Not only is the range of relevant spatial and temporal scales excessive, but the flows of interest arise in a configuration that is often close to hydrostatic equilibrium. Such simulations pose a number of challenges to the underlying numerical techniques. 2020), have tried to overcome this shortcoming. 2004 Meakin & Arnett 2006, 2007 Woodward et al. Recent attempts to simulate inherently multidimensional and dynamical processes, such as convection in stellar interiors (e.g., Browning et al.
The price for this success is a parametrization of multidimensional and dynamical processes that limits the predictive power of such theoretical models and requires their calibration with observations. 2012) enable successful qualitative modeling of the evolution of stars through different stages. The resulting equations of stellar structure (e.g., Kippenhahn et al.
Apart from this dimensional reduction, the assumption of hydrostatic equilibrium considerably simplifies the modeling of the – in reality rather complex – structure of stars. A prominent example are stars, modeled in classical approaches as spherically symmetric gaseous objects. Such systems can attain stationary equilibrium configurations in which a pressure gradient balances gravity, that is hydrostatic equilibrium. They are commonly described by the equations of fluid dynamics with a gravitational source term – viscous effects are negligible in most astrophysical systems and therefore the nonviscous Euler equations are used. Key words: hydrodynamics / methods: numerical / convectionĪstrophysical modeling often involves self-gravitating fluids. Overall, we find the well-balanced treatment of gravity in combination with low Mach number flux functions essential to reproducing correct physical solutions to challenging stellar slow-flow problems on affordable collocated grids. The Cargo–LeRoux method fares substantially worse in our tests, although its simplicity may still offer some merits in certain situations.Ĭonclusions. The deviation method also substantially increases accuracy of maintaining stationary orbital motions in a Keplerian disk on long timescales. They accurately conserve minuscule entropy fluctuations advected in an isentropic stratification, which enables the methods to reproduce the expected scaling of convective flow speed with the heating rate. We find that the α- β and deviation well-balancing methods can accurately maintain hydrostatic solutions provided that gravitational potential energy is included in the total energy balance. We compare how the schemes perform in four numerical experiments addressing some of the challenges imposed by typical problems in stellar hydrodynamics.
#FLUID DYNAMICS SIMULATIONS CODE#
Three such schemes were applied in the implicit, finite-volume S EVEN-L EAGUE H YDRO code in combination with a low-Mach-number numerical flux function. Well-balanced numerical schemes can deal with this problem. We demonstrate how discretization errors on grids of reasonable size can lead to spurious flows orders of magnitude faster than the physical flow. Because the typically slow flows are merely tiny perturbations on top of a close balance between gravity and the pressure gradient, such simulations place heavy demands on numerical hydrodynamics schemes.Īims. Accurate simulations of flows in stellar interiors are crucial to improving our understanding of stellar structure and evolution.
Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Philosophenweg 12, 69120 Heidelberg, GermanyĬontext. Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut, Mönchhofstr. X Computational Physics (XCP) Division and Center for Theoretical Astrophysics (CTA), Los Alamos National Laboratory, Los Alamos, NM 87545, USAĮ-mail: Institut für Theoretische Studien, Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germanyįaculty of Physics and Astronomy, Würzburg University, Am Hubland, 97074 Würzburg, Germanyĭepartment of Mathematics, Würzburg University, Emil-Fischer-Str.
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