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The mathematical part covers the implementation and§comparison of different numerical schemes to solve§the equations of radiation hydrodynamics. One and the§same two-dimensional model of solar granulation is§simulated with different high resolution numerical§methods (essentially non-oscillatory and convex§non-oscillatory) and non-grey short characteristic§radiative transfer. Furthermore the influence of§artificial diffusivities is studied. The second part§covers two astrophysical applications. A§two-dimensional non-grey high resolution simulation§of a downflowing plume in the sun and a grey§three-dimensional simulation of the quiet sun are§presented.