  In the recent years, global coronal models have experienced an ongoing
increase in popularity as tools for forecasting solar weather. Within the
domain of up to 21.5Rsun, magnetohydrodynamics (MHD) is used to resolve the
coronal structure using magnetograms as inputs at the solar surface. Ideally,
these computations would be repeated with every update of the solar magnetogram
so that they could be used in the ESA Modelling and Data Analysis Working Group
(MADAWG) magnetic connectivity tool (http://connect-tool.irap.omp.eu/). Thus,
it is crucial that these results are both accurate and efficient. While much
work has been published showing the results of these models in comparison with
observations, not many of it discusses the intricate numerical adjustments
required to achieve these results. These range from details of boundary
condition formulations to adjustments as large as enforcing parallelism between
the magnetic field and velocity. By omitting the electric field in ideal-MHD,
the description of the physics can be insufficient and may lead to excessive
diffusion and incorrect profiles. We formulate inner boundary conditions which,
along with other techniques, reduce artificial electric field generation.
Moreover, we investigate how different outer boundary condition formulations
and grid design affect the results and convergence, with special focus on the
density and the radial component of the B-field. The significant improvement in
accuracy of real magnetic map-driven simulations is illustrated for an example
of the 2008 eclipse.
