FARGO3D

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The energy equation implemented in FARGO reads:

where is the thermal energy density (thermal energy per unit area), denotes the flow velocity, is the vertically integrated pressure, and () denote heating (cooling) source terms, assumed to be positive quantities. In this beta version of Fargo adiabatic, there is no cooling source term: . A heating source term due to the disk viscosity is however implemented, that reads ([[D'Angelo, G., Henning, T., & Kley, W. 2003, ApJ, 599, 548]]):

where denotes the cinematic viscosity (calculated with function FViscosity in Viscosity.c), , and are the components of the viscous stress tensor (calculated in function ComputeViscousTerms, as well as , in Viscosity.c). An ideal equation of state is used to close the hydrodynamics equations:

where denotes the universal gas constant, the mean molecular weight and the gas temperature. and are fixed to unity (see fondam.h). Furthermore, and are connected with:

where denotes the adiabatic index. Its value is given by the ADIABATICINDEX parameter (default value: 1.4). Our equation of state therefore reads:

and can also be recast as:

where denotes the adiabatic sound speed. We comment that is connected with the isothermal sound speed with .

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