The Structure of Close Binaries in Two Dimensions
  The structure and evolution of close binary stars has been studied using the two-dimensional (2D) stellar structure algorithm developed by Deupree (1995). We have calculated a series of solar composition stellar evolution sequences of binary models, where the mass of the 2D model is 8Msun with a point-mass 5Msun companion. We have also studied the structure of the companion in 2D, by considering the zero-age main-sequence (ZAMS) structure of a 5Msun model with an 8Msun point-mass companion. In all cases the binary orbit was assumed to be circular and co-rotating with the rotation rate of the stars. We considered binary models with three different initial separations, a = 10, 14 and 20Rsun. These models were evolved through central hydrogen burning or until the more massive star expanded to fill its critical potential surface or Roche lobe. The calculations show that evolution of the deep interior quantities is only slightly modified from those of single star evolution. Describing the model surface as a Roche equipotential is also satisfactory until very close to the time of Roche lobe overflow, when the self gravity of the model about to lose mass develops a noticeable aspherical component and the surface time scale becomes sufficiently short that it is conceivable that the actual surface is not an equipotential. 
R. G. Deupree and A. I. Karakas