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We present a numerical method for the study of double white dwarf (DWD)binary systems at the onset of super-Eddington mass transfer. We incorporatethe physics of ideal inviscid hydrodynamical flow, Newtonian self-gravity, andradiation transport on a three-dimensional uniformly rotating cylindricalEulerian grid. Care has been taken to conserve the key physical quantities suchas angular momentum and energy. Our new method conserves total energy to ahigher degree of accuracy than other codes that are presently being used tomodel mass-transfer in DWD systems. We present the results of verificationtests and we simulate the first 20+ orbits of a binary system of mass ratio q =0.7 at the onset of dynamically unstable direct impact mass transfer. The masstransfer rate quickly exceeds the critical Eddington limit by many orders ofmagnitude, and thus we are unable to model a trans-Eddington phase. It appearsthat radiation pressure does not significantly effect the accretion flow in thehighly super-Eddington regime. An optically thick common envelope forms aroundthe binary within a few orbits. Although this envelope quickly exceeds thespatial domain of the computational grid, the fraction of the common envelopethat exceeds zero gravitational binding energy is extremely small, suggestingthat radiation-driven mass loss is insignificant in this regime. It remains tobe seen whether simulations that capture the trans-Eddington phase of suchflows will lead to the same conclusion or show that substantial material getsexpelled.

A Numerical Method for Studying Super-Eddington Mass Transfer in Double White Dwarf Binaries