Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows
arXiv:2402.16706 · doi:10.1051/0004-6361/202348882
Abstract
High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. In this work, we use our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We consider Mach numbers in the range from to in a well-posed, 2D, Kelvin--Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. We find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a "low-dissipation" Riemann solver and a sextic reconstruction scheme, (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same, (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate, (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow, (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.
References in corpus (37)
- E pur si muove: Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh
- The PLUTO Code for Adaptive Mesh Computations in Astrophysical Fluid Dynamics
- Turbulent Convection in Stellar Interiors. I. Hydrodynamic Simulation
- Probing the interior physics of stars through asteroseismology
- Accretion-Driven Turbulence as Universal Process: Galaxies, Molecular Clouds, and Protostellar Disks
- Hydrodynamics of core-collapse supernovae and their progenitors
- Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence
- A Well-Posed Kelvin-Helmholtz Instability Test and Comparison
- Bottleneck effect in three-dimensional turbulence simulations
- A Second Order Godunov Method for Multidimensional Relativistic Magnetohydrodynamics
- A Validated Nonlinear Kelvin-Helmholtz Benchmark for Numerical Hydrodynamics
- Computational Eulerian Hydrodynamics and Galilean Invariance
- New numerical solver for flows at various Mach numbers
- ANTARES -- A Numerical Tool for Astrophysical RESearch -- With applications to solar granulation
- 3D hydrodynamic simulations of C ingestion into a convective O shell
- A divergence-free semi-implicit finite volume scheme for ideal, viscous and resistive magnetohydrodynamics
- Towards a new generation of multi-dimensional stellar evolution models: development of an implicit hydrodynamic code
- Fully compressible simulations of waves and core convection in main-sequence stars
- Implicit large eddy simulations of anisotropic weakly compressible turbulence with application to core-collapse supernovae
- Convective boundary mixing in main-sequence stars: theory and empirical constraints
- Numerical comparison of Riemann solvers for astrophysical hydrodynamics
- On the Kelvin-Helmholtz instability with smooth initial conditions -- Linear theory and simulations
- Star-in-a-box simulations of fully convective stars
- Experimental Study of the Bottleneck in Fully Developed Turbulence
- Benchmarking the Multi-dimensional Stellar Implicit Code MUSIC
- 3D stellar evolution: hydrodynamic simulations of a complete burning phase in a massive star
- Dynamics in a stellar convective layer and at its boundary: Comparison of five 3D hydrodynamics codes
- Testing a one-dimensional prescription of dynamical shear mixing with a two-dimensional hydrodynamic simulation
- Well-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers
- Multidimensional low-Mach number time-implicit hydrodynamic simulations of convective helium shell burning in a massive star
- Three-dimensional hydrodynamical CO5BOLD model atmospheres of red giant stars VI. First chromosphere model of a late-type giant
- A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors
- APSARA: A multi-dimensional unsplit fourth-order explicit Eulerian hydrodynamics code for arbitrary curvilinear grids
- HOW-MHD: A High-Order WENO-Based Magnetohydrodynamic Code with a High-Order Constrained Transport Algorithm for Astrophysical Applications
- Turbulent dynamo action and its effects on the mixing at the convective boundary of an idealized oxygen-burning shell
- Toward fully compressible numerical simulations of stellar magneto-convection with the RAMSES code
- A Hybrid Adaptive Low-Mach-Number/Compressible Method: Euler Equations