An Advanced Simulation and Computing (ASC) Academic Strategic Alliances Program (ASAP) Center at The University of Chicago The Center for Astrophysical Thermonuclear Flashes Fidelity of Type Ia Supernovae Nucleosynthesis with Tracer Particles George (Cal) Jordan Tomek Plewa

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago qIndustry q Combustion in Engine q Rockets qSafety q Pool fires C-Safe ASC center, University of Utah Reactive Flows in “Real” World NASA

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Reactive Flows in Astrophysics qExplosive nucleosynthesis q Nova nucleosynthesis: q Rapid catalyzed proton burning. q Type II/Ib/Ic supernovae q r-process nucleosynthesis q Freezeout from equilibrium q Type Ia Supernovae q Deflagration q Detonation q X-Ray Bursts q 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

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago qPossible to fully model reactive flows with full chemistry? qFrequently too expensive! qWant a cheap way to approximate the continuum solution qIntroduce “tracer particles” qCan use tracer particles to provide a lagrangian view of the system: q Particle records the thermodynamic history of a mass element q Post-process: use this information as input to reaction network Feasible Reactive Flow Computations

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Particles in Physics Modeling qUsed to represent gravitating elements q Numerical cosmology (PM, SPH, treecodes) (Dubinski et al.) qUsed to track interfaces q Level-sets with particles for material interfaces (ink jet) (Enright et al.) qUsed to directly model microscopic processes q Direct Simulation Monte Carlo for shockwave profiles (Anderson et al.) q Multiphase flows q fuel + solid oxidizer in rocket engines (Rider et al.)

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Requirements for Tracing with Particles qTracer particles follow evolution of individual fluid elements qParticles evolve simultaneously with the flow field qNeed to make sure that flow/particle coupling is strong qIs stochastic sampling of the hydro field with the particles reliable? (i.e., can we represent the flow field properties with particles correctly)? q What about properties of the flow field that aren’t resolved in the simulation? qMetric for determining accuracy of particle sample q Post-processing example: Compare final yields, particle trajectories

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Turbulent Flows qStarts as R-T unstable and transits to turbulence. qWide range of length scales; can’t capture all in the model simultaneously qMust use subgrid scale model to account for unresolved scales Cabot et al Non-Reactive turbulent flow

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Turbulent Flows 0.1 km resolution Reactive turbulent flow Zingale et al cm resolution

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Turbulent Flames with Tracer Particles Concentration of NO, particles compared to continuum. Bell et al. (2005) qApplication of “stochastic” particles to turbulent chemical flames q Traces individual atoms through the simulation q Particles advect through the system according to hydro q Diffusion of the particles are treated as a random walk q Since tracing individual atoms, particles can react, this is treated as a Markov process

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Particle Tracing Applications qType Ia supernova models q Travaglio et al. (2004) q Brown et al. (2005) qType II supernova modeling q Travaglio et al. (2004) q Nagataki et al. (1997) qFlash Center q validation studies (shock-cylinder) q turbulence (BG/L 1,800 3 model) q turbulent reactive flows (this work) Jordan (2005): Shock-cylinder + particles Tracer particles in Type Ia simulation Travaglio et al. (2004)

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago FLASH Modeling Framework The FLASH code q Eulerian hydro code q Godunov method q PPM q AMR q Highly scalable q Multiplatform q Efficient, parallel IO q Tracer particles

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago FLASH Example: K95 Flame Model qSimulates Chandrasekhar mass white dwarf qStarts with flame at bottom of domain. qEvolving RT-unstable deflagration front, followed by turbulent mixing qQuestion: Can we characterize the complex flows of the flame? qAnswer: Yes, use tracer particles Zhang et al. (2006): Simulation of turbulent flame. Based on calculation and setup in Khokhlov (1995)

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Tracer Particles in FLASH Tracer Particle Solve with Predictor-Corrector Method (v, T, , X i, …) i-1,j-1 (v, T, , X i, …) i-1,j (v, T, , X i, …) i,j-1 (v, T, , X i, …) i,j (v, T, , X i, …) i-1,j+1 (v, T, , X i, …) i,j+1 (v, T, , X i, …) i+1,j-1 (v, T, , X i, …) i+1,j (v, T, , X i, …) i+1,j+1

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago K95+particles: Turbulent 2-D Flame Model

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago 12 C 24 Mg ~ 1 km { K95+particles: Turbulent 3-D Flame Model q125,000 total tracer particles qThe particles were uniformly seeded 100 km above the initial position of the flame spread over a height of 120 km qExamine particles and continuum properties in horizontal slabs (specifically temperature and density)

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Temperature Distribution for Complete Set of Particles qTemperature bins are in units of 1X10 8 K qColors: Contours of percentage of particles in a temperature bin qBlack line: horizontal average temperature from hydro (continuum)

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Temperature distribution from random samples of 10% and 1% of the particles

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Density Distribution for Complete Set of Particles qDensity bins are in units of 2x10 6 g/cm 3 qColors: Contours of percentage of particles in a density bin qBlack line: horizontal average of density from hydro (continuum)

The ASCI/Alliances Center for Astrophysical Thermonuclear Flashes The University of Chicago Summary qPost-processing is a necessary element of complex hydrodynamic models with nuclear reactions qThe concept of tracer particles successfully implemented in the FLASH code and used in actual applications q Studies underway towards understanding of convergence properties of particle-enabled simulations towards continuum limit qProven to work in other applications, there is a promise we can put strict error limits on our thermonuclear hydro results