ET Workshop Fall 2011 RAD

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