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 FlashesThe University of Chicago

Industry Combustion in Engine Rockets

Safety Pool fires

C-Safe ASC center, University of Utah

Reactive Flows in “Real” World

NASA

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

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

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

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

Feasible Reactive Flow Computations

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

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.)

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

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 aren’t resolved in the

simulation?

Metric for determining accuracy of particle sample Post-processing example: Compare final yields, particle trajectories

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

Turbulent Flows

Starts as R-T unstable and transits to turbulence.

Wide range of length scales; can’t capture all in the model simultaneously

Must use subgrid scale model to account for unresolved scales

Cabot et al. 2005

Non-Reactive turbulent flow

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

Turbulent Flows

0.1 km resolutionReactive turbulent flow

Zingale et al. 2005

0.1cm resolution

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

Turbulent Flames with Tracer Particles

Concentration of NO, particles compared to continuum.

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

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

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)

Jordan (2005): Shock-cylinder + particles

Tracer particles in Type Ia simulation Travaglio et al. (2004)

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

FLASH Modeling Framework

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

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

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)

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

Tracer Particles in FLASH

Tracer Particle

Solve with Predictor-Corrector Method

(v, T, , Xi, …)i-1,j-1(v, T, , Xi, …)i-1,j

(v, T, , Xi, …)i,j-1

(v, T, , Xi, …)i,j

(v, T, , Xi, …)i-1,j+1

(v, T, , Xi, …)i,j+1

(v, T, , Xi, …)i+1,j-1(v, T, , Xi, …)i+1,j (v, T, , Xi, …)i+1,j+1

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

K95+particles: Turbulent 2-D Flame Model

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

12C

24Mg

~ 1 km {

K95+particles: 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)

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

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)

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

Temperature distribution from random samples of 10% and 1% of the particles

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

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)

The ASCI/Alliances Center for Astrophysical Thermonuclear FlashesThe University of Chicago

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