The dynamical conservation equations are integrated in two spatial dimensions and time near the peak of the core helium flash. The two-dimensional nature eliminates the need for a phenomenological theory of convection, as convective flow patterns are followed. Calculations indicate that the core helium flash is nonviolent, but that the relation between convection and the thermal runaway is considerably more complex than heretofore believed. It is found that the region interior to the flash peak is significantly heated by downward convection energy transport, and presumably mixed as well. Subsidiary calculations indicate that this heating will begin well before the peak of the thermal runaway. Effects of composition variation are discussed.