Fourth-order accurate finite-volume CWENO scheme for astrophysical MHD problems

In this work, a simple fourth-order accurate finite-volume semidiscrete scheme is introduced to solve astrophysical magnetohydrodynamic (MHD) problems on Cartesian meshes. Hydrodynamic quantities like density, momentum, and energy are discretized as volume averages. The magnetic field and electric field components are discretized as area and line averages, respectively, so as to employ the constrained transport technique, which preserves the solenoidality of the magnetic field to machine precision. The present method makes use of a dimension-by-dimension approach employing a 1D fourth-order accurate centrally weighted essentially non-oscillatory (1D-CWENO4) reconstruction polynomial. A fourth-order accurate, strong stability preserving Runge-Kutta method is used to evolve the semidiscrete MHD equations in time. Higher order accuracy of the scheme is confirmed in various linear and non-linear multidimensional tests and the robustness of the method in avoiding unphysical numerical artefacts in the solution is demonstrated through several complex MHD problems.