Assessing Uncertainties in Radiative Shock Modeling James Paul Holloway University of Michegan...
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![Page 1: Assessing Uncertainties in Radiative Shock Modeling James Paul Holloway University of Michegan Joslin Goh, Mike Grosskopf, Bruce Fryxell, Derek Bingham.](https://reader035.fdocuments.in/reader035/viewer/2022062511/551b358955034607418b65ed/html5/thumbnails/1.jpg)
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
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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
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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
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System is observed with x-ray radiography
1 ns, 3.8 kJ laser irradiates Be disk
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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
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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
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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
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2D CRASH can predict shock location fairly well
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2D CRASH can predict shock location fairly well
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Selection of output matters a lot for calibration
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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
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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
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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
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Leave one out predictions of BOT
1D sims
2D sims
Measurement
Tuned 1D
Tuned 2D
Tuned prediction
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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
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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
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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
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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
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Leave one out predictions tell us how we are doing
2008 SL experiments 2009 BOT experiments
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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
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How do we launch the shock?
300 times too slow
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Calibrated onbreak out time