be formed around the binary whereas no circumbinary disc is formed in the SPH calculation. This is due to the larger separation of the binary when $M_{\rm acc}\simgreat 3$ and the large shear viscosity in the SPH calculation.

### Test Case 2

Unlike test case 1, the PBE code predicts that a massive circumbinary disc should be produced very early in the evolution of test case 2. Thus, test case 2 provides a better test of how well the PBE code predicts the formation of a circumbinary disc and its evolution. We note that, although the PBE code records the amount of gas which settles into a circumbinary disc, it does not attempt to take account of the interaction between the binary and the circumbinary disc. In reality, this interaction is expected to result in the transfer of angular momentum from the orbit of the binary into the gas of the circumbinary disc and, hence, in a smaller separation. Furthermore, if the separation decreases, more of the infalling gas would be expected to settle into the circumbinary disc and, for the same increase in the binary’s mass, the mass ratio should increase more rapidly because the gas has a greater 