Planetary Equations of State

Configuring SWIFT with the --with-equation-of-state=planetary and --with-hydro=planetary options enables the use of multiple equations of state (EoS). Every SPH particle then requires and carries the additional MaterialID flag from the initial conditions file. This flag indicates the particle’s material and which EoS it should use.

It is important to check that the EoS you use are appropriate for the conditions in the simulation that you run.

So far, we have implemented several Tillotson, ANEOS, SESAME, and Hubbard & MacFarlane (1980) materials, with more on the way. The material’s ID is set by a base type ID (multiplied by 100), plus a minor type:

  • Tillotson (Melosh, 2007): 1
    • Iron: 100
    • Granite: 101
    • Water: 102
  • Hubbard & MacFarlane (1980): 2
    • Hydrogen-helium atmosphere: 200
    • Ice H20-CH4-NH3 mix: 201
    • Rock SiO2-MgO-FeS-FeO mix: 202
  • SESAME (and similar): 3
    • Iron (2140): 300
    • Basalt (7530): 301
    • Water (7154): 302
    • Senft & Stewart (2008) water in a SESAME-style table: 303
  • ANEOS (in SESAME-style tables): 4
    • Forsterite (Stewart et al. 2019): 400
    • Iron (Stewart, 401
    • Fe85Si15 (Stewart, 402

Unlike the EoS for an ideal or isothermal gas, these more complicated materials do not always include transformations between the internal energy, temperature, and entropy. At the moment, we have implemented \(P(\rho, u)\) and \(c_s(\rho, u)\), which is sufficient for the Planetary (Density-Energy, Multi-Material) SPH hydrodynamics scheme, but makes these materials currently incompatible with entropy-based schemes.

The data files for the tabulated EoS can be downloaded using the examples/EoSTables/ script.

The Tillotson sound speed was derived using \(c_s^2 = \left. ( \partial P / \partial \rho ) \right|_S \) as described in Kegerreis et al. (2019). Note that there is a typo in the sign of \(du = T dS - P dV = T dS + (P / \rho^2) d\rho \), which was not used in the derivation.