ET Workshop Fall 2011 RAD

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Possibilities

  • Leakage scheme
    • very ad-hoc
    • only mimicks loss due to radiation
  • Diffusion equation
    • accurate only when mean free path is really short
    • almost always implicit to avoid strong CFL limit
    • cheap, usually inaccurate
  • Flux limited diffusion
    • Diffusion + "trick" at lower optical depths
    • also simple, and has been used for supernovae simulations
    • unclear if working in GR
    • limits radiation speed: ad-hoc
    • also not very accurate
  • Two-Moment-Scheme / Truncated moment scheme
    • start with Boltzmann equation
    • decompose into moments
    • truncate series
    • close using some prescription (approximate the rest of the series)
  • Full Transport equation
    • Full discretization of Boltzmann equation
    • extremely complex
    • used, e.g., in reactor simulations
    • SN/PN discretize equation in different way
    • SN not scaling well
    • PN might work better
  • Monte-Carlo
    • no equations, direct simulations
    • very simple to implement complicated processes
    • more expensive
    • given enough computational power, very accurate
    • in 3D competitive with other methods in terms of computational needs

Implementations in "GR"

  • Shibata et al.
    • Leakage
    • Truncated Moment Formalism
  • Shapiro et al.
    • Diffusion approximation, grey, 3D
  • Garching
    • Full Boltzmann transport
    • 1D, ray-by-ray
  • Caltech / Cactus
    • Leakage scheme
    • Monte-Carlo
      • 1D only
  • AEI
    • Leakage