天体物理学中的压缩低马赫数流：非线性牛顿数值解
Compressed low Mach number flows in astrophysics: a nonlinear Newtonian numerical solver
摘要：
在引力稳定的天体，如太阳、恒星和致密恒星内部的内部流动是压缩的，并且是极亚音速的。这种低马赫数流通常在研究恒星、行星中的发电机作用、中子星和矮新星上X射线爆发的流体热力学时遇到。处理这样的流动是数值上复杂和具有挑战性的任务。我们的目标是提出一个强大的数值工具，使建模的时间演化或准静态的分层低马赫数流在天体物理条件下。有人认为，天体物理低马赫数流不能被认为是不可压缩流的渐近极限，而是作为高度压缩流与极刚性的压力项。与不可压缩流体中的伪压力不同，对压力的Possion类处理将不必要地平滑物理引起的声学扰动，从而违反可压缩方程的守恒特性。此外，经典的尺寸分裂技术，如ADI或线高斯赛德尔方法被发现不适合模拟低马赫数的可压缩流。在本文中，我们提出了一个非线性牛顿型求解器，是基于缺陷校正迭代过程中，近似因式分解方法（AFM）被用作预条件。该求解器被发现是足够鲁棒的，并且能够捕获马赫数小至$\mcal{M} \approx 10^{-3},$的粘性旋转流的定常解，即，接近不可压缩极限。
英文摘要：
Internal flows inside gravitationally stable astrophysical objects, such as the Sun, stars and compact stars are compressed and extremely subsonic. Such low Mach number flows are usually encountered when studying for example dynamo action in stars, planets, the hydro-thermodynamics of X-ray bursts on neutron stars and dwarf novae. Treating such flows is numerically complicated and challenging task. We aim to present a robust numerical tool that enables modeling the time-evolution or quasi-stationary of stratified low Mach number flows under astrophysical conditions. It is argued that astrophysical low Mach number flows cannot be considered as an asymptotic limit of incompressible flows, but rather as highly compressed flows with extremely stiff pressure terms. Unlike the pseudo-pressure in incompressible fluids, a Possion-like treatment for the pressure would smooth unnecessarily the physically induced acoustic perturbations, thereby violating the conservation character of the compressible equations. Moreover, classical dimensional splitting techniques, such as ADI or Line-Gauss-Seidel methods are found to be unsuited for modeling compressible flows with low Mach numbers. In this paper we present a nonlinear Newton-type solver that is based on the defect-correction iteration procedure and in which the Approximate Factorization Method (AFM) is used as a preconditioner. This solver is found to be sufficiently robust and is capable of capturing stationary solutions for viscous rotating flows with Mach number as small as $\mcal{M} \approx 10^{-3},$ i.e., near the incompressibility limit.
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