Two-dimensional numerical simulations of an accretion flow in a close binary system are performed by solving the Euler equations with radiative transfer. In the present study, the specific heat ratio is assumed to be constant while the radiative cooling effect is included as a non-adiabatic process. The cooling effect of the disc is considered by discharging energy in the vertical directions from the top and bottom surfaces of the disc. We use the flux-limited diffusion approximation to calculate the radiative heat flux values. Our calculations show that a disc structure appears and spiral shocks are formed on the disc. These features are similar to those observed in the case of an adiabatic gas with a lower specific heat ratio, γ = 1.01. It is found that, when the radiative cooling effect is accounted for, the mass of the disc becomes larger than that assuming γ = 5/3, and smaller than that assuming γ = 1.01. We conclude that employing an adiabatic gas with a lower specific heat ratio is almost a valid assumption for simulating an accretion disc with the radiative cooling effect.
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