  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
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 the spiral
shocks are formed on the disc. These features are similar to that observed in
the case of an adiabatic gas with a lower specific heat ratio, $\gamma=1.01$.
It is found that when radiative cooling effect is accounted for, the mass of
the disc becomes larger than that assuming $\gamma=5/3$, and smaller than that
assuming $\gamma=1.01$. It is concluded that employing an adiabatic gas with a
lower specific heat ratio is almost a valid assumption for simulating accretion
disc with radiative cooling effect.
