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 LLNL-PRES-700484 1 / 12
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 � ǫ nuc = N A B i ∆ Y i i ◮ B i ◮ Binding energy for nuclide i ◮ Y i ◮ Dimensionless abundance for nuclide i Need ∆ � Y to compute energy generation LLNL-PRES-700484 2 / 12
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 dY i � � = Y ℓ Y k λ k , j ( ℓ ) Y i Y j λ j , k ( i ) − dt j , k j , k ���� � �� � � �� � Change Rate Gain Rate Loss Rate ◮ Number of nucleons is conserved ◮ The set of conservation equations in a reaction network forms a system of coupled Ordinary Differential Equations LLNL-PRES-700484 3 / 12
Computing Isotope Evolution ◮ The system of conservation equations is of the form Y = d � Y J � 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 LLNL-PRES-700484 4 / 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 28 Si to 56 Ni 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 28 Si to 56 Ni equilibrium link Alpha Network ( αα, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) 24 Mg 4 He 12 C 16 O 20 Ne 28 Si 32 S 36 Ar 40 Ca 44 Ti 48 Cr 52 Fe 56 Ni ( 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 28 Si to 56 Ni equilibrium link Alpha Network ( αα, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) 24 Mg 4 He 12 C 16 O 20 Ne 28 Si 32 S 36 Ar 40 Ca 44 Ti 48 Cr 52 Fe 56 Ni ( 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 ( αα, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) (7 α, γ ) 24 Mg 4 He 12 C 16 O 20 Ne 28 Si 56 Ni ( 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 54 Fe n p ( αα, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) ( α, γ ) 4 He 12 C 16 O 20 Ne 24 Mg 28 Si 32 S 36 Ar 40 Ca 44 Ti 48 Cr 52 Fe 56 Ni ( 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 ) 3 He 14 N 1 H LLNL-PRES-700484 6 / 12
495 Isotope Network LLNL-PRES-700484 7 / 12
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 LLNL-PRES-700484 8 / 12
Hydrostatic Isotope Evolution Si burn: T = 6 × 10 9 K, ρ = 1 × 10 7 g/cm 3 7 Isotope Network 19 Isotope Network 10 1 10 1 10 0 10 0 10 − 1 10 − 1 10 − 2 10 − 2 Mass Fraction Mass Fraction 10 − 3 10 − 3 10 − 4 10 − 4 10 − 5 10 − 5 10 − 6 10 − 6 10 − 7 10 − 7 4 He 12 C 16 O 20 Ne 24 Mg 28 Si 56 Ni 4 He 12 C 16 O 20 Ne 24 Mg 28 Si 56 Ni 10 − 8 10 − 8 10 − 10 10 − 9 10 − 8 10 − 7 10 − 6 10 − 5 10 − 4 10 − 3 10 − 2 10 − 1 10 0 10 1 10 2 10 − 10 10 − 9 10 − 8 10 − 7 10 − 6 10 − 5 10 − 4 10 − 3 10 − 2 10 − 1 10 0 10 1 10 2 Time (s) Time (s) 495 Isotope Network 10 1 10 0 10 − 1 10 − 2 Mass Fraction 10 − 3 10 − 4 10 − 5 10 − 6 10 − 7 4 He 12 C 16 O 20 Ne 24 Mg 28 Si 56 Ni 10 − 8 10 − 8 10 − 7 10 − 6 10 − 5 10 − 4 10 − 3 10 − 2 10 − 1 10 0 10 1 Time (s) LLNL-PRES-700484 9 / 12
Hydrostatic Energy Generation Total Energy Generation 10 25 10 24 10 23 Energy (ergs) 10 22 10 21 10 20 NetNuc7 10 19 NetNuc19 Torch495 10 18 10 − 10 10 − 9 10 − 8 10 − 7 10 − 6 10 − 5 10 − 4 10 − 3 10 − 2 10 − 1 10 0 10 1 10 2 Time (s) LLNL-PRES-700484 10 / 12
Hydrostatic Verification Results ◮ Compare total energy generated from 7 and 19 isotope networks to 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 × 10 9 K, ρ = 1 × 10 7 g/cm 3 ◮ 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 × 10 9 K, ρ = 1 × 10 7 g/cm 3 ◮ 19: under predicted by 2.65% ◮ 7: under predicted by 32% ◮ 19 is 12 times more accurate than 7 ◮ Si burn: T = 5 × 10 9 K, ρ = 1 × 10 9 g/cm 3 ◮ 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 × 10 9 K, ρ = 1 × 10 7 g/cm 3 ◮ 19: under predicted by 2.65% ◮ 7: under predicted by 32% ◮ 19 is 12 times more accurate than 7 ◮ Si burn: T = 5 × 10 9 K, ρ = 1 × 10 9 g/cm 3 ◮ 19: over predicted by 1.1% ◮ 7: over predicted by 5.4% ◮ 5 times more accurate ◮ CO burn: T = 3 × 10 9 K, ρ = 1 × 10 9 g/cm 3 ◮ 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 × 10 9 K, ρ = 1 × 10 7 g/cm 3 ◮ 19: under predicted by 2.65% ◮ 7: under predicted by 32% ◮ 19 is 12 times more accurate than 7 ◮ Si burn: T = 5 × 10 9 K, ρ = 1 × 10 9 g/cm 3 ◮ 19: over predicted by 1.1% ◮ 7: over predicted by 5.4% ◮ 5 times more accurate ◮ CO burn: T = 3 × 10 9 K, ρ = 1 × 10 9 g/cm 3 ◮ Both within .05% of 495 isotope network ◮ He burn: T = 3 × 10 9 K, ρ = 1 × 10 8 g/cm 3 ◮ 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 × 10 9 K, ρ = 1 × 10 7 g/cm 3 ◮ 19: under predicted by 2.65% ◮ 7: under predicted by 32% ◮ 19 is 12 times more accurate than 7 ◮ Si burn: T = 5 × 10 9 K, ρ = 1 × 10 9 g/cm 3 ◮ 19: over predicted by 1.1% ◮ 7: over predicted by 5.4% ◮ 5 times more accurate ◮ CO burn: T = 3 × 10 9 K, ρ = 1 × 10 9 g/cm 3 ◮ Both within .05% of 495 isotope network ◮ He burn: T = 3 × 10 9 K, ρ = 1 × 10 8 g/cm 3 ◮ Both within .07% 19 isotope network is only 3% slower! LLNL-PRES-700484 11 / 12
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 of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344
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