Development and astrophysical application of a well-balanced asymptotic preserving scheme for ideal magnetohydrodynamics with gravity

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This project arises from an established cooperation of a mathematics group at Würzburg university (Christian Klingenberg) and an astrophysics group at Heidelberg university (Friedrich Röpke). We aim to develop a new numerical method for ideal magnetohydrodynamics (MHD) with gravity which is well-balanced and asymptotic preserving. This means that the method is able to maintain (magneto-)hydrostatic states exactly and correctly reproduce relevant limits of MHD with gravity, i.e. different low Mach number limits. These properties are important for several stellar astrophysical applications: The well-balanced property can maintain the basic structure of the star while the asymptotic preserving property enables the resolution of slow fluid flows compared to the speed of magnetosonic and Alvén waves. The new scheme will then be implemented in an existing three-dimensional astrophysical finite volume code. The method will enable us to examine the following three-dimensional astrophysical problems numerically: Firstly, we will examine the effect of magnetic fields on dynamical shear instabilities in differentially rotating stars. Secondly, we are interested in the magnetic field configuration in the onset of core-collapse supernovae.