Characteristic boundary conditions for magnetohydrodynamic equations. (15th June 2022) - Makaremi-Esfarjani, Paria; Najafi-Yazdi, Alireza
Abstract: In the present study, a characteristic-based boundary condition scheme is developed for the compressible magnetohydrodynamic (MHD) equations in the general curvilinear coordinate system, which is an extension of the characteristic boundary scheme for the Navier–Stokes equations. The eigenstructure and the complete set of characteristic waves are derived for the ideal MHD equations in general curvilinear coordinates ( ξ, η, ζ ) . The characteristic boundary conditions are derived and implemented in a high-order MHD solver where the sixth-order compact scheme is used for the spatial discretization. The fifth-order Weighted Essentially Non-Oscillatory (WENO) scheme is also employed for the spatial discretization of problems with discontinuities. In our MHD solver, the fourth-order Runge–Kutta scheme is utilized for time integration. The characteristic boundary scheme is first verified for the non-magnetic (i.e., B = 0 ) Sod shock tube problem. Then, various in-house test cases are designed to examine the derived MHD characteristic boundary scheme for three different types of boundaries: non-reflecting inlet and outlet, solid wall, and single characteristic wave injection. The numerical examples demonstrate the accuracy and robustness of the MHD characteristic boundary scheme. Highlights: Derivation of characteristic boundary conditions for the MHD equations. Extending the MHD characteristic boundary scheme in the general curvilinear grids. Obtaining the ideal compressible MHD eigensystem in the general curvilinear grids. Introducing test cases to verify the derived scheme for the MHD simulations. Investigating the derived scheme for wall, inlet, and non-reflecting boundaries.