Implementing a 19 Isotope Reaction Network in Cosmos++ Sam Olivier - - PowerPoint PPT Presentation

Implementing a 19 Isotope Reaction Network in Cosmos++

Sam Olivier

Mentors: Rob Hoffman, Peter Anninos August 16, 2016

Introduction to Cosmos++

◮ Cosmos++ is a massively parallel collection of multidimensional

multiphysics packages

◮ Used to simulate a wide variety of problems in astrophysics

◮ Supernovae ◮ Accretion of matter by black holes ◮ Big bang simulations

◮ Many physics packages

◮ Fluid dynamics ◮ Radiation transport ◮ Radiation pressure ◮ Magnetic fields ◮ Gravity ◮ Nuclear energy generation

Goal of Project

Compute nuclear energy generation more accurately

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Introduction to Cosmos++

◮ Cosmos++ is a massively parallel collection of multidimensional

multiphysics packages

◮ Used to simulate a wide variety of problems in astrophysics

◮ Supernovae ◮ Accretion of matter by black holes ◮ Big bang simulations

◮ Many physics packages

◮ Fluid dynamics ◮ Radiation transport ◮ Radiation pressure ◮ Magnetic fields ◮ Gravity ◮ Nuclear energy generation

Goal of Project

Compute nuclear energy generation more accurately

LLNL-PRES-700484 1 / 12

Computing Energy Generation

ǫnuc = NA

• i

Bi∆Yi

◮ Bi

◮ Binding energy for nuclide i

◮ Yi

◮ Dimensionless abundance for nuclide i

Need ∆ Y to compute energy generation

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Reaction Networks

◮ A reaction network is the set of isotopes chosen to model a

reactor

◮ Each isotope has its own Conservation Equation that describes

the evolution of its abundance

Conservation of Nuclide i

dYi dt

• Change Rate

=

• j,k

YℓYkλk,j(ℓ)

• Gain Rate

−

• j,k

YiYjλj,k(i)

• Loss Rate

◮ Number of nucleons is conserved ◮ The set of conservation equations in a reaction network forms a

system of coupled Ordinary Differential Equations

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Computing Isotope Evolution

◮ The system of conservation equations is of the form

J Y = d Y dt

◮ Tracking more isotopes makes the Jacobian larger and more

expensive to solve

◮ The network solve is just one of many physics packages to be run

for each cell and time step

Need to reduce the number of isotopes tracked while maintaining accuracy

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Network Approximations

◮ Track as few isotopes as required ◮ Balance functionality, accuracy and computational expense ◮ 7 isotope network

◮ Current network in Cosmos ◮ Simplified alpha network ◮ 17 reactions ◮ No hydrogen burning ◮ Inaccurate 28Si to 56Ni equilibrium link LLNL-PRES-700484 5 / 12

Network Approximations

◮ Track as few isotopes as required ◮ Balance functionality, accuracy and computational expense ◮ 7 isotope network

◮ Current network in Cosmos ◮ Simplified alpha network ◮ 17 reactions ◮ No hydrogen burning ◮ Inaccurate 28Si to 56Ni equilibrium link

Alpha Network

4He 12C 16O 20Ne 24Mg 28Si 32S 36Ar 40Ca 44Ti 48Cr 52Fe 56Ni

(αα, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ)

LLNL-PRES-700484 5 / 12

Network Approximations

◮ Track as few isotopes as required ◮ Balance functionality, accuracy and computational expense ◮ 7 isotope network

◮ Current network in Cosmos ◮ Simplified alpha network ◮ 17 reactions ◮ No hydrogen burning ◮ Inaccurate 28Si to 56Ni equilibrium link

Alpha Network

4He 12C 16O 20Ne 24Mg 28Si 32S 36Ar 40Ca 44Ti 48Cr 52Fe 56Ni

(αα, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ)

7 Isotope Network 4He 12C 16O 20Ne 24Mg 28Si 56Ni

(αα, γ) (α, γ) (α, γ) (α, γ) (α, γ) (7α, γ) (α, p)(p, γ)

LLNL-PRES-700484 5 / 12

19 Isotope Network

◮ New network added to Cosmos ◮ 101 reactions ◮ Complete alpha network ◮ Has hydrogen burning capability ◮ Photodisintegration 19 Isotope Network

1H 3He 4He 12C 16O 20Ne 24Mg 28Si 32S 36Ar 40Ca 44Ti 48Cr 52Fe 56Ni 14N 54Fe

(αα, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ) (α, γ)

n p

(α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ) (α, p)(p, γ)

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495 Isotope Network

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Hydrostatic Tests

◮ Compare timing and accuracy of 19 and 7 isotope networks for

known test problems

◮ Isolate the nuclear energy generation package ◮ Non dimensional point star ◮ Evolve the isotopes under a constant temperature and pressure

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Hydrostatic Isotope Evolution

Si burn: T = 6 × 109 K, ρ = 1 × 107 g/cm3

10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102 Time (s) 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 Mass Fraction

7 Isotope Network

4He 12C 16O 20Ne 24Mg 28Si 56Ni

10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102 Time (s) 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 Mass Fraction

19 Isotope Network

4He 12C 16O 20Ne 24Mg 28Si 56Ni

10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 Time (s) 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 Mass Fraction

495 Isotope Network

4He 12C 16O 20Ne 24Mg 28Si 56Ni

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Hydrostatic Energy Generation

10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102 Time (s) 1018 1019 1020 1021 1022 1023 1024 1025 Energy (ergs)

Total Energy Generation NetNuc7 NetNuc19 Torch495

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Hydrostatic Verification Results

◮ Compare total energy generated from 7 and 19 isotope networks

to 495 isotope network

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Hydrostatic Verification Results

◮ Compare total energy generated from 7 and 19 isotope networks

to 495 isotope network

◮ Si burn: T = 6 × 109 K, ρ = 1 × 107 g/cm3

◮ 19: under predicted by 2.65% ◮ 7: under predicted by 32% ◮ 19 is 12 times more accurate than 7 LLNL-PRES-700484 11 / 12

Hydrostatic Verification Results

◮ Compare total energy generated from 7 and 19 isotope networks

to 495 isotope network

◮ Si burn: T = 6 × 109 K, ρ = 1 × 107 g/cm3

◮ 19: under predicted by 2.65% ◮ 7: under predicted by 32% ◮ 19 is 12 times more accurate than 7

◮ Si burn: T = 5 × 109 K, ρ = 1 × 109 g/cm3

◮ 19: over predicted by 1.1% ◮ 7: over predicted by 5.4% ◮ 5 times more accurate LLNL-PRES-700484 11 / 12

Hydrostatic Verification Results

◮ Compare total energy generated from 7 and 19 isotope networks

to 495 isotope network

◮ Si burn: T = 6 × 109 K, ρ = 1 × 107 g/cm3

◮ 19: under predicted by 2.65% ◮ 7: under predicted by 32% ◮ 19 is 12 times more accurate than 7

◮ Si burn: T = 5 × 109 K, ρ = 1 × 109 g/cm3

◮ 19: over predicted by 1.1% ◮ 7: over predicted by 5.4% ◮ 5 times more accurate

◮ CO burn: T = 3 × 109 K, ρ = 1 × 109 g/cm3

◮ Both within .05% of 495 isotope network LLNL-PRES-700484 11 / 12

Hydrostatic Verification Results

◮ Compare total energy generated from 7 and 19 isotope networks

to 495 isotope network

◮ Si burn: T = 6 × 109 K, ρ = 1 × 107 g/cm3

◮ 19: under predicted by 2.65% ◮ 7: under predicted by 32% ◮ 19 is 12 times more accurate than 7

◮ Si burn: T = 5 × 109 K, ρ = 1 × 109 g/cm3

◮ 19: over predicted by 1.1% ◮ 7: over predicted by 5.4% ◮ 5 times more accurate

◮ CO burn: T = 3 × 109 K, ρ = 1 × 109 g/cm3

◮ Both within .05% of 495 isotope network

◮ He burn: T = 3 × 109 K, ρ = 1 × 108 g/cm3

◮ Both within .07% LLNL-PRES-700484 11 / 12

Hydrostatic Verification Results

◮ Compare total energy generated from 7 and 19 isotope networks

to 495 isotope network

◮ Si burn: T = 6 × 109 K, ρ = 1 × 107 g/cm3

◮ 19: under predicted by 2.65% ◮ 7: under predicted by 32% ◮ 19 is 12 times more accurate than 7

◮ Si burn: T = 5 × 109 K, ρ = 1 × 109 g/cm3

◮ 19: over predicted by 1.1% ◮ 7: over predicted by 5.4% ◮ 5 times more accurate

◮ CO burn: T = 3 × 109 K, ρ = 1 × 109 g/cm3

◮ Both within .05% of 495 isotope network

◮ He burn: T = 3 × 109 K, ρ = 1 × 108 g/cm3

◮ Both within .07%

19 isotope network is only 3% slower!

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Conclusions

◮ The 19 isotope network provides an increase in accuracy for

almost no additional computational cost

◮ 19 is more accurate than 7 for heavy nuclide burns ◮ Cosmos now has hydrogen burning and full photodisintegration

support

◮ Future Work

◮ Verify 19 isotope network under hydrodynamic conditions LLNL-PRES-700484 12 / 12

Thanks to my mentors Rob Hoffman and Peter Anninos. This work was performed under the auspices of the U.S. Department

• f Energy by Lawrence Livermore National Laboratory under

Contract DE-AC52-07NA27344