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MHD simulations of sunspots have successfully reproduced many aspects ofsunspot fine structure as consequence of magneto convection in inclinedmagnetic field. We study how global sunspot properties and penumbral finestructure depend on the magnetic top boundary condition as well as on gridspacing. The overall radial extent of the penumbra is subject to the magnetictop boundary condition. All other aspects of sunspot structure and penumbralfine structure are resolved at an acceptable level starting from a gridresolution of 48 [24] km (horizontal [vertical]). We find that the amount ofinverse polarity flux and the overall amount of overturning convective motionsin the penumbra are robust with regard to both, resolution and boundaryconditions. At photospheric levels Evershed flow channels are stronglymagnetized. We discuss in detail the relation between velocity and magneticfield structure in the photosphere and point out observational consequences.

Numerical sunspot models: Robustness of photospheric velocity and magnetic field structure