Description:

This patch for ZEUS3D v3.4.2 implements new cooling which is able to work in case of extremely fast cooling like for instance during the thermal instability of the gas. It is achieved by using more stable root finding algorithm (Brent's method) for solving the energy equation, and in particular by controlling the size of the time-step by the cooling rate.

The "cooling" time-step is defined dt_cool = e/[ρΛ(T,z)] where ρ and e are the local mass and energy densities, Λ(T,z) is the cooling function, and CCN is the "cooling Courant number" - a dimensionless quantity which denotes the relative amount of internal energy that can be radiated away during dt_cool.

Local sub-steps for the computation of the energy equation are used to increase the code performance; the global time-step is

where dt_HD is the hydrodynamic time-step and δ (typically δ≈0.1) is a dimensionless parameter.

This procedure does not let the global time-step decrease below δ× dt_HD. However, the accuracy in solving the equation of energy is ensured by the sub-steps of size dt_cool which are only applied to fast cooling regions.

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Diagram of subroutine calls