  We simulate numerically the surface flow of a gas-supplying companion star in
a semi-detached binary system. Calculations are carried out for a region
including only the mass-losing star, thus not the mass accreting star. The
equation of state is that of an ideal gas characterized by a specific heat
ratio gamma, and the case with gamma=5/3 is mainly studied. A system of eddies
appears on the surface of the companion star: an eddy in the low pressure
region near the L1 point, one around the high pressure at the north pole, and
one or two eddies around the low pressure at the opposite side of the L1 point.
Gas elements starting near the pole region rotate clockwise around the north
pole (here the binary system rotates counter-clockwise as seen from the north
pole). Because of viscosity, the gas drifts to the equatorial region, switches
to the counter-clockwise eddy near the L1 point and flows through the L1 point
to finally form the L1 stream. The flow field in the L1 region and the
structure of the L1 stream are also considered.
