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

该项目源于维尔茨堡大学（Christian Klingenberg）的一个数学小组和海德堡大学（Friedrich Röpke）的一个天体物理小组的合作。我们的目标是发展一种新的数值方法，理想磁流体力学（MHD）与重力，这是良好的平衡和渐近保持。这意味着该方法能够准确地保持（磁）流体静力学状态，并正确地再现MHD与重力的相关限制，即不同的低马赫数限制。这些性质对于一些恒星天体物理学的应用是重要的：良好平衡的性质可以保持星星的基本结构，而渐近保持的性质可以分辨与磁声波和阿尔文波速度相比的缓慢流体流动。新方案将在现有的三维天体物理有限体积代码中实现。该方法将使我们能够研究以下三维天体物理问题的数值：首先，我们将研究磁场对动力学剪切不稳定性的影响，在差分旋转的恒星。第二，我们感兴趣的是在核心坍缩超新星爆发的磁场配置。

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.