Fidelity of Type Ia Supernovae Nucleosynthesis with Tracer Particles

1
Fidelity of Type Ia Supernovae Nucleosynthesis
with Tracer Particles

• George (Cal) Jordan
• Tomek Plewa

2
Reactive Flows in Real World

• Industry
• Combustion in Engine
• Rockets
• Safety
• Pool fires

C-Safe ASC center, University of Utah
NASA
3
Reactive Flows in Astrophysics

• Explosive nucleosynthesis
• Nova nucleosynthesis
• Rapid catalyzed proton burning.
• Type II/Ib/Ic supernovae
• r-process nucleosynthesis
• Freezeout from equilibrium
• Type Ia Supernovae
• Deflagration
• Detonation
• X-Ray Bursts
• Burning in thin dense layers on surface of a
  compact object, very strong gravity

Nova Vel 1999
Supernova 1987a
Supernova DEM l71
Depiction of accretion leading to an x-ray burst
4
Feasible Reactive Flow Computations

• Possible to fully model reactive flows with full
  chemistry?
• Frequently too expensive!
• Want a cheap way to approximate the continuum
  solution
• Introduce tracer particles
• Can use tracer particles to provide a lagrangian
  view of the system
• Particle records the thermodynamic history of a
  mass element
• Post-process use this information as input to
  reaction network

5
Particles in Physics Modeling

• Used to represent gravitating elements
• Numerical cosmology (PM, SPH, treecodes)
  (Dubinski et al.)
• Used to track interfaces
• Level-sets with particles for material interfaces
  (ink jet) (Enright et al.)
• Used to directly model microscopic processes
• Direct Simulation Monte Carlo for shockwave
  profiles (Anderson et al.)
• Multiphase flows
• fuel solid oxidizer in rocket engines (Rider et
  al.)

6
Requirements for Tracing with Particles

• Tracer particles follow evolution of individual
  fluid elements
• Particles evolve simultaneously with the flow
  field
• Need to make sure that flow/particle coupling is
  strong
• Is stochastic sampling of the hydro field with
  the particles reliable? (i.e. , can we represent
  the flow field properties with particles
  correctly)?
• What about properties of the flow field that
  arent resolved in the simulation?
• Metric for determining accuracy of particle
  sample
• Post-processing example Compare final yields,
  particle trajectories

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Turbulent Flows
Non-Reactive turbulent flow

• Starts as R-T unstable and transits to
  turbulence.
• Wide range of length scales cant capture all in
  the model simultaneously
• Must use subgrid scale model to account for
  unresolved scales

Cabot et al. 2005
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Turbulent Flows
Reactive turbulent flow
0.1 km resolution
0.1cm resolution
Zingale et al. 2005
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Turbulent Flames with Tracer Particles
Bell et al. (2005)

• Application of stochastic particles to
  turbulent chemical flames
• Traces individual atoms through the simulation
• Particles advect through the system according to
  hydro
• Diffusion of the particles are treated as a
  random walk
• Since tracing individual atoms, particles can
  react, this is treated as a Markov process

Concentration of NO, particles compared to
continuum.
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Particle Tracing Applications

• Type Ia supernova models
• Travaglio et al. (2004)
• Brown et al. (2005)
• Type II supernova modeling
• Travaglio et al. (2004)
• Nagataki et al. (1997)
• Flash Center
• validation studies (shock-cylinder)
• turbulence (BG/L 1,8003 model)
• turbulent reactive flows (this work)

Tracer particles in Type Ia simulation Travaglio
et al. (2004)
Jordan (2005) Shock-cylinder particles
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FLASH Modeling Framework

• The FLASH code
• Eulerian hydro code
• Godunov method
• PPM
• AMR
• Highly scalable
• Multiplatform
• Efficient, parallel IO
• Tracer particles

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FLASH Example K95 Flame Model

• Simulates Chandrasekhar mass white dwarf
• Starts with flame at bottom of domain.
• Evolving RT-unstable deflagration front, followed
  by turbulent mixing
• Question Can we characterize the complex flows
  of the flame?
• Answer Yes, use tracer particles

Zhang et al. (2006) Simulation of turbulent
flame. Based on calculation and setup in Khokhlov
(1995)
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Tracer Particles in FLASH
(v, T, r, Xi, )i-1,j
(v, T, r, Xi, )i-1,j1
(v, T, r, Xi, )i-1,j-1
Solve with Predictor-Corrector Method
(v, T, r, Xi, )i,j1
(v, T, r, Xi, )i,j-1
(v, T, r, Xi, )i,j
(v, T, r, Xi, )i1,j
(v, T, r, Xi, )i1,j-1
(v, T, r, Xi, )i1,j1
Tracer Particle
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K95particles Turbulent 2-D Flame Model
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K95particles Turbulent 3-D Flame Model

• 125,000 total tracer particles
• The particles were uniformly seeded 100 km above
  the initial position of the flame spread over a
  height of 120 km
• Examine particles and continuum properties in
  horizontal slabs (specifically temperature and
  density)

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Temperature Distribution for Complete Set of
Particles

• Temperature bins are in units of 1X108 K
• Colors
• Contours of percentage of particles in a
  temperature bin
• Black line horizontal average temperature from
  hydro (continuum)

17
Temperature distribution from random samples of
10 and 1 of the particles
18
Density Distribution for Complete Set of Particles

• Density bins are in units of 2x106 g/cm3
• Colors
• Contours of percentage of particles in a
  density bin
• Black line horizontal average of density from
  hydro (continuum)

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Summary

• Post-processing is a necessary element of complex
  hydrodynamic models with nuclear reactions
• The concept of tracer particles successfully
  implemented in the FLASH code and used in actual
  applications
• Studies underway towards understanding of
  convergence properties of particle-enabled
  simulations towards continuum limit
• Proven to work in other applications, there is a
  promise we can put strict error limits on our
  thermonuclear hydro results