SFUMATO: A self-gravitational MHD AMR code
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Transcript of SFUMATO: A self-gravitational MHD AMR code
SFUMATO: SFUMATO: A self-gravitational MHD AMR codeA self-gravitational MHD AMR code
Tomoaki Matsumoto
( Hosei Univerisity )Circumstellar disk
Outflow
Magnetic field
Protostar
Computational domain is1,000 times larger.
Matsumoto (2006) Submitted to PASJ, astro-ph/0609105
Introduction:Introduction:From a cloud to a protostarFrom a cloud to a protostar
H13CO+ core
Orion molecular cloud( optical + radio )
Molecular cloud corein Taurus ( radio )
Outflow and Protostar(radio)
Introduction:Introduction:From a cloud core to a protostarFrom a cloud core to a protostar
B
0.1 – 0.01 pc
Gravitationalcollapse B
Molecular cloud core Protostar, protoplanetary diskand outflow
1-10 AU
100 - 1000 AU
1AU/0.1pc = 5×10-5
First core ⇒ Second core ⇒ CTTS ⇒ WTTS ⇒ Main sequence
Protostar
MULTI-SCALE SIMULATION
MULTI-SCALE SIMULATION
EXTREMELY HIGH-RESOLUTION
EXTREMELY HIGH-RESOLUTION
Matsumoto (2006) Submitted to PASJ, astro-ph/0609105
Nested Grid, static grids AMR, dynamically allocated grids
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Self-gravitational Fluid-dynamics Utilizing Mesh Adaptive Technique with Oct-tree.
Developed in 2003 Matsumoto & Hanawa (2003)
Cf., Talks of Mikmi, Tomisaka, Machida(male), Hanawa
What is SfumatoWhat is Sfumato Sfumato originally denotes a
painting technique developed by Leonardo da Vinci (14521519).
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
Mona Lisa, Leonardo da Vinci (1503–1507)
Several types of AMRSeveral types of AMR(a) Block-structured grid
Origin of AMR Most commonly used Enzo, ORION, RIEMANN, etc.
(b) Self-similar block-structured grid Commonly used FLASH, NIRVANA, SFUMATO, e
tc.
(c) Unstructured rectilinear grid (cell-by-cell grid) Also used in astrophysics
(d) Unstructured triangle grid Not used in astrophysics It takes advantage so that cells ar
e fitted to boundaries/body
Level = 0 ~ 2
(a) Block-structured (b) Self-similar block-structured
(c) Unstructured rectilinear
(d) Unstructured triangle
AMR in astrophysicsAMR in astrophysicsMHD and Self-gravity areimplemented in many AMR codes
Code name Author(s) Main targets Grid type MHDSelf-gravity
Dark Matter
Radiative transfer
ORION R. Klein Star formation (a) Y Y N Y
Enzo M. Norman Cosmology (a) Y Y Y N
FLASH ASC/U-Chicago Any (b) Y Y ( Y ) ( Y )
BAT-R-US K. G. Powell Space weather (b) Y Y N N
NIRVANA U. Ziegler Any (b) Y Y N N
RIEMANN D. Balsara ISM (a) Y Y N N
RAMSES R. Teyssier Cosmology (c) Y Y Y N
? M.A. de Avillez ISM (b) Y N N N
VPP-AMR H. Yahagi Cosmology (c) N Y Y N
SFUMATO T. Matsumoto Star formation (b) Y Y N N
(a) Block-structured (b) Self-similar block-structured
(c) Unstructured rectilinear
(d) Unstructured triangle
Summary of implementation of SfumatoSummary 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 curv
e)
HD ・ MHD Based on the method of Berger & Colella (1989) . Numerical fluxes are conserved Scheme: TVD, Roe scheme, predictor-corrector method (2nd order accur
acy 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
Conservation of numerical fluxConservation of numerical flux
cyclesub surface
hhhHHH tSFtSF
Flux conservation requires
Flux on coarse cell surface = sum of four fluxes on fine cell surfaces
FH is modified for HD, MHD, and self-gravity Berger & Collela (1989) Matsumoto & Hanawa (2003)
Numerical results 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 hydr
o-dynamics) Double Mach reflection problem (Hydro-dynamics) MHD rotor problem (MHD)
Convergence test of self-gravty
Binary formation by AMR:Binary formation by AMR:Initial condition. Initial condition.
0.14 pc
Number of cells inside a block = 83
Initial condition Almost equilibrium Slowly rotation Non-magnetized Small velocity perturbation of m = 3. Isothermal gas
Isothermal gas
Same model as Matsumoto & Hanawa (2003)
Binary formation by AMR:Binary formation by AMR:The cloud collapses and a oblate first core formsThe cloud collapses and a oblate first core forms
30 AU
Number of cells inside a block = 83
Isothermal gas
Polytorpe gas
Binary formation by AMR:Binary formation by AMR:It deforms into a ring.It deforms into a ring.
30 AU
Binary formation by AMR:Binary formation by AMR:The ring begins to fragment.The ring begins to fragment.
30 AU
Binary formation by AMR: Binary formation by AMR: A binary system forms.A binary system forms.
30 AU
Spiral arm
Close binary
Binary formation by AMR: Binary formation by AMR: A spiral arm becomes a new companion.A spiral arm becomes a new companion.
30 AU
Companion
Close binary
Binary formation by AMR: Binary formation by AMR: A triplet system forms (last stage).A triplet system forms (last stage).
30 AUClose binary
Companion
Binary formation by AMR: Binary formation by AMR: Zooming-outZooming-out (( 1/21/2 ))
500 AU
Binary formation by AMR: Binary formation by AMR: Zooming-outZooming-out (( 2/22/2 ))
2000 AU
Cloud collapse and outflow formationCloud collapse and outflow formationSelf-gravitational MHDSelf-gravitational MHD
Density distribution
Magnetic field lines
Radial velocity
Level 11
Level 12
Level 13
Same model as Matsumoto & Tomisaka (2004)
Fragmentation of a rotating isothermal cloudFragmentation of a rotating isothermal cloud10% of bar perturbation, 10% of bar perturbation, = 0.26, = 0.26, = 0.16 = 0.16
ORION: Truelove et al. (1998) SFUMATO: Matsumoto (2006)
Level = 3 - 7
Double Mach reflection problemDouble Mach reflection problem
Wall
Wind
Shock wave
density
blocks
Level 0: h = 1/64Level 1: h = 1/128Level 2: h = 1/256Level 3: h = 1/512Level 4: h = 1/1024
MHD rotor problemMHD rotor problem
Toth (2000) Crockett et al. (2005) This work
B = 5P = 1= 10, 1 = 20
10.2
pressure
Estimation of error of gravity Estimation of error of gravity for binary spheresfor binary spheres
||/||log exex ggg
Convergence testchanging number of cells inside a block as23, 43, 83, 163,323 cells
Uniform spheres
Level 0 Level 3
Convergence test of multi-grid method:Convergence test of multi-grid method:22ndnd order accuracy order accuracy
Source: binary stars Maximum level = 4 Distribution of
blocks is fixed. Number of cells
inside a block is changed.
Error h∝ max2
◇ level = 0○ level = 1
◆ level = 2● level = 3■ level = 4
323/block
163
83
43
23
Cell width of the finest level
L2
no
rm o
f err
or o
f gra
vity
SummarySummary 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. HD ・ MHD
Cell-centered, TVD, Roe’s 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