New numerical solver for flows at various Mach numbers
arXiv:1409.8289 · doi:10.1051/0004-6361/201425059
Abstract
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.
16 pages, 8 figures, accepted for publication by A&A
References in corpus (9)
- Simulations of core convection in rotating A-type stars: Differential rotation and overshooting
- A Well-Posed Kelvin-Helmholtz Instability Test and Comparison
- MAESTRO: An Adaptive Low Mach Number Hydrodynamics Algorithm for Stellar Flows
- Energy Conservation and Gravity Waves in Sound-proof Treatments of Stellar Interiors: Part I Anelastic Approximations
- ANTARES -- A Numerical Tool for Astrophysical RESearch -- With applications to solar granulation
- Towards a new generation of multi-dimensional stellar evolution models: development of an implicit hydrodynamic code
- A Low Mach Number Solver: Enhancing Applicability
- Comparison of different nonlinear solvers for 2D time-implicit stellar hydrodynamics
- Curvilinear Grids for WENO Methods in Astrophysical Simulations
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