An optimization principle for computing stationary MHD equilibria with solar wind flow

In this work we describe a numerical optimization method for computing stationary MHD equilibria. The newly developed code is based on a nonlinear force-free optimization principle. We apply our code to model the solar corona using synoptic vector magnetograms as boundary condition. Below about two solar radii the plasma $\beta $ and Alfven Mach number $M_{A}$ are small and the magnetic field configuration of stationary MHD is basically identical to a nonlinear force-free field, whereas higher up in the corona (where $\beta $ and $M_{A}$ are above unity) plasma and flow effects become important and stationary MHD and force-free configuration deviate significantly. The new method allows for the reconstruction of the coronal magnetic field further outwards than with potential field, nonlinear force-free or magnetostatic models. This way the model might help to provide the magnetic connectivity for joint observations of remote sensing and in-situ instruments on Solar Orbiter and Parker Solar Probe.