Features¶
The library provides a method to recover primitive variables \(\rho, \epsilon, Y_e, P, v^i, W, E^i\) from the evolved variables \(D, \tau, S_i, Y_e^T, B^i\) of the conservation-law formulation of relativistic ideal magnetohydrodynamics. The code implements exactly the algorithm described in the acompanying article.
The implementation determines whether the evolved variables correspond to valid primitives or not. Valid means that the matter state \(\rho,\epsilon,Y_e\) is in the valid range of the EOS, in particular that the fluid internal energy is above the value at zero temperature. In addition, one can specify technical restrictions if meaningful for the evolution code: a speed limit and bound for magnetization.
Further, the code can project the evolved variables back onto the valid regime. The main correction is to set the fluid internal energy to the closest value valid at given mass density for the EOS. In addition, the velocity can be limited to the speed limit by rescaling the momentum, and the electron fraction can be adjusted to the valid range of the EOS. The magnetic field is never corrected, as this cannot be done locally in a meaningful way.
If a given correction is applied is decided by a parametrized error policy. The implemented policy is geared towards simulations of isolated neutron stars, binary neutron mergers, and collapse to black hole. It only contains simple conditions, as everything more involved is likely specific to the evolution code.
In detail, the policy is characterized by the following parameters:
A density above which the only allowed corrections are adjusting internal energy below zero temperature value and the electron fraction to the allowed range (“strict” regime).
A maximum velocity above which failure is reported in the strict regime and momentum rescaling applied otherwise.
An upper limit for the ratio of magnetic and mass energy densities, above which failure is reported (at any density).
A flag whether to restrict the electron fraction to the allowed range also in the strict regime, or whether to report failure.
It is simple to declare different error policies and apply them in different regimes. For example, the evolution code could use the lapse function to estimate if a point is inside a black hole, and then apply a more lenient policy.
Finally, the implementation can enforce an artificial atmosphere on the fluid. In detail, below a given mass density, \(\rho,\epsilon,Y_e\) are set to specified values, and the velocity set to zero. For the EM part, the electric field is set to zero and the magnetic field is left unchanged. The evolved variables are set consistent with those primitives. This is a very crude approach that might lead to incorrect evolution of the magnetic field in regions with atmosphere. Any improvement is specific to the evolution code and should be handled there.