  This paper explores and compares the pitfalls of modelling the
three-dimensional wind of a spherical star with a cartesian grid. Several
numerical methods are compared, using either uniform and stretched grid or
adaptative mesh refinement (AMR). An additional numerical complication is
added, when an orbiting planet is considered. In this case a rotating frame is
added to the model such that the orbiting planet is at rest in the frame of
work. The three-dimensional simulations are systematically compared to an
equivalent two-dimensional, axisymmetric simulation. The comparative study
presented here suggests to limit the rotation rate of the rotating frame below
the rotating frame of the star and provides guidelines for further
three-dimensional modelling of stellar winds in the context of close-in
star-planet interactions.

Solar and Stellar Astrophysics