Discontinuous Galerkin method with constrained transport for modelling solar wind in spherical coordinates

In this paper, the discontinuous Galerkin (DG) method is used to simulate the steady-state solar wind with constrained transport method. A cell-based piecewise quadratic polynomial solution is obtained through the DG scheme, while the face-averaged magnetic field is discretized using constrained-transport method. Then, a globally divergence-free magnetic field is constructed by combining the quadratic polynomial of magnetic field with the face-averaged magnetic field. For the time discretization, third-order Runge–Kutta method is applied. The resulting method can reach three order of accuracy in space and time. We test the method by computing the solar wind in Carrington rotation 2234, and compare the result with both remote sensing observations from SOHO and SDO as well as in situ observations from Parker Solar Probe and a dataset of Open to the Maximum Number of Investigators (OMNI). The agreement between the modelled results and the observations demonstrates the capability of the developed scheme.