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GPUs TO MARS Full Scale Simulation of SpaceX’s Mars Rocket Engine
Adam Lichtl, Stephen Jones, GTC 2015
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Background
Independent space launch company
Build and operate our own rocket & capsule
Operations in CA, TX & FL
Founded in 2002, first launch in 2008
18 successful missions to date
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Design
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Build
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Launch
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Mars
Length of day 24 hours, 40 minutes
Length of year 687 days
Gravity 0.375gs
Distance from Sun 1.53 AU
Mars Air CO2 (96%), N2 (2%)
Earth Air O2 (21%), N2 (78%)
Atmosphere 1% density / pressure of Earth
Temperature -284 / +86 / -81 F (low / high / avg)
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Human Mars Mission Classes
Credit: CollectSpace
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Mass to Mars
Apollo Command &
Service Module
Mass: 46 tons
Terrestrial assembly
NASA Mars Architecture
Mass: 300 tons
3x heavy-lift
launches
In-orbit assembly
International Space Station
Mass: 450 tons
36x Space Shuttle,
5x Proton launches
Image Credit: Mark Benson & Kerbal Space Program Image Credit: NASA Image Credit: NASA
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Methane Fuel
O H H
O
O
C
O H
H
O O C
Water from below ground
Carbon dioxide from atmosphere
Synthesize return-journey fuel on Mars
2H2O + CO2 -> CH4 + 2O2
O
O O
O
H
H C
H
H
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Rocket Engine Design
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Why Simulation?
1. Investigate what cannot be measured
2. Reduce need for testing
3. Design optimisation: narrow design space
4. Proactive instead of reactionary design
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seconds 10-11 10-9 10-8 10-6 10-10 10-7 10-5 10-3 10-4
Diffusion
Reaction
Advection Acoustics
Chamber Residence
Time scales vary by
8 orders of magnitude
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Total points: (103)6 = 1018 = 1,000,000,000,000,000,000 points @1kB per point -> Yottabytes of data
kmax kmin
log E(k)
Injection
Cascade
Viscous dissipation
Kolmogorov Scale: ~1µm
Combustion Chamber: ~1m
Length scales vary by
6 orders of magnitude
Eddy Wavenumber
Edd
y En
ergy
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Structure in Turbulence
Credit: SpaceWeather
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Simulation Meshing
Structured Grid Adaptive Grid Unstructured Grid
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Fourier Transform: Spectral Compression
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Wavelets: Local Fractal Basis
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Wavelet Compression
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Wavelet Compression
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Wavelet Compression
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Wavelet Compression
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Wavelet Compression
δ
δ > ε (ε is some tolerance)
δ < ε
δ
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Wavelet Compression
Transform Output
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Decompression
Transform Output
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Decompression
Transform Output
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Decompression
Transform Output
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Decompression
+δ
Transform Output
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Decompression
Transform Output
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Decompression
Transform Output
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Decompression
Transform Output
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Decompression
Transform Output
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Decompression
Transform Output
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Regular Grid: Direct Indexing
Index (x, y, z) = p Index (x, y+1, z) = p + Nx
(x, y, z)
(x, y+1, z)
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Sparse Grid: Difficult Indexing
Index (x, y, z) = p Index (x, y+1, z) = ???
(x, y, z)
(x, y+1, z)
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Sparse Grid Point Lookup
Linear search
Tree-based search
Hybrid tree search + dense indexing
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Grid Point Contains Reference to Data
Location (x,y,z)
Data Reference
(x, y, z)
Grid Point 14
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Grid Point Contains Reference to Data
Location (x,y,z)
Data Reference
(x, y, z)
Grid Index
Grid Point 14
Grid Data
14 15 16
(11,12,5)
8
(11,11,5)
3
(Location)
(Reference)
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Grid Point Contains Reference to Data
ρu4
ρ4
ρw4
ρv4
E4
ρu7
ρ7
ρw7
ρv7
E7
ρu9
ρ9
ρw9
ρv9
E9
ρu0
ρ0
ρw0
ρv0
E0
ρu5
ρ5
ρw5
ρv5
E5
ρu1
ρ1
ρw1
ρv1
E1
ρu8
ρ8
ρw8
ρv8
E8
ρu3
ρ3
ρw3
ρv3
E3
ρu6
ρ6
ρw6
ρv6
E6
ρu2
ρ2
ρw2
ρv2
E2
Simulation Data
density
X-momentum
Y-momentum
Z-Momentum
Energy
Location (x,y,z)
Data Reference
(x, y, z)
Grid Point 14
Grid Data
Grid Index 14 15 16
(11,12,5)
8
(11,11,5)
3
…
…
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Grid Point Contains Reference to Data
ρu4
ρ4
ρw4
ρv4
E4
ρu7
ρ7
ρw7
ρv7
E7
ρu9
ρ9
ρw9
ρv9
E9
ρu0
ρ0
ρw0
ρv0
E0
ρu5
ρ5
ρw5
ρv5
E5
ρu1
ρ1
ρw1
ρv1
E1
ρu8
ρ8
ρw8
ρv8
E8
ρu3
ρ3
ρw3
ρv3
E3
ρu6
ρ6
ρw6
ρv6
E6
ρu2
ρ2
ρw2
ρv2
E2
Simulation Data
density
X-momentum
Y-momentum
Z-Momentum
Energy
Location (x,y,z)
Data Reference
(x, y, z)
Grid Point 14
(11,12,5)
8
(11,11,5)
3
…
… Grid Data
14 15 16 Grid Index
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P0 P1 P2 P3 P4 P5 P6 P7 P8 P9
Grid Adaptation
0 1 2 3 4 5 6 7 8
x0y0 x1y1 x2y2 x3y3 x4y4 x5y5 x6y6 x7y7 x8y8 x9y9
9
Location
Reference
Grid Index
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P0 P1 P2 P3 P4 P5 P6 P7 P8 P9
Grid Adaptation
0 1 2 3 4 5 6 7 8
x0y0 x1y1 x2y2 x3y3 x4y4 x5y5 x6y6 x7y7 x8y8 x9y9
9
Location
Reference
Grid Index
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P0 P1 P2 P3 P4 P5 P6 P7 P8 P9
Grid Adaptation
0 1 2 3 4 5 6 7 8
x0y0 x1y1 x2y2 x3y3 x4y4 x5y5 x6y6 x7y7 x8y8 x9y9
9
Location
Reference
Grid Index
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P0 P2 P4 P6 P8
Grid Adaptation
0 2 4 6 8
x0y0 x2y2 x4y4 x6y6 x8y8 Location
Reference
Grid Index
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P0 P1 P2 P3 P4
Grid Adaptation
0 2 4 6 8
x0y0 x2y2 x4y4 x6y6 x8y8 Location
Reference
Grid Index
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P0 P1 P2 P3 P4 P5 P6 P7 P8 P9
Grid Transformations Track Data
0 1 2 3 4 5 6 7 8
x0y0 x1y1 x2y2 x3y3 x4y4 x5y5 x6y6 x7y7 x8y8 x9y9
9
Location
Reference
Grid Index
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P0 P1 P2 P3 P4 P5 P6 P7 P8 P9
Grid Transformations Track Data
0 1 2 3 4 5 6 7 8
x0y0 x1y1 x2y2 x3y3 x4y4 x5y5 x6y6 x7y7 x8y8 x9y9
9
Location
Reference
Delete Add
Sort
Transpose
Grid Index
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P0 P1 P2 P3 P4 P5 P6 P7 P8 P9
P0 P1 P2 P3 P4 P5 P6 P7 P8 P9
Grid Transformations Track Data
0 1 2 3 4 5 6 7 8
x0y0 x1y1 x2y2 x3y3 x4y4 x5y5 x6y6 x7y7 x8y8 x9y9
9
Location
Reference
Grid Index
Location
Delete Add
Sort
Transpose
Grid Index
4 7 9 0 5 1 8 3 6 2 Reference
x4y4 x7y7 x9y9 x0y0 x5y5 x1y1 x8y8 x3y3 x6y6 x2y2
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P0 P1 P2 P3 P4 P5 P6 P7 P8 P9
Losing Coalesced Memory Access
4 7 9 0 5 1 8 3 6 2
ρu4
ρ4
ρw4
ρv4
E4
ρu7
ρ7
ρw7
ρv7
E7
ρu9
ρ9
ρw9
ρv9
E9
ρu0
ρ0
ρw0
ρv0
E0
ρu5
ρ5
ρw5
ρv5
E5
ρu1
ρ1
ρw1
ρv1
E1
ρu8
ρ8
ρw8
ρv8
E8
ρu3
ρ3
ρw3
ρv3
E3
ρu6
ρ6
ρw6
ρv6
E6
ρu2
ρ2
ρw2
ρv2
E2
Coalesced Simulation Data
Grid Index
Reference
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P0 P1 P2 P3 P4 P5 P6 P7 P8 P9
Losing Coalesced Memory Access
4 7 9 0 5 1 8 3 6 2
ρu4
ρ4
ρw4
ρv4
E4
ρu7
ρ7
ρw7
ρv7
E7
ρu9
ρ9
ρw9
ρv9
E9
ρu0
ρ0
ρw0
ρv0
E0
ρu5
ρ5
ρw5
ρv5
E5
ρu1
ρ1
ρw1
ρv1
E1
ρu8
ρ8
ρw8
ρv8
E8
ρu3
ρ3
ρw3
ρv3
E3
ρu6
ρ6
ρw6
ρv6
E6
ρu2
ρ2
ρw2
ρv2
E2
Uncoalesced Simulation Data
Grid Index
Reference
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P0 P1 P2 P3 P4 P5 P6 P7 P8 P9
4 7 9 0 5 1 8 3 6 2
x4y4 x7y7 x9y9 x0y0 x5y5 x1y1 x8y8 x3y3 x6y6 x2y2
Restoring Coalesced Memory Access
ρu4
ρ4
ρw4
ρv4
E4
ρu7
ρ7
ρw7
ρv7
E7
ρu9
ρ9
ρw9
ρv9
E9
ρu0
ρ0
ρw0
ρv0
E0
ρu5
ρ5
ρw5
ρv5
E5
ρu1
ρ1
ρw1
ρv1
E1
ρu8
ρ8
ρw8
ρv8
E8
ρu3
ρ3
ρw3
ρv3
E3
ρu6
ρ6
ρw6
ρv6
E6
ρu2
ρ2
ρw2
ρv2
E2
Uncoalesced Simulation Data
Location
Reference
Grid Index
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P0 P1 P2 P3 P4 P5 P6 P7 P8 P9
4 7 9 0 5 1 8 3 6 2
x4y4 x7y7 x9y9 x0y0 x5y5 x1y1 x8y8 x3y3 x6y6 x2y2
P0 P1 P2 P3 P4 P5 P6 P7 P8 P9
Restoring Coalesced Memory Access
ρu4
ρ4
ρw4
ρv4
E4
ρu7
ρ7
ρw7
ρv7
E7
ρu9
ρ9
ρw9
ρv9
E9
ρu0
ρ0
ρw0
ρv0
E0
ρu5
ρ5
ρw5
ρv5
E5
ρu1
ρ1
ρw1
ρv1
E1
ρu8
ρ8
ρw8
ρv8
E8
ρu3
ρ3
ρw3
ρv3
E3
ρu6
ρ6
ρw6
ρv6
E6
ρu2
ρ2
ρw2
ρv2
E2
0 1 2 3 4 5 6 7 8 9
Reorder Simulation
Data
Uncoalesced Simulation Data
ρu4
ρ4
ρw4
ρv4
E4
ρu7
ρ7
ρw7
ρv7
E7
ρu9
ρ9
ρw9
ρv9
E9
ρu0
ρ0
ρw0
ρv0
E0
ρu5
ρ5
ρw5
ρv5
E5
ρu1
ρ1
ρw1
ρv1
E1
ρu8
ρ8
ρw8
ρv8
E8
ρu3
ρ3
ρw3
ρv3
E3
ρu6
ρ6
ρw6
ρv6
E6
ρu2
ρ2
ρw2
ρv2
E2
Coalesced Simulation Data
Reset Indices
x4y4 x7y7 x9y9 x0y0 x5y5 x1y1 x8y8 x3y3 x6y6 x2y2 Location
Reference
Grid Index
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Coupled Multi-Physics
Chemistry
Diffusion
Advection
Thermodynamics
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Real Gas Properties
Extreme pressure requires real-gas properties, evaluated at each grid node
Viscosity
Conductivity
Diffusion constants
Per-species diffusion rates
Independent Calculations
Massively Parallelizable O2 phase diagram, Z-axis is density (colour: liquid is blue, gas is white)
Pressure
Temperature
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Strong Temperature Dependence
Arrhenius equation includes temperature in exponent
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Chemical Kinetic Model
H H
O
H H
O
O
O H H
H H +
H2 O2 H2O
![Page 79: GPUs TO MARS - NVIDIAon-demand.gputechconf.com/gtc/2015/presentation/S5398... · 2015-03-27 · GPUs TO MARS Full Scale Simulation of SpaceX’s Mars Rocket Engine Adam Lichtl, Stephen](https://reader034.vdocuments.us/reader034/viewer/2022043022/5f3e5b792f54f95424580aab/html5/thumbnails/79.jpg)
Chemical Kinetic Model
O H
OH
O
O
O H
O
HO2
H
O H
O
H2O2
H
H
H H
O
H H
O
O
O H H
H H +
H2 O2 H2O
X
![Page 80: GPUs TO MARS - NVIDIAon-demand.gputechconf.com/gtc/2015/presentation/S5398... · 2015-03-27 · GPUs TO MARS Full Scale Simulation of SpaceX’s Mars Rocket Engine Adam Lichtl, Stephen](https://reader034.vdocuments.us/reader034/viewer/2022043022/5f3e5b792f54f95424580aab/html5/thumbnails/80.jpg)
Chemical Kinetic Model
O H
OH
O
O
O H
O
HO2
H
O H
O
H2O2
H
H
H H
O
H H
O
O
O H H
H H +
H2 O2 H2O
![Page 81: GPUs TO MARS - NVIDIAon-demand.gputechconf.com/gtc/2015/presentation/S5398... · 2015-03-27 · GPUs TO MARS Full Scale Simulation of SpaceX’s Mars Rocket Engine Adam Lichtl, Stephen](https://reader034.vdocuments.us/reader034/viewer/2022043022/5f3e5b792f54f95424580aab/html5/thumbnails/81.jpg)
Methane Chemistry
O
O
O
O H
C
H H
H +
O2 CH4
H H
O
H H
O C
O
O
+
H2O CO2
![Page 82: GPUs TO MARS - NVIDIAon-demand.gputechconf.com/gtc/2015/presentation/S5398... · 2015-03-27 · GPUs TO MARS Full Scale Simulation of SpaceX’s Mars Rocket Engine Adam Lichtl, Stephen](https://reader034.vdocuments.us/reader034/viewer/2022043022/5f3e5b792f54f95424580aab/html5/thumbnails/82.jpg)
Methane Chemistry
O
O
O
O H
C
H H
H +
O2 CH4
H H
O
H H
O C
O
O
+
H2O CO2
53 Species, 325 Reactions
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(Actual simulation data, rendered with a ray tracer)
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Acknowledgements
Oleg Vasilyev, University of Colorado Boulder Department of Mechanical Engineering
Jonathan Regele, Iowa State University Department of Aerospace Engineering
Don Lamb The Flash Center for Computational Science
Joseph Oefelein, Sandia National Laboratories Combustion Research Facility
Praveen Ramaprabhu University of North Carolina at Charlotte
Marc Massot Ecole Centrale, Paris
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