Assessing Uncertainties in Radiative Shock Modeling

1. Assessing Uncertainties in Radiative Shock Modeling Michigan James Paul HollowayUniversity of Michegan JoslinGoh, Mike Grosskopf, Bruce Fryxell, Derek Bingham Uncertainty in Computer Modeling – Sheffield 2012 Supported by DOE NNSA/ASC under the Predictive Science Academic Alliance Program DEFC52-08NA28616

2. Shock waves become radiative when … • radiative energy flux would exceed incoming material energy flux • Setting these fluxes equal gives a threshold velocity of 60 km/s for our system: unshocked preheated Ts4 ∝ us8ous3/2 shocked Material xenon gas Density 6.5 mg/cc Initial shock velocity 200 km/s Initial ion temperature 2 keV Typ. radiation temp. 50 eV

3. The CRASH problem in the lab 1 ns, 3.8 kJ laser irradiates Be disk Launches shock at 200km/s through Be into Xe-filled tube ~4mm longand .6 to 1.2 mm diameter Shock reaches 2 mm in 20 ns

4. System is observed with x-ray radiography 1 ns, 3.8 kJ laser irradiates Be disk

5. We have several outputs & inputs • Outputs ( ) • Shock location • Shock breakout time • Wall shock location • Axial centroid of Xe • Area of dense Xe • Inputs ( ) • Observation time • Laser energy • Be disk thickness • Xe fill gas pressure • Tube geometry • Calibration parameters () • Vary with model • Electron flux limiter • Laser scale factor … Shock location Wall shock location Area of dense Xe Fixed window Centroid of dense Xe

6. We can measure and we can compute 600 µm 1200 µm Circular Elliptical tube tube nozzle nozzle 26 ns gray Goal is to predict outputs for elliptical tube and uncertainty, without using any data from elliptical tube experiments 13 ns MG

7. We need to move models into new regions of input Variability in true response Measurements pdf at desired input x Simulator response True mean response Note: measurement might be of secondary response! x

8. 2D CRASH can predict shock location fairly well

9. 2D CRASH can predict shock location fairly well

10. Selection of output matters a lot for calibration

11. Tales from the trenches • We challenge the measurements in ways the surprise, but seldom delight, the experimental team • We stress the code in ways the surprise, but seldom delight, the code developer and modeling team • Explorations of extrapolation – calibrating with one data set and predicting in an unexplored region of input, or predicting a different output • Exploration of combining models – calibrating across model fidelity

12. Do we understand the uncertainty in inputs? Note day-to-day uncertainty vs. within day uncertainty Omega laser energy has unexpected variability Raises an argument: what is prediction? Omega improved in response to this… but

13. Calibrating across two simulation codes • We have 1024 BOT from 1D simulations • We have 104 BOT from 2D simulations • Can we combine these 1D and 2D runs? • Note that the 1D code and 2D code have: • Some thetas that are the same: electron flux limiter • Some that are different: • 1D – Laser Energy Scale Factor • 2D – Be-Gamma and Plastic Opacity Scale Factor • Need a model structure to combine these

14. Combining two simulation codes Common theta values put in 1D code 1D-theta tuned to 2D code Theta values put in 1D code only Theta values in 2D code only Tuned values of theta

15. Leave one out predictions of BOT Tuned prediction Tuned 1D Tuned 2D 1D sims Measurement 2D sims

16. We have learned a few things… • The distributions of inputs are often not well known, and are not fixed… • Quantities that calibrate well in one model might not in another (e.g. EFL in 1D vs. 2D) • Calibration on one output may be very different from calibration on another. This is a physics problem. • We need ways to extrapolate from one region of input to another. Physics should help with this. • There is a real need to combine models when neither is “better” • Culture change matters. More important than tools

17. Thanks!

18. Our primary goal is to predict QOI in the oval tube • Use all available simulations &field data from circular tubes to create predictive interval for shock location in oval tube • Perform O(10) experiments on the nominal target design and confirm that expected fraction the observations are within predicted interval • Oval tube field data will never be used for predictive model construction • Discrepancy is assumed independent of eccentricity & nozzle geometry • Necessary to transfer discrepancy from circular tubes to oval tubes in absence of field measurements • We will have only a few field experiments with a circular nozzle

19. Convergence study (RS5) • Most parameters showed no problem • But spatial mesh and number of groups raised concerns and show interaction • Identified need toimprove several aspects of solver: • treatment of electron/photon coupling • preconditioner efficiency Code improved in response to this

20. Model 1: Predicting SL at 20 and 26 ns Calibration usingBreakout Time(BOT) small model calibrates AssessingShock Location (SL) prediction Prediction andestimate ofuncertainty Move discrepancy andreplication error to newregion of inputs

21. Leave one out predictions tell us how we are doing 2009 BOT experiments 2008 SL experiments

22. We can now compare with measurement Median Shock Location • 2750 mm2741 mm@ 20 ns • 3200 mm3442 mm@ 26 ns

23. Predictive intervals for shock locations (4 examples) • This demonstrates the ability to combine models • We will be combining 2D, 3D, Gray and Multigroup models to predict the oval tube experiment 1D 2D Full Model 2D calibrated 1D calibrated Field

24. How do we launch the shock? 300 times too slow

25. Calibrated on break out time