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

这个项目源于<s:1>茨堡大学数学小组（Christian Klingenberg）和海德堡大学天体物理学小组（Friedrich Röpke）的长期合作。我们的目的是建立一种新的具有良好平衡和渐近保持的理想磁流体力学数值方法。这意味着该方法能够准确地维持（磁-）流体静力状态，并正确地再现重力下MHD的相关极限，即不同的低马赫数极限。这些特性对于一些恒星天体物理应用很重要：良好的平衡特性可以维持恒星的基本结构，而渐近保持特性可以分辨与磁子波和阿尔夫萨曼波速度相比的慢流体流动。新的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在数值上研究以下三维天体物理问题：首先，我们将研究磁场对差旋转恒星动态剪切不稳定性的影响。其次，我们对核心坍缩超新星爆发时的磁场结构感兴趣。

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.