Convection project update

Project description

Phase 1: Putting OPAL Equation of state (EOS) into AstroBEAR
Phase 2: Run simulations will new EOS

OPAL EOS

History: Developed mainly by Forrest J. Rogers in 1990s, revised in 1996 and 2002

Includes

  1. non-relativistic Fermi-Dirac electrons
  2. classical ions
  3. all stages of ionization and excitation
  4. molecular hydrogen
  5. degenerate Columb correction
  6. quantum electron diffraction
  7. electron exchange
  8. pressure ionization
  9. terms arising from the so-called ladder diagrams of full quantum theory

Excludes

  1. pseudopotential method for going to higher order in electron-electro and electron-ion interaction (as far as in Rogers 1996)

Accurate to the order of

  1. Quantum diagrammatic procedure are used to calculate terms to order
  2. In the case of hydrogen, it agrees with -order correction

Online OPAL EOS table ​https://opalopacity.llnl.gov/opal.html

  1. 4 versions, the lastest is created in 2005 and updated in 2006.
  2. To determine which table we should use, we need Mentality and Hydrogen or Helium concentration or .
  3. Data ranges from to ; to
  4. Some interpolation code written in Fortran is also provided.

Ideal gas EOS

Assumes ideal, adiabatic and monoatomic gas

  2. adiabatic:
  3. Energy:

Comparision between Ideal gas EOS and OPAL EOS =

Red: OPAL
Green: Ideal

Pressure - density - temperature



Pressure - density - temperature - energy
X axis: density
Y axis: energy


By the way…
In run 143, frame 46 (reduSol)

min max
rho 1.483e-09 0.003275
T 2721.12 8.695e06
P 16007.5 1.0592e12

Next Step

  1. Understanding the difference between Ideal EOS and OPAL EOS

| Pressure comparison is much harder because pressure is a dependent variable in the table.

  1. Understand and use the Interpolation code
  2. Try to put them in AstroBEAR

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