Two-dimensional simulation of convection in a red giant envelope

The problem of modeling the convection in red giant envelopes is addressed with two-dimensional nonlinear and nonadiabatic simulations. Hydrostatic envelopes, in thermal equilibrium, were integrated using the mixing-length theory (MLT) for different values of the mixing-length parameter λ. We examined the energy balance for two-dimensional simulations by using the MLT envelopes as initial model. On the basis of these two-dimensional simulations, we identify a model that is close to two-dimensional equilibrium. Such a model is characterized by an initial mixing-length parameter. Its value depends upon the numerical resolution, varying from 1.0 for low resolution to 1.5 for the best resolution at present.