1 / 26

SFUMATO: A self-gravitational MHD AMR code

SFUMATO: A self-gravitational MHD AMR code. Outflow. Circumstellar disk. Tomoaki Matsumoto （ Hosei Univerisity ）. Matsumoto (2006) Submitted to PASJ, astro-ph/0609105. Magnetic field. Protostar. Computational domain is 1,000 times larger. H 13 CO + core.

crevan
Télécharger la présentation

SFUMATO: A self-gravitational MHD AMR code

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SFUMATO: A self-gravitational MHD AMR code Outflow Circumstellar disk Tomoaki Matsumoto （Hosei Univerisity） Matsumoto (2006) Submitted to PASJ, astro-ph/0609105 Magnetic field Protostar Computational domain is 1,000 times larger.

  2. H13CO+core Introduction:From a cloud to a protostar Outflow and Protostar (radio) Molecular cloud core in Taurus （radio） Orion molecular cloud （optical＋radio）

  3. B B 0.1 – 0.01 pc Introduction:From 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 = 5×10-5 1-10 AU First core ⇒ Second core ⇒ CTTS ⇒ WTTS ⇒ Main sequence 100 - 1000 AU Protostar

  4. ★ ★ ★ ★ 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

  5. Mona Lisa, Leonardo da Vinci (1503–1507) 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

  6. 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 (b) Self-similar block-structured (a) Block-structured (c) Unstructured rectilinear (d) Unstructured triangle Several types of AMR Level = 0 ～ 2

  7. (b) Self-similar block-structured (a) Block-structured (d) Unstructured triangle (c) Unstructured rectilinear AMR in astrophysics MHD and Self-gravity are implemented in many AMR codes

  8. 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) • HD・MHD • 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

  9. 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)

  10. 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

  11. Same model as Matsumoto & Hanawa (2003) Binary formation by AMR:Initial condition. 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

  12. 30 AU Binary formation by AMR:The cloud collapses and a oblate first core forms Isothermal gas Number of cells inside a block ＝　83 Polytorpe gas

  13. 30 AU Binary formation by AMR:It deforms into a ring.

  14. 30 AU Binary formation by AMR:The ring begins to fragment.

  15. 30 AU Binary formation by AMR: A binary system forms. Spiral arm Close binary

  16. 30 AU Binary formation by AMR: A spiral arm becomes a new companion. Companion Close binary

  17. 30 AU Binary formation by AMR: A triplet system forms (last stage). Companion Close binary

  18. Binary formation by AMR: Zooming-out（1/2） 500 AU

  19. Binary formation by AMR: Zooming-out（2/2） 2000 AU

  20. Level 11 Level 12 Level 13 Same model as Matsumoto & Tomisaka (2004) Cloud collapse and outflow formationSelf-gravitational MHD Magnetic field lines Radial velocity Density distribution

  21. 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

  22. Shock wave Wind Wall 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

  23. MHD rotor problem B = 5 P = 1 r = 10, 1 W = 20 0.2 1 Crockett et al. (2005) Toth (2000) This work pressure

  24. 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

  25. Convergence test of multi-grid method:2nd 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

  26. 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. • 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

More Related