1. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Simulating Astrophysical Combustion with the FLASH code Jonathan Dursi (and many, many others) Canadian Institute for Theoretical Astrophysics University of Toronto

2. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Outline ● Combustion in Astrophysics ● The FLASH code ● Testing / V&V ● Towards Multiscale/subgrid approaches (Röpke, Max Planck Institute for Astrophysics)

3. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Combustion in Astrophysics ● Almost all astrophysical systems are fluid – Hot, dense ● Many interesting phenomenon involve energetic phase transitions -- `burning' ● Some very exotic – phase transitions in early universe – quark-matter deconfinement (Röpke, Max Planck Institute for Astrophysics) Vladimirova, FLASH Center

4. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Combustion in Astrophysics ● Most systems: – Burning = thermonuclear reactions ● Stable burning (simmering/smouldering): – Stars like the sun (well-mixed reactor) ● Explosive burning (thermonuclear flashes): – Novae – X-Ray Bursts – Supernovae : SOHO - EIT Consortium, ESA, NASASOHOEIT ConsortiumESANASA

5. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Combustion in Astrophysics ● Differences from terrestrial combustion: – Thermonuclear reactions, not chemical ● Fairly minor differences in behaviour ● Arrhenius-like ● Much simpler `chemistry'! – Energetics captured with ~10 species (Wikipedia)

6. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Combustion in Astrophysics ● Differences from terrestrial combustion: – Equation of State – (Partially) degenerate material ● Supported by degenerate electron pressure – Pressure insensitive to temperature at high densities ● Explosive burning Andrew Truscott & Randall Hulet (Rice U.)Randall HuletRice U.

7. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Combustion in Astrophysics: Novae ● Burning on surface of white dwarf ● Accretes matter (hydrogen, helium) from neighbor faster then can stably burn ● Burst of convective burning, lifts accreted envelope, sends burned material into surroundings ● Important source of heavy elements for new stars, planets Courtesy Hubble STScI

8. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Combustion in Astrophysics: Novae ● Simulations: – Unstable burning in convecting atmosphere – Burning ~subsonic, mixes through atmosphere as it lifts – Plane-parallel simulations looking at little piece of the white dwarf atmosphere – Mixing into white dwarf crucial for mechanism Kercek, Hillebrandt, Truran (1999)

9. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Combustion in Astrophysics: X-Ray Bursts ● Burning on surface of neutron star ● Higher gravity: higher densities ● Burning proceeds as deflagration (detonation?) ● Visible in X-rays from great distances. Gravity too strong for important amounts of ejecta Courtesy Chandra X-Ray Observatory

10. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Combustion in Astrophysics: X-Ray Bursts ● Surface of a large (~30 km) body: can consider local piece ● Burning propagates along layer of fuel as flame or detonation ● Heats, roils atmosphere ● Simulations of large scale behaviour, small scale flame/detonation physics Zingale, SUNY Stony Brook

11. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Combustion in Astrophysics: Supernovae Ia ● White dwarf accretes material slowly ● Centre gets hotter, denser ● Simmering, rotating -- highly turbulent ● Burning begins in centre of star as flame ● Transition to detonation? ● Total incineration of white dwarf ● One of largest explosions in universe Courtesy Hubble STScI

12. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 ● Basic combustion simulations: – Cellular detonations in white dwarfs – (unburned pockets potentially very interesting in Type Ia context) Combustion in Astrophysics: Supernovae Ia

13. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 ● Effect of strain/curvature on thermonuclear flame speed (`Markstein Length') Combustion in Astrophysics: Supernovae Ia

14. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Combustion in Astrophysics: Supernovae Ia ● Large-scale simulations of system – Some assumed turbulent burning model

15. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Modeling Combustion in Astrophysics ● Large, small scale simulations ● Turbulent burning, flames, detonations ● Complex EOS, highly compressible ● Want code that is – Robust – Well-tested methods – Could scale to masssively parallel systems

16. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 The Flash Code Cellular detonation Compressed turbulence Helium burning on neutron stars Richtmyer-Meshkov instability Laser-driven shock instabilities Nova outbursts on white dwarfs Rayleigh-Taylor instability Flame-vortex interactions Gravitational collapse/Jeans instability Wave breaking on white dwarfs Shortly: Relativistic accretion onto NS Orzag/Tang MHD vortex Type Ia Supernova Intracluster interactions Magnetic Rayleigh-Taylor

17. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 Cellular detonation Compressed turbulence Helium burning on neutron stars Richtmyer-Meshkov instability Laser-driven shock instabilities Nova outbursts on white dwarfs Rayleigh-Taylor instability Flame-vortex interactions Gravitational collapse/Jeans instability Wave breaking on white dwarfs Shortly: Relativistic accretion onto NS Orzag/Tang MHD vortex Type Ia Supernova Intracluster interactions Magnetic Rayleigh-Taylor FLASH code: Explicit reactive hydrodynamics code AMR, massively parallel (65536 procs+) Scales very well Highly portable Used, tested on wide variety of problems Rigorously tested Modular (easy to add/change physics modules) Widely available (http://flash.uchicago.edu) The Flash Code

18. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 The Flash Code – AMR ● Required because of very large dynamic range of scales. ● Permitted by locality of problems ● Can do bigger problems ● But hard because: ● Frequent redistribution ● Load balancing ● Irregular, unpredictable memory/message patterns; hard to precompute things ● Refinement/derefinement a black art.

19. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 The Flash Code – AMR ● PARAMESH library developed at NASA/GSFC ● Local physics occurs on a block as if isolated. ● Number of guardcells depends on stencil size. ● Number of interior points : ● More cells - more efficient (until block too big for cache) ● Fewer cells - can refine more quickly in smaller area. Guard Cells Interior Cells

20. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 The Flash Code – AMR ● Blocks and refinement are in an oct-tree structure. ● Refining block -> 2 d children created, each with 2x resolution of parent ● Neighbor blocks must differ by at most one level of refinement. ● Drawback: resolution can only fall of linearly in distance. ● Feature: simplifies, speeds up accurate calculation of `boundary conditions' (guardcells) 10 11 6 18 12 2 8 7 9 1419 20 21 1 4 5 13 16 15 17 3 Refinement Level 10 1345 2 6 789 1112 13 14 1516 17 18 192021

21. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 The Flash Code – Hydrodynamics ● Hydrodynamics algorithms informed by highly compressible problems typical in astrophysics ● Finite volume Godunov schemes ● Dimensionally split ● Extremely capable for modelling shocks, detonations

22. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 The Flash Code – Hydrodynamics ● Piecewise Parabolic Method ● Defines an upwinded parabola at each point with correct cell average ● Very aggressive `flattening' to enforce a very strict measure of monotonicity ● Also flattens at contact discontinuities ● Long history in compressible astrophysical flows

23. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 The Flash Code – Hydrodynamics ● Parabolas improve space accuracy ● To improve time accuracy, must modify how left,right states are chosen for Riemann solve ● Estimate characteristic speeds in cell and find region which is connected to interface in timestep ● Average over reconstruction in that region ● Those are left, right states for Riemann solve

24. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 ● Simulating situations unavailable to experiment ● Testing code results particularly important ● Testing must take such forms as it can FLASH V&V

25. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 ● Simplest: check for bugs from multiple developers, compilers... ● Test suite run nightly on multiple platforms ● Includes each physics module, integration ● Differences (to machine precision) are flagged, along with code changes FLASH V&V

26. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 ● Test suite includes standard test cases for physics modules with known solutions ● More complicated test cases with `benchmark' solutions FLASH V&V

27. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 ● Validation: Cannot compare to astrophysical problems directly ● Compare to experiments of relevant fluid instabilities ● Very challenging tests FLASH V&V

28. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 FLASH V&V ● Collaboration w/ experimenters essential for comparison ● Iterative process ● Instabilities: can only compare statistically

29. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 FLASH V&V

30. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 ● Propagation of turbulent flame ● Total burning needed for large- scale models ● Simulations of buoyantly turbulent flames in low-speed code ● Development of models for inclusion into large-scale models ● Turbulent burning is challenging! Development of subgrid models: flames Zingale, SUNY Stony Brook

31. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 ● Ignition in supernovae likely happen at `turbulent hotspots' ● Large-scale reactive turbulence ● For given turbulence intensity, how does ignition happen? Development of subgrid models: ignition

32. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 ● Many 1d spherical simulations of igniting hotspots ● Determine `flammability limits’ ● Highly nonlinear ● Non-igniting hotspots contribute little energy to flow Development of subgrid models: ignition

33. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 ● Large 1d, 3d simulations of compressible reactive turbulence ● Extract temperature, hotspot PDF ● Need large simulations – ignition points are necessarily rare events Development of subgrid models: ignition

34. CITA|ICAT Jonathan Dursi CAIMS-MITACS 2006 June 19 ● Development/Integration of all-speed solvers essential for modeling ignition through explosion ● Development of meaningful subgrid models must continue ● Continuing testing methods against instability experiments: often interesting research problems in their own right. Future Work