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Published online by Cambridge University Press: 30 March 2016
Numerical radiation hydrodynamics simulations of stellar surface convection have gained a high level of reliability and perform very well in the confrontation with observations. Similar simulations of convection zones in stellar interiors are much more difficult to set up because of the huge range of time-scales to cover. Therefore, simplified models have to be used, where the results have to be carefully extrapolated to apply them to stellar interiors. Simulations of shallow surface convection zones show that the overshooting velocity fields extend far beyond the region with significant convective energy flux.