SFUMATO: A selfgravitational MHD AMR code

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SFUMATO A self-gravitational MHD AMR code
Outflow

• Tomoaki Matsumoto
• (Hosei Univerisity)

Circumstellar disk
Matsumoto (2006) Submitted to PASJ,
astro-ph/0609105
Magnetic field
Protostar
Computational domain is 1,000 times larger.
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IntroductionFrom a cloud to a protostar
Outflow and Protostar (radio)
Molecular cloud core in Taurus (radio)
Orion molecular cloud (opticalradio)
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IntroductionFrom a cloud core to a protostar
EXTREMELY HIGH-RESOLUTION
Protostar, protoplanetary disk and outflow
Molecular cloud core
Gravitational collapse
MULTI-SCALE SIMULATION
1AU/0.1pc 510-5
1-10 AU
First core ? Second core ? CTTS ? WTTS ? Main
sequence
100 - 1000 AU
Protostar
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Self-gravitational Fluid-dynamics Utilizing Mesh
Adaptive Technique with Oct-tree.
AMR, dynamically allocated grids
Nested Grid, static grids
Developed in 2003 Matsumoto Hanawa
(2003) Cf., Talks of Mikmi, Tomisaka,
Machida(male), Hanawa
Matsumoto (2006) Submitted to PASJ,
astro-ph/0609105
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What is Sfumato

• Sfumato originally denotes a painting technique
  developed by Leonardo da Vinci (1452-1519).
• It was used by many painters in the Renaissance
  and Baroque.
• The outline of an object becomes obscure and
  diffusive as it is located in dense gas.
• Artists expressed AIR.
• The code expresses GAS.
• Sfumato Smoky in Italian
• NOT anagram of Matsumoto

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Several types of AMR
Level 0 2

• Block-structured grid
• Origin of AMR
• Most commonly used
• Enzo, ORION, RIEMANN, etc.
• Self-similar block-structured grid
• Commonly used
• FLASH, NIRVANA, SFUMATO, etc.
• Unstructured rectilinear grid (cell-by-cell grid)
• Also used in astrophysics
• Unstructured triangle grid
• Not used in astrophysics
• It takes advantage so that cells are fitted to
  boundaries/body

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AMR in astrophysics
MHD and Self-gravity are implemented in many AMR
codes
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Summary of implementation of Sfumato

• Block structured AMR
• Every block has same size in memory space.
• Data is managed by the oct-tree structure.
• Parallelized and vectorized (ordering via
  Peano-Hilbert space filling curve)
• HDMHD
• Based on the method of Berger Colella (1989) .
• Numerical fluxes are conserved
• Scheme TVD, Roe scheme, predictor-corrector
  method (2nd order accuracy in time and space)
• Cell-centered sheme
• Hyperbolic cleaning of ?B (Dedner et al. 2002)
• Self-gravity
• Multi-grid method (FMG-cycle, V-cycle)
• Numerical fluxes are conserved in FMG-cycle

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Conservation of numerical flux
Flux conservation requires
Flux on coarse cell surface sum of four fluxes
on fine cell surfaces
Berger Collela (1989)
FH is modified for HD, MHD, and self-gravity
Matsumoto Hanawa (2003)
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Numerical results

• Recalculation of our previous simulations
• Binary formation (self-gravitational
  hydro-dynamics)
• Matsumoto Hanawa (2003)
• Outflow formation (self-gravitational MHD)
• Matsumoto Tomisaka (2004)
• Standard test problems
• Fragmentation of an isothermal cloud
  (self-gravitational hydro-dynamics)
• Double Mach reflection problem (Hydro-dynamics)
• MHD rotor problem (MHD)
• Convergence test of self-gravty

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Binary formation by AMRInitial condition.
Same model as Matsumoto Hanawa (2003)
Number of cells inside a block 83
Isothermal gas

• Initial condition
• Almost equilibrium
• Slowly rotation
• Non-magnetized
• Small velocity perturbation of m 3.
• Isothermal gas

0.14 pc
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Binary formation by AMRThe cloud collapses and
a oblate first core forms
Isothermal gas
Number of cells inside a block 83
Polytorpe gas
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Binary formation by AMRIt deforms into a ring.
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Binary formation by AMRThe ring begins to
fragment.
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Binary formation by AMR A binary system forms.
Spiral arm
Close binary
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Binary formation by AMR A spiral arm becomes a
new companion.
Companion
Close binary
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Binary formation by AMR A triplet system forms
(last stage).
Companion
Close binary
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Binary formation by AMR Zooming-out(1/2)
500 AU
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Binary formation by AMR Zooming-out(2/2)
2000 AU
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Cloud collapse and outflow formationSelf-gravitat
ional MHD
Same model as Matsumoto Tomisaka (2004)
Magnetic field lines
Radial velocity
Density distribution
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Fragmentation of a rotating isothermal cloud10
of bar perturbation, a 0.26, b 0.16
ORION Truelove et al. (1998)
SFUMATO Matsumoto (2006)
Level 3 - 7
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Double Mach reflection problem
Level 0 h 1/64 Level 1 h 1/128 Level 2 h
1/256 Level 3 h 1/512 Level 4 h 1/1024
density
blocks
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MHD rotor problem
B 5 P 1 r 10, 1 W 20
0.2
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Crockett et al. (2005)
Toth (2000)
This work
pressure
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Estimation of error of gravity for binary spheres
Uniform spheres
Level 3
Level 0
Convergence test changing number of cells inside
a block as 23, 43, 83, 163,323 cells
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Convergence test of multi-grid method2nd order
accuracy

• Source binary stars
• Maximum level 4
• Distribution of blocks is fixed.
• Number of cells inside a block is changed.

? level 0 ? level 1 ? level 2 ? level 3
level 4
23
43
83
L2 norm of error of gravity
163
323/block
Error ? hmax2
Cell width of the finest level
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Summary

• A self-gravitational MHD AMR code was developed.
• Block-structured grid with oct-tree data
  management
• Vectorized and parallelized
• Second order accuracy in time and space.
• HDMHD
• Cell-centered, TVD, Roes scheme,
  predictor-corrector method
• Hyperbolic cleaning of ?B
• Conservation of numerical flux
• Self-gravity
• Multi-grid method
• Conservation of numerical flux
• Numerical results
• Consistent with the previous simulations
• Pass the standard test problems