Abstract
Many problems in stellar astrophysics feature low Mach number flows. However,
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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