Multi - D Simulations of the Thermonuclear Runaway on a White

We present the results of two-and three-dimensional calculations of turbulent nuclear burning of hydrogen-rich material accreted onto a white dwarf of 1.0 M. The main aim of the present paper is to investigate the question as to whether and how the general properties of the burning are aaected by dimension-ality and numerical resolution eeects. In particular, we want to see whether or not convective overshooting into the surface layers of the C+O white dwarf can lead to self-enrichment of the initially solar composition of the hydrogen-rich envelope with carbon and oxygen from the underlying white dwarf core.