Post on 15-Aug-2021
PECOSPredictive Engineering and Computational Sciences
Full System Simulation Progress
Roy H. Stogner
The University of Texas at Austin
October 17, 2012
Stogner 2012 FSS October 17, 2012 1 / 27
Outline
1 Prior Work
2 New Formulations
3 New Models
4 New Calibrations
5 New Results
6 Ongoing Work
Stogner 2012 FSS October 17, 2012 2 / 27
Prior Work
1 Prior Work
2 New Formulations
3 New Models
4 New Calibrations
5 New Results
6 Ongoing Work
Stogner 2012 FSS October 17, 2012 3 / 27
Prior Work
Full System Uncertainties
• High enthalpy aerothermochemistry, hypersonic flow
• Model uncertainties (turbulence, nitridation, kinetics)
• Numerical unknowns (discretization, UQ error)
• Modeling unknowns (missing/wrong physics)
Stogner 2012 FSS October 17, 2012 4 / 27
Prior Work
2010-2011 Model Calibrations
Ablator Nitridation Uncertainty• Probability of C(s)+N(g) => CN(g) at surface
• 4 OOM Prior Uncertainty range in literature
• βN sensitivity enormous in prior, negligible after calibration
Air Reaction Chemistry Uncertainty• Strong output sensitivities to N2 + O, NO + O reactions
• Calibration via shock tube spectroscopy
Turbulence Model Uncertainty• Prior “Turbulence augmentation” uncertainty: 0− 150% range
• Posterior: 8-parameter Spalart-Allmaras calibrated againstsupersonic boundary layer data, DNS
Stogner 2012 FSS October 17, 2012 5 / 27
New Formulations
1 Prior Work
2 New Formulations
3 New Models
4 New Calibrations
5 New Results
6 Ongoing Work
Stogner 2012 FSS October 17, 2012 6 / 27
New Formulations
Stabilized Navier-Stokes
∂U
∂t+∂F i
∂xi=∂Gi
∂xi+ S
Find U satisfying the essential boundary and initial conditions such that∫Ω
[W ·
(∂U
∂t− S
)+∂W
∂xi·(Kij
∂U
∂xj−AiU
)]dΩ
+
nel∑e=1
∫Ωe
τSUPG∂W
∂xk·Ak
[∂U
∂t+Ai
∂U
∂xi− ∂Gi
∂xi− S
]dΩ
+
nel∑e=1
∫Ωe
νDCO
(∂W
∂xi· gij ∂U
∂xj
)dΩ−
∮ΓW · (g − f) dΓ = 0
for all W in an appropriate function space.
Stogner 2012 FSS October 17, 2012 7 / 27
New Formulations
Stabilized Navier-Stokes
∂U
∂t+Ai
∂U
∂xi=
∂
∂xi
(Kij
∂U
∂xj
)+ S
Find U satisfying the essential boundary and initial conditions such that∫Ω
[W ·
(∂U
∂t− S
)+∂W
∂xi·(Kij
∂U
∂xj−AiU
)]dΩ
+
nel∑e=1
∫Ωe
τSUPG∂W
∂xk·Ak
[∂U
∂t+Ai
∂U
∂xi− ∂Gi
∂xi− S
]dΩ
+
nel∑e=1
∫Ωe
νDCO
(∂W
∂xi· gij ∂U
∂xj
)dΩ−
∮ΓW · (g − f) dΓ = 0
for all W in an appropriate function space.
Stogner 2012 FSS October 17, 2012 7 / 27
New Formulations
Stabilized Navier-Stokes
∂U
∂t+Ai
∂U
∂xi=
∂
∂xi
(Kij
∂U
∂xj
)+ S
Find U satisfying the essential boundary and initial conditions such that∫Ω
[W ·
(∂U
∂t− S
)+∂W
∂xi·(Kij
∂U
∂xj−AiU
)]dΩ
+
nel∑e=1
∫Ωe
τSUPG∂W
∂xk·Ak
[∂U
∂t+Ai
∂U
∂xi− ∂Gi
∂xi− S
]dΩ
+
nel∑e=1
∫Ωe
νDCO
(∂W
∂xi· gij ∂U
∂xj
)dΩ−
∮ΓW · (g − f) dΓ = 0
for all W in an appropriate function space.
Stogner 2012 FSS October 17, 2012 7 / 27
New Formulations
Stabilization Improvements
Formulation Consistency• Penalty→ Dirichlet boundary conditions
I Still adjoint-consistent in libMesh tests• Avoid reinterpolation of primitive variables, gradients
I Accurate MMS convergence to finer grids• Calculate τSUPG at quadrature points, not nodes
I More stable convergence with Gaussian quadrature, strong reactions
Stogner 2012 FSS October 17, 2012 8 / 27
New Formulations
Stabilization Improvements
Formulation Sophistication• Selective Discontinuity Capturing Operator disabling• Discontinuity Capturing Operator based on Roe’s flux splitting
I Still using straightforward ν from LeBeau & Tezduyar for capsule runs• “Eigen-decomposition” based SUPG τ from Erwin et. al.
I τ−1 =∑i∈nodes
∣∣∣ ∂φi
∂xjAj
∣∣∣I New default FIN-S stabilizationI No longer Lagrange-basis-dependent
With 2011 FSS physics, we can get iterative convergence on steadycapsule runs to machine precision! No more transient oscillations after 6OOM!
Stogner 2012 FSS October 17, 2012 9 / 27
New Models
1 Prior Work
2 New Formulations
3 New Models
4 New Calibrations
5 New Results
6 Ongoing Work
Stogner 2012 FSS October 17, 2012 10 / 27
New Models
Transition Modeling
Motivations• Turbulence: most significant initial parameter uncertainty
• Turbulence remained significant after calibration
• Transition to turbulence is critical to peak heat flux, ablation rate
Models• User-specified transition location
I Testing purposes• Momentum thickness transition model
I θ ≡∫ ρu(y)
ρ0u0
(1− u(y)
u0
)dy
I PDE→ Integro-differential equation
Stogner 2012 FSS October 17, 2012 11 / 27
New Models
Parallel Transition Evaluation
Issues• Integrals cross
subdomains
• Must “batch”communication
Stogner 2012 FSS October 17, 2012 12 / 27
New Models
Parallel Transition Evaluation
Line Construction• At each boundary node
• Iterate up outward normal
• Find local element intersections
• Save “local lines”, link interior andboundary ranks
Integral Evaluation• Freestream evaluations→
boundary→ interior
• Boundary layer edge candidates→boundary→ interior
• Integral subline contributions→boundary, sum
Stogner 2012 FSS October 17, 2012 13 / 27
New Calibrations
1 Prior Work
2 New Formulations
3 New Models
4 New Calibrations
5 New Results
6 Ongoing Work
Stogner 2012 FSS October 17, 2012 14 / 27
New Calibrations
Carbon Reaction Chemistry
k = ATne−TrT
C2 + M −−−− 2 C + M
CN + M −−−− C + N + M
CO + M −−−− C + O + M
CO + C −−−− C2 + O
CO + O −−−− O2 + C
CO + N −−−− CN + O
N2 + C −−−− CN + N
CN + O −−−− NO + C
CN + C −−−− C2 + N
CO + C2−−−− C3 + O
10-3
10-2
10-1
Distance [m]
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Mol
ar F
ract
ion
[-]
COCOCO
2
N2
CNCN
C2
N
O
Uncertain Reaction Rates• Arrhenius pre-exponential
uncertainty: +/- 1 OOM
• Strong ablation sensitivities toN2 + C, CO + N, CO + C2
• Joint calibration
Stogner 2012 FSS October 17, 2012 15 / 27
New Calibrations
Carbon Reaction Chemistry
Experimental Data• Spectroscopy as part of Mars test campaign, Electric Arc Shock Tube
(EAST) facility, NASA Ames
• 96%CO2 + 4%N2 test gas
• 6-7 km/s shock speeds
Numerical Calibration• SHOCKING: 1D Eulerian shock code
• QUESO Markov-Chain Monte Carlo parameter estimation
• Data shows more rapid thermochemical relaxation than predicted byPark1994 or Park2001!
Stogner 2012 FSS October 17, 2012 16 / 27
New Results
1 Prior Work
2 New Formulations
3 New Models
4 New Calibrations
5 New Results
6 Ongoing Work
Stogner 2012 FSS October 17, 2012 17 / 27
New Results
Baseline With Transition
• Spalart-Allmaras ν reduced ten-fold
Stogner 2012 FSS October 17, 2012 18 / 27
New Results
Off-Baseline Convergence: 2011
0 50 100 150 200 250Iteration N
108
109
1010
1011
1012
Uns
tead
yR
esid
ual
ISS Offbaseline Convergence - Dataset 270
10−10
10−9
10−8
10−7
Tim
eS
tep
[s]
‖du/dt‖∞∆t
0 50 100 150 200 250Iteration N
10−6
10−5
QoI
Valu
e
ISS Offbaseline Convergence - Dataset 270
10−10
10−9
10−8
10−7
Tim
eS
tep
[s]
QoI∆t
Convergence• Large initial transients, QoI
change
• Secondary transient spike
• 250 time steps
• 6 OOM convergence
• Reaction stabilization?
Stogner 2012 FSS October 17, 2012 19 / 27
New Results
Off-Baseline Convergence: 2012
0 50 100 150 200 250 300 350 400Iteration N
103
104
105
106
107
108
109
Uns
tead
yR
esid
ual(
Nor
mal
ized
)
ISS Offbaseline Convergence - Dataset 20
10−8
10−7
10−6
10−5
10−4
Tim
eS
tep
[s]
‖du/dt‖∞∆t
0 50 100 150 200 250 300 350 400Iteration N
10−8
10−7
10−6
10−5
10−4
Tim
eS
tep
[s]
ISS Offbaseline Convergence - Dataset 20
10−6
10−5
10−4
QoI
Valu
e
∆t
∆t
Convergence• Aggressive + paranoid
adaptive time steppingI Orders of magnitude
higher time stepsI Ought to be replaced with
estimator-basedadaptivity
• Secondary transient spikewell captured
• 8 OOM convergenceI Transition smoothing
needed?
Stogner 2012 FSS October 17, 2012 20 / 27
New Results
Ablation Rate PDFs
0 0.5 1 1.5 2 2.5 3
x 10−5
−1
0
1
2
3
4
5
6
7
8x 10
5 Capsule Peak Ablation Rate Distributions
Probability Density
Abl
atio
n R
ate,
m/s
UQ Output• Dramatic prediction changes
I 2010: ≈ 2.0× 10−5m/sI 2011: ≈ 4.4× 10−6m/sI 2012: ≈ 7.8× 10−6m/s
• 2010-2011: 100× lowernitridation
• 2011-2012: Faster C kinetics?
Stogner 2012 FSS October 17, 2012 21 / 27
Ongoing Work
1 Prior Work
2 New Formulations
3 New Models
4 New Calibrations
5 New Results
6 Ongoing Work
Stogner 2012 FSS October 17, 2012 22 / 27
Ongoing Work
Built-in Reaction, Catalysis Chemistry
Surface Catalysis• Accelerated recombination of atomic→ molecular gasses at solid
surface
• Significant to heat flux uncertainty at some conditions
• Under testing in Arcjet simulations
FIN-S Reaction Chemistry• Gas-phase, high-enthalpy focus unlike Cantera
• Speed optimized unlike Chemay
Stogner 2012 FSS October 17, 2012 23 / 27
Ongoing Work
Speedup – Multithreading
# Threads
Spe
edup
1 2 3 4 5 61
2
3
4
5
6
Ideal3D, perfect gas2D, 13 species
• Physics cost overwhelms assembly contention
Stogner 2012 FSS October 17, 2012 24 / 27
Ongoing Work
Adjoint Refinement Error Estimator
Error Estimators• eQ ≡ Q(uh; ξ)−Q(u; ξ)
• R(uh, z; ξ) = eQ −RQ +RRI RQ and RR: higher order, typically quadratic in
∣∣∣∣u− uh∣∣∣∣.
• Q(uH)−Q(uh) = −R(uh, zH) +O(e2)
• Higher order z:I Project uh to uH in a refined spaceI Jacobian calculation, linear adjoint solve on refined meshI Residual evaluation on refined mesh
• Linear-only solve on refined mesh
• 1± 2−p asymptotic effectivity
• Element-by-element QoI contributions
Stogner 2012 FSS October 17, 2012 25 / 27
Ongoing Work
RadiationOne-way coupling• FIN-S generates Ttr, Tve, P , molar fractions
• PECOS libradiation generates chemistry-dependent kabs• deal.II-based SPN radiation transport
I −µ2n∇ · ∇I+M + σaI
+m = σa
14πacT
4
I Exact for 1D problems, accurate for “locally 1D” problems
• Adjoint-based error using SN model
Stogner 2012 FSS October 17, 2012 26 / 27
Ongoing Work
ConclusionsForward Uncertainty Propagation• Wide priors require fat, well-resolved tails
I Adaptive importance sampling?• Model inadequacy must be propagated too!
I “Unknown unknowns” can dwarf “known unknowns”
Rapid Application Development• Rapid development and testing is practical:
I FIN-S 2008: “toy” perfect gas problemsI FIN-S 2012: high-enthalpy reacting multiphysicsI 5 part-time contributors, 0 full-time FIN-S developers
• Critical factors:I Modularity first, physics secondI Multidisciplinary expertiseI “Not invented here” not believed hereI Collaborative development
Any questions?Stogner 2012 FSS October 17, 2012 27 / 27