal Testcase Description Finite element method y Hot air outflow • P k , k = 1 , ..., 4 Lagrange elements Γ 3 • Weak treatment of Dirichlet Ω 43 conditions Ω 4 ( Air ) = ∪ 4 i = 1 Ω 4 i e IC • CIP Stabilisation • Locally Discontinuous FEM Γ 32 = Γ 23 Ω 2 ( IC 2 ) h IC = Ω 2 ∩ Ω 3 functions x 2 h PCB Γ 1 Γ 2 Validation Ω 42 Ω 44 e IC • Comparison between Γ 1 Comsol(EADS) and Feel++ Γ 31 = Γ 13 Ω 1 ( IC 1 ) h IC = Ω 1 ∩ Ω 3 • Extensive testing and comparisons x 1 Ω 41 • Implementation validated, ref. Ω 3 ( PCB ) Γ 4 config. max rel error < 1% x e PCB e a • Diff. : mesh, stabilisation, Dirichlet Cooling air inflow (fan) C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References Thermal Testcase Description y Hot air outflow Γ 3 Ω 43 Ω 4 ( Air ) = ∪ 4 i = 1 Ω 4 i e IC Γ 32 = Γ 23 Ω 2 ( IC 2 ) h IC = Ω 2 ∩ Ω 3 x 2 h PCB Γ 1 Γ 2 Ω 42 Ω 44 e IC Γ 1 Γ 31 = Γ 13 Ω 1 ( IC 1 ) h IC = Ω 1 ∩ Ω 3 x 1 Ω 41 Ω 3 ( PCB ) Γ 4 Figure : Temperature plot for x e PCB e a e a ∈ { 2 . 5 e − 3 , 8 e − 3 , 5 e − 2 } Cooling air inflow (fan) C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References Chorus Aerothermal Flow Benchmark C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References Aerothermic : air conditioning/environment control systems y 1 • Steady Navier-Stokes/Heat Γ 4 Γ f transfer problem T 0 Γ 1 Γ 3 Heat flux Ω( Fluid ) • 2 parameters : Grashof and Γ 2 Prandtl number 0 W • Study the average temperature x 0 W on heated surface with respect to parameters Figure : Geometry of the 2D model. Consider an extrusion of this geometry • Application to aerothermal in 3D case is the extrusion in z axis of studies (buildings, cars, airplane length 1. cabins,...) C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References Aerothermic : air conditioning/environment control systems • Steady Navier-Stokes/Heat transfer problem • Coupling 2D/3D mesh based aerothermal model with ECS modelica model • ECS and A/C design Figure : Design and sizing of thermal parameters to be optimized control of avionic bay and cabin (a) Airplane Cabin (b) Airplane Bay (c) 2D temperature iso- surfaces C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References HiFiMagnet project High Field Magnet Modeling C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References Laboratoire National des Champs Magnétiques Intenses Large scale user facility in France • High magnetic field : from 24 T • Grenoble : continuous magnetic field (36 T) • Toulouse : pulsed magnetic field (90 T) Application domains Magnetic Field • Magnetoscience • Earth : 5 . 8 · 10 − 4 T • Solide state physic • Supraconductors : 24 T • Chemistry • Continuous field : 36 T • Biochemistry • Pulsed field : 90 T Access • Call for Magnet Time : 2 × per year • ≈ 140 projects per year C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References High Field Magnet Modeling C. Prud’homme RB & HPC
Motivations and Framework Introduction Non Linear & MultiPhysics RB Feel++ Applications Features Conclusions High Performance Computing References Why use Reduced Basis Methods ? Challenges • Modeling : multi-physics non-linear models, complex geometries, genericity • Account for uncertainties : uncertainty quantification, sensitivity analysis • Optimization : shape of magnets, robustness of design Objective 1 : Fast Objective 2 : Reliable • Complex geometries • Field quality • Large number of dofs • Design optimization • Uncertainty quantification • Certified bounds • Large number of runs • Reach material limits C. Prud’homme RB & HPC
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