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Register a new userWell-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers
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Accurate simulations of flows in stellar interiors are crucial to improving our understanding of stellar structure and evolution. 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. We demonstrate how discretization errors on grids of reasonable size can lead to spurious flows orders of magnitude faster than the physical flow. Well-balanced numerical schemes can deal with this problem. Three such schemes were applied in the implicit, finite-volume Seven-League Hydro (SLH) code in combination with a low-Mach-number numerical flux function. We compare how the schemes perform in four numerical experiments addressing some of the challenges imposed by typical problems in stellar hydrodynamics. We find that the $alpha$-$beta$ and deviation well-balancing methods can accurately maintain hydrostatic solutions provided that gravitational potential energy is included in the total energy balance. 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. The deviation method also substantially increases accuracy of maintaining stationary orbital motions in a Keplerian disk on long timescales. The Cargo-LeRoux method fares substantially worse in our tests, although its simplicity may still offer some merits in certain situations. 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.
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Using a perturbative approach we solve stellar structure equations for low-density (solar-type) stars whose interior is described with a polytropic equation of state in scenarios involving a subset of modified gravity theories. Rather than focusing on particular theories, we consider a model-independent approach in which deviations from General Relativity are effectively described by a single parameter $xi$. We find that for length scales below those set by stellar General Relativistic radii the modifications introduced by modified gravity can affect the computed values of masses and radii. As a consequence, the stellar luminosity is also affected. We discuss possible further implications for higher density stars and observability of the effects before described.
Convection is an important physical process in astrophysics well-studied using numerical simulations under the Boussinesq and/or anelastic approximations. However these approaches reach their limits when compressible effects are important in the high Mach flow regime, e.g. in stellar atmospheres or in the presence of accretion shocks. In order to tackle these issues, we propose a new high performance and portable code, called ARK with a numerical solver well-suited for the stratified compressible Navier-Stokes equations. We take a finite volume approach with machine precision conservation of mass, transverse momentum and total energy. Based on previous works in applied mathematics we propose the use of a low Mach correction to achieve a good precision in both low and high Mach regimes. The gravity source term is discretized using a well-balanced scheme in order to reach machine precision hydrostatic balance. This new solver is implemented using the Kokkos library in order to achieve high performance computing and portability across different architectures (e.g. multi-core, many-core, and GP-GPU). We show that the low-Mach correction allows to reach the low-Mach regime with a much better accuracy than a standard Godunov-type approach. The combined well-balanced property and the low-Mach correction allowed us to trigger Rayleigh-Benard convective modes close to the critical Rayleigh number. Furthermore we present 3D turbulent Rayleigh-Benard convection with low diffusion using the low-Mach correction leading to a higher kinetic energy power spectrum. These results are very promising for future studies of high Mach and highly stratified convective problems in astrophysics.
Resonant lines are powerful probes of the interstellar and circumgalactic medium of galaxies. Their transfer in gas being a complex process, the interpretation of their observational signatures, either in absorption or in emission, is often not straightforward. Numerical radiative transfer simulations are needed to accurately describe the travel of resonant line photons in real and in frequency space, and to produce realistic mock observations. This paper introduces RASCAS, a new public 3D radiative transfer code developed to perform the propagation of any resonant line in numerical simulations of astrophysical objects. RASCAS was designed to be easily customisable and to process simulations of arbitrarily large sizes on large supercomputers. RASCAS performs radiative transfer on an adaptive mesh with an octree structure using the Monte Carlo technique. RASCAS features full MPI parallelisation, domain decomposition, adaptive load-balancing, and a standard peeling algorithm to construct mock observations. The radiative transport of resonant line photons through different mixes of species (e.g. ion{H}{i}, ion{Si}{ii}, ion{Mg}{ii}, ion{Fe}{ii}), including their interaction with dust, is implemented in a modular fashion to allow new transitions to be easily added to the code. RASCAS is very accurate and efficient. It shows perfect scaling up to a minimum of a thousand cores. It has been fully tested against radiative transfer problems with analytic solutions and against various test cases proposed in the literature. Although it was designed to describe accurately the many scatterings of line photons, RASCAS may also be used to propagate photons at any wavelength (e.g. stellar continuum or fluorescent lines), or to cast millions of rays to integrate the optical depths of ionising photons, making it highly versatile.
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.
Numerical aspects of dynamos in periodic domains are discussed. Modifications of the solutions by numerically motivated alterations of the equations are being reviewed using the examples of magnetic hyperdiffusion and artificial diffusion when advancing the magnetic field in its Euler potential representation. The importance of using integral kernel formulations in mean-field dynamo theory is emphasized in cases where the dynamo growth rate becomes comparable with the inverse turnover time. Finally, the significance of microscopic magnetic Prandtl number in controlling the conversion from kinetic to magnetic energy is highlighted.
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