Computational astrophysics is a firmly established research methodology by now, and in modelling
flows in stars (in particular convection, on which we focus) we presently witness vibrant activity
along those lines. A considerable number of codes has been developed in the recent past and much
of the pertinent work consists in the development of numerical methodology in response to the
requirements of (astro-)physics. In particular, low Mach number flows (as encountered e.g. in the
bulk of the solar convection zone) pose more difficulties than high speed flows. Here, as well as in
time integration and other topics, important recent accomplishments have been achieved. – Still, it
is not our purpose to dwell on code writing or numerics only but we will also discuss research items
under active investigation in solar and stellar physics.
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