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tokens: envelope for the AGB case, apparently because outward energy transport by spiral shocks is impeded by a dense inner envelope in the RGB case. For the volume-integrated energy terms (normalized by the total initial energy), there was a high level of agreement between the two runs, but with a few notable differences. The potential energy term involving the primary core and envelope is relatively more important in the AGB case (higher particle mass, more centrally condensed envelope), while the potential energy terms involving the secondary and envelope and self-gravity of the envelope are relatively more important in the RGB case (larger envelope mass). Our setup can eventually be improved by using a synchronously rotating primary initialized at the Roche limit separation (MacLeod, Ostriker Stone 2018 ; Reichardt et al. 2019 ), although this comes at a much higher computational cost. Radiative transfer and a more realistic non-ideal equation of state are needed. Including these ingredients will allow us to model ionization and recombination, radiative cooling, and convection, all of which are likely important for the budget and redistribution of energy in the envelope, and more accurate modelling of envelope unbinding. Despite these caveats, the projection of to unbind the envelope suggests that the universal failure in previous simulations to eject it without recombination is unlikely a consequence of insufficient physics, but the result of a combination of numerical limitations and insufficient run time. Nevertheless, the need to improve both the physics and the numerical capabilities of simulations remains, while also expanding into new regions of phenomenologically relevant parameter space. APPENDIX A: INITIAL CONDITIONS Initial profiles for the AGB primary star used are presented in Fig. A1 . We refer the reader to Chamandy et al. ( 2019a ) for the same profiles for the RGB star used. Figure A1. Top panel: radial profile of gas density for the AGB star modelled using mesa (thick orange curve) and the envelope of our 3D AGB star in the simulation at t = 0 (thin black curve). Middle panel: comparison of the internal energy density profiles in the mesa model, the simulation initial envelope, and the mesa model with the equation of state replaced with an ideal gas equation of state, as in the simulation (dashed red curve). Bottom panel: comparison of (negative of) potential energy density profiles in the mesa model and the simulation initial envelope. APPENDIX B: ENERGY NON-CONSERVATION The degree to which energy conservation is satisfied for our AGB run (denoted Model A) and two lower resolution AGB runs (Models B and C) is shown in Fig. B1 , where the fractional change in the total energy (accounting for flux through the domain boundaries) is plotted. The level of adherence to energy conservation is sensitive to the resolution around the primary core particle, and, after the first periastron passage, also to the resolution around the