Sfumato AMR

What is Sfumato

Sfumato is an astrophysical simulation code with AMR (adaptive mesh refinement) technique for solving self-gravitational MHD problems. The main features are:

  • AMR
    • Block-structured grid with oct-tree data management
    • Three-dimensional Cartesian grid
    • Vectorized in unit of a block
    • Parallelization via MPI and ordering of the Peano-Hilbert space filling curve
    • Both of adaptive and synchronous time-step-modes are supported.
  • MHD (hyperbolic equation)
    • Roe’s and HLLD approximate Riemann solvers
    • 2nd order accuracy via TVD and predictor-corrector methods
    • Fully cell-centered scheme
    • Flux conservation at grid interfaces
    • Hyperbolic cleaning of divergence error
  • Self-gravity (Poisson equation; elliptic equation)
    • Multigrid method
    • FMG-cycle for main iteration
    • 2nd order accuracy via flux conservation at grid interfaces
  • Languages
    • The codes are written by Fortran90. MPI library, cpp, perl, sed are required for compiling the code.
  • Visualization
  • Misc
    • Implicit schemes for heat conduction and Ohmic dissipation
    • Sink particles
    • cure of carbuncle phenomena
    • Support of remapping data to an uniform grid


At this moment, Sfumato is not distributed because of issue of priority.


Tomoaki Matsumoto (Hosei University)


see “Image gallery”:research/image-gallery and Movie theater .


You can get some information on Sfumato.

  • An Implicit Scheme for Ohmic Dissipation with Adaptive Mesh Refinement,
    Tomoaki Matsumoto, * Publication of Astronoical Society of Japan, 63(2), 317-323, (2011) *
    [ preprint ]
  • Protostellar Collapse of Magneto-turbulent Cloud Cores: Shape during Collapse and Outflow Formation,
    Tomoaki Matsumoto & Tomoyuki Hanawa, *ApJ, Vol 728, Issue 1, article id. 47 * (2011) [ preprint ]
  • Self-gravitational Magnetohydrodynamics with Adaptive Mesh Refinement for Protostellar Collapse,
    Tomoaki Matsumoto, *PASJ, Vol.59, No.5, pp.905-927 * (2007)
    [ preprint ]
  • Development of Self-Gravitational Adaptive Mesh Refinement for Simulating Binary Star Formation,
    Tomoaki Matsumoto, Proceeding of Protostars and Planets V (2005)
    [ preprint ]

Code name

A code name, “SFUMATO”, comes from “Self-gravitational Fluid-dynamics Utilizing Mesh Adaptive Technique with Oct-tree.”

Ordinarily, a term, sfumato, denotes a painting technique used by many painters in the periods of Renaissance and Baroque. By means of sfumato, the outline of an object becomes obscure and diffusive as it is located in dense gas (see Wikipedia for detail). The most famous painter using this technique is Leonardo da Vinci . I also recommend you to see paints of Peter Paul Rubens . He also used this technique effectively. I would say, the code SFUMATO does not always reproduce diffusive solutions, I guess … 🙂