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

理想重力磁流体动力学的平衡渐近保持方案的开发和天体物理应用

• 批准号: 418833237
• 负责人: Professor Dr. Christian Klingenberg, Ph.D.
• 金额: --
• 依托单位: Lehrstuhl für Mathematik VI: Mathematik in den Naturwissenschaften
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/418833237?language=en
• 关键词: Development; astrophysical; application; well; balanced

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.

这个项目是由维尔茨堡大学的一个数学小组(克里斯蒂安·克林根贝格)和海德堡大学的一个天体物理学小组(弗里德里希·罗普克)共同完成的。我们的目标是发展一种新的具有重力的理想磁流体力学(MHD)的数值方法，该方法具有良好的平衡性和渐近性。这意味着该方法能够准确地保持(磁)流体静力状态，并正确地再现MHD在重力作用下的相关极限，即不同的低马赫数极限。这些性质对于几种恒星天体物理应用是很重要的：平衡良好的性质可以维持恒星的基本结构，而渐近保持性质能够分辨慢速流体流动，而与磁声波和阿尔文波的速度相比。然后，新方案将在现有的三维天体物理有限体积代码中实施。该方法将使我们能够用数值方法研究以下三维天体物理问题：首先，我们将研究磁场对差动自转恒星中动态剪切不稳定性的影响。其次，我们感兴趣的是核心塌缩超新星爆发时的磁场构型。