Can we understand the turbulent solar wind via turbulent simulations?

We attempt to assess the present understanding of the turbulent solar wind using numerical simulations. The solar wind may be considered as a kind of wind tunnel with peculiar properties: the tunnel is spherical; the source of the wind is rotating; and the medium is a plasma containing a large-scale magnetic field. These constraints lead to anisotropic dynamics of the fluctuations on the one hand, and to non-standard (turbulent?) transport properties of the global plasma on the other hand. How much of this rich physics can we approach today via numerical simulations?