Predictive Engineering and Computational Sciences. Full System Simulations. Algorithms and Uncertainty Quantification. Roy H.

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1 PECOS Predictive Engineering and Computational Sciences Full System Simulations Algorithms and Uncertainty Quantification Roy H. Stogner The University of Texas at Austin October 12, 2011 Roy H. Stogner FSS October 12, / 26

2 Outline 1 Introduction 2 Forward Uncertainty Propagation Convergence 3 Goal-Oriented Refinement Theory Current Results Roy H. Stogner FSS October 12, / 26

3 Introduction Traditional Validation Calibration Data Stage 1: Maps Calibration Data to Validation Observables Model with unknown parameter(s) Calibration Process Calibrated Parameter(s) Model Evaluation Observables Challenge Experimental Validation Data Roy H. Stogner FSS October 12, / 26

4 Introduction Bayesian Validation in the Context of the QoI Stage 1: Maps Calibration Data to QoI Intervene Calibration Data Model with unknown parameter(s) m Bayesian Inference Calibrated Parameter(s) m c Model Evaluation Q c Model rejected No M(Q c,q v) < γ Stage 2: Maps Validation Data to QoI - Traditional Validation is Embedded Yes Model with parameter(s) m Model Evaluation Bayesian Inference Challenge Validation Data Model Evaluation Q v Model not rejected Roy H. Stogner FSS October 12, / 26

5 Introduction Atmospheric Reentry Problem High enthalpy aerothermochemistry, hypersonic flow Surface pyrolysis, ablation, radiation Unreliable models (turbulence, ablation, carbon chemistry) Roy H. Stogner FSS October 12, / 26

6 Introduction Calibrated Uncertainty Quantification QoI Multiphysics Analysis Forward FIN-S QUESO/Dakota Calibration/Validation Turbulence Chemistry/Shocktube Ablation Inversion FIN-S libmesh Boost SHOCKING MUTATION GSL Plug Flow ABLATION1D GSL QUESO MASA GRVY External Libraries LDV Flow Measurements NASA EAST Molecular Beam (O 2 ) Shocktube Heated Flow Titration (N Measurements 2 ) Experimental Data Roy H. Stogner FSS October 12, / 26

7 Introduction Ablator Nitridation Uncertainty ṁ kb T N,c = ρy N β N (T ) 2πm N Ma = 31 q r ad q cond Pyrolysis Gas Flow q chem= q r e r ad ṁ g h g Shock Layer ṡ P N s i =1 J i h i Char Pyrolysis Zone Boundary Layer Virgin Material ṁ (( ch = ρ chṡ Substrate C100H89.4O17.8N8(SiO2)64.2 Nitridation coefficient β N Value from initial literature survey: 0.3 Disagreement, uncertainty range: ( , 0.4) Highest predicted submodel uncertainty contribution Calibrated mean: Calibrated std dev: Roy H. Stogner FSS October 12, / 26

8 Introduction Nitridation Coefficient Calibration Laboratory Investigation of Active Carbon Nitridation by Atomic Nitrogen, Zhang et. al. Roy H. Stogner FSS October 12, / 26

9 Introduction Reaction Chemistry Uncertainty ( ) T n k = A e Ea RT T 0 N + e N + + 2e O + e O + + 2e N 2 + N 2N + N N 2 + N 2 2N + N 2 N 2 + e 2N + e NO + O O 2 + N N 2 + O NO + N T N2 = (T (1 q) tr Tve) q T O2 = (T (1 q) tr Tve) q Uncertain Reaction Rates Arrhenius pre-exponential uncertainty: +/- 1 OOM Strong output sensitivities to N 2 + O, NO + O reactions Joint calibration Details: Marco Panesi s talk Roy H. Stogner FSS October 12, / 26

10 Introduction Reaction Chemistry Calibration Electric Arc Shock Tube (EAST) Spectroscopy Roy H. Stogner FSS October 12, / 26

11 Introduction Turbulence Model Uncertainty A Priori Uncertainty Algebraic (Baldwin-Lomax) model, no transition model Scalar Turbulence augmentation factor Uncertainty range: (0, 1.5) Second greatest contribution to output uncertainty Calibrated Uncertainty Spalart-Allmaras PDE-based model Joint calibration, 8 uncertain parameters Multi-model Bayesian validation Details: Todd Oliver s talk Roy H. Stogner FSS October 12, / 26

12 Introduction Turbulence Model Calibration Bowersox Supersonic BL data Direct Numerical Simulation u [m/s] Luker (2000) y [m] Future UT experiments: near-wall Particle Image Velocimetry measurements Roy H. Stogner FSS October 12, / 26

13 Forward Uncertainty Propagation Latin Hypercube and Calibration LHS Quantile bins in each parameter 1 sample per bin Reduce variance from additive response components Calibrated joint PDFs are not separable tensor products! LHS+MCMC LHS for uncalibrated variables SRS from each calibrated joint distribution Roy H. Stogner FSS October 12, / 26

14 Forward Uncertainty Propagation Convergence Off-baseline Samples Unsteady Residual ISS Offbaseline Convergence - Dataset 270 du/dt t Iteration N Time Step [s] Convergence Large initial transients Secondary transient spike Change propagation? No tertiary spikes 6 OOM convergence stall Vibrational energy stabilization Reaction stabilization? Roy H. Stogner FSS October 12, / 26

15 Forward Uncertainty Propagation Convergence Off-baseline QoI Convergence QoI Value 10 5 QoI t ISS Offbaseline Convergence - Dataset Iteration N Time Step [s] Ablation Rate Convergence Immediate change from baseline Less rapid change until transient spike New value after transient spike Within tolerance: 250 time steps Roy H. Stogner FSS October 12, / 26

16 Forward Uncertainty Propagation Convergence Calibrated Forward Propagation Results UQ Output More than 2 lower mean ablation mass loss than with uncalibrated submodels Primary driver: 100 lower nitridation coefficient than initial prior UQ Performance Latin Hypercube Paradox: Significant parameters are calibrated; LHS convergence is unavailable Other parameters are insignificant; LHS convergence is irrelevant LHSD methods may still show some improvement over SRS Performance 10 improvement in transient convergence 4 increase in wall clock time Roy H. Stogner FSS October 12, / 26

17 Goal-Oriented Refinement Theory Adjoint Refinement Error Estimator Error Estimators e Q Q(ũ h ; ξ) Q(ũ; ξ) R(ũ h, z; ξ) = e Q R Q + R R RQ and R R : higher order, often quadratic in ũ ũ h. R(ũ h, z h ; ξ) = 0 Higher order approximation of z: Project ũ h to a refined space Jacobian calculation, linear adjoint solve on refined mesh Residual evaluation on refined mesh No nonlinear solve on refined mesh Asymptotically bounded effectivity Improved QoI estimates Element-by-element QoI contributions Roy H. Stogner FSS October 12, / 26

18 Goal-Oriented Refinement Theory Adjoint Residual Error Indicator Error Indicators Efficiently bounding e Q via per-element terms From our error estimator, R(ũ h, z; ξ) = R E (ũ h E, z E ; ξ) E z h is cheaper than higher order approximation of z Ignoring higher order terms: q q h = R u (ũ, z z h ; ξ)(ũ ũ h ) q q h Ru B(U,V ) ũ ũ h U z z h V q q h R E u B(U E,V E ) ũ E ũ h E U z E E z h E V E E Roy H. Stogner FSS October 12, / 26

19 Goal-Oriented Refinement Theory Adjoint Residual Error Indicator AdjointResidualErrorEstimator Procedure Calculate equal-order adjoint solution z h Use existing (patch recovery) estimators for ũ ũ h and z z h on each element Combine element-by-element AdjointResidualErrorEstimator Limitations Asymptotic overestimate No estimation of R E u Would require local DenseMatrix inversion, multiplication, 2-norm estimate Roy H. Stogner FSS October 12, / 26

20 Goal-Oriented Refinement Current Results Shock Simulation with Goal-Oriented AMR Shock Hanging Nodes Shock thickness h No artificial transverse velocity No ringing, overshoot, instability Immediate δt reduction required Rapid δt growth possible Reconvergence: 6 OOM in time steps Fully automatic convergence from very coarse meshes? Roy H. Stogner FSS October 12, / 26

21 Goal-Oriented Refinement Current Results Viscous Boundary Layer with Goal-Oriented AMR Boundary Layer Hanging Nodes Stress test: Ungraded boundary layer Underresolved viscous fluxes Valid initial refinement step Subsequent refinements: Coarse elements currently overestimate convective flux Fine element equilibrium temperature drops Peak surface value QoI location moves Wasteful overrefinement downstream Roy H. Stogner FSS October 12, / 26

22 Goal-Oriented Refinement Current Results Viscous Boundary Layer with Goal-Oriented AMR Boundary Layer Improvements Primal Stabilization: Full viscous terms in DCO In testing, Benjamin Kirk Adjoint Regularization: DCO-aware suberror estimates Mesh-aware forcing term for peak value QoI derivatives Smoothed adjoint forcing term for peak value QoI derivatives Standard practice, a priori graded boundary layer meshes Doctor, it hurts when I do this Roy H. Stogner FSS October 12, / 26

23 Goal-Oriented Refinement Current Results Shock Patch Recovery: Primal Error Estimation Shock Layer Error: True Error: Discontinuity Capturing Operator Artificial Diffusion Partitioning Independent Local Error Estimates: H 1 Patch Recovery Partitioning Dependent Shock narrowing decreases error, increases estimate! Roy H. Stogner FSS October 12, / 26

24 Goal-Oriented Refinement Current Results Shock Patch Recovery: Primal Error Estimation Shock Layer Improvements Improved Local Estimates: L2 Patch Recovery Partitioning-independent Patch Recovery Multiphysics-aware weighting Refined adjoint test functions Roy H. Stogner FSS October 12, / 26

25 Goal-Oriented Refinement Current Results Continuing Work Uncertainty Quantification Adjoint-enhanced control variate surrogates Uncertain parameters exposed to internal perturbation Algorithms Goal-oriented adaptivity verification AMR with coarse initial elements Hanging nodes on curved 3D boundaries Optimizations Analytic derivatives replacing finite differencing in boundary Jacobians Weighting load balancing in partitioning Caching common subcalculations Roy H. Stogner FSS October 12, / 26

26 Goal-Oriented Refinement Current Results Thank you! Questions? Roy H. Stogner FSS October 12, / 26