不同马赫数下流动的新数值解
New numerical solver for flows at various Mach numbers
摘要：
恒星天体物理学中的许多问题都是以低马赫数下的流动为特征的。该领域常用的传统可压缩流体动力学方案是针对跨音速区域开发的，并且对这些流动表现出过度的数值耗散。虽然提出的方案严格地在低马赫数范围内解决流体动力学问题，从而限制了它们的适用性，但我们的目标是开发一种在宽马赫数范围内正确工作的方案。基于对欧拉方程在低马赫极限下的渐近行为的分析，我们提出了一种新的方案，该方案能够保持低马赫数流动设置，同时保留所有可压缩性的影响。这是通过对众所周知的Roe求解器进行适当修改来实现的。数值试验表明，即使在中等数值分辨率下，这种新格式也能再现慢流结构。我们的方案提供了一个有前途的方法，一致的多维流体动力学处理天体物理低马赫数问题，如对流，不稳定性，混合在恒星演化。
英文摘要：
Many problems in stellar astrophysics feature flows at low Mach numbers. Conventional compressible hydrodynamics schemes frequently used in the field have been developed for the transonic regime and exhibit excessive numerical dissipation for these flows. While schemes were proposed that solve hydrodynamics strictly in the low Mach regime and thus restrict their applicability, we aim at developing a scheme that correctly operates in a wide range of Mach numbers. Based on an analysis of the asymptotic behavior of the Euler equations in the low Mach limit we propose a novel scheme that is able to maintain a low Mach number flow setup while retaining all effects of compressibility. This is achieved by a suitable modification of the well-known Roe solver. Numerical tests demonstrate the capability of this new scheme to reproduce slow flow structures even in moderate numerical resolution. Our scheme provides a promising approach to a consistent multidimensional hydrodynamical treatment of astrophysical low Mach number problems such as convection, instabilities, and mixing in stellar evolution.
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