A New MHD Model with a Rotated-hybrid Scheme and Solenoidality-preserving Approach

In this paper, the rotated-hybrid scheme is applied for the first time to 3D magnetohydrodynamics (MHD) equations in the finite-volume frame. This scheme is devised by decomposing a cell-face normal vector into two orthogonal directions and combining the Roe solver, a full-wave or complete Riemann solver, and the Rusanov solver, an incomplete Riemann solver, into one rotated-hybrid Riemann solver. To keep the magnetic field divergence-free, we propose two kinds of divergence-cleaning approaches by combining the least-squares reconstruction of magnetic field with the divergence-free constraints. One is the locally solenoidality-preserving method designed to locally maintain the magnetic solenoidality exactly, not just in a least-squares sense, and another is the globally solenoidality-preserving (SP) approach that is implemented by adding a global constraint but abandons the exactness of the locally divergence-free condition. Both SP methods are employed for 3D MHD with a rotated-hybrid scheme in the finite-volume frame. To validate and demonstrate the capabilities of the rotated-hybrid scheme for MHD, we perform an Orszag-Tang MHD vortex problem and a numerical study for the steady-state coronal structures of Carrington rotation 2068 during the solar activity minimum. The numerical tests show the robustness of the proposed scheme and demonstrate the capability of these two SP approaches to keep the magnetic divergence errors to the expected accuracy.