Assessing Uncertainties in Radiative Shock

ModelingJames Paul Holloway

University of Michegan

Joslin Goh, 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

Michigan

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:

Material xenon gas

Density 6.5 mg/cc

Initial shock velocity 200 km/s

shockedunshockedpreheated

Ts4 u∝ s

8 ous3/2

Initial ion temperature 2 keV

Typ. radiation temp. 50 eV

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 long and .6 to 1.2 mm diameter

Shock reaches 2 mm in 20 ns

System is observed with x-ray radiography

1 ns, 3.8 kJ laser irradiates Be disk

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

Centroid of dense Xe

Area of dense Xe

Fixed window

Wall shock location

We can measure and we can compute

600 µm 1200 µm Circular Ellipticaltube tube nozzle nozzle

13 ns MG

26 ns gray

Goal is to predict outputs for elliptical tube and uncertainty, without using any data from elliptical tube experiments

We need to move models into new regions of input

Measurements

Variability in true response

True mean response

Simulator response

pdf at desired input x

x

2D CRASH can predict shock location fairly well

2D CRASH can predict shock location fairly well

Selection of output matters a lot for calibration

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

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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

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

Combining two simulation codes

Theta values put in 1D code only

Common theta values put in 1D code

1D-theta tuned to 2D code

Theta values in 2D code only

Tuned values of theta

Leave one out predictions of BOT

1D sims

2D sims

Measurement

Tuned 1D

Tuned 2D

Tuned prediction

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

Thanks!

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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

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

Calibration usingBreakout Time(BOT)

Model 1: Predicting SL at 20 and 26 ns

AssessingShock Location (SL) prediction

Prediction andestimate ofuncertaintyMove discrepancy and

replication error to newregion of inputs

small model calibrates

Leave one out predictions tell us how we are doing

2008 SL experiments 2009 BOT experiments

We can now compare with measurement

Median ShockLocation

• 2750 mm2741 mm @ 20 ns

• 3200 mm3442 mm@ 26 ns

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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

1D c

alib

rate

d

2D c

alib

rate

d

Ful

l Mod

el

Fie

ld

How do we launch the shock?

300 times too slow

Calibrated onbreak out time