A High-performance and Portable All-Mach Regime Flow Solver Code with Well-balanced Gravity. Application to Compressible Convection
Résumé
Convection is an important physical process in astrophysics well-studied using numerical simulations under theBoussinesq and/or anelastic approximations. However, these approaches reach their limits when compressibleeffects are important in the high-Mach flow regime, e.g., in stellar atmospheres or in the presence of accretionshocks. In order to tackle these issues, we propose a new high-performance and portable code called “ARK” with anumerical solver well suited for the stratified compressible Navier–Stokes equations. We take a finite-volumeapproach with machine precision conservation of mass, transverse momentum, and total energy. Based on previousworks in applied mathematics, we propose the use of a low-Mach correction to achieve a good precision in bothlow and high-Mach regimes. The gravity source term is discretized using a well-balanced scheme in order to reachmachine precision hydrostatic balance. This new solver is implemented using the Kokkos library in order toachieve 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 betteraccuracy than a standard Godunov-type approach. The combined well-balanced property and the low-Machcorrection allowed us to trigger Rayleigh–Bénard convective modes close to the critical Rayleigh number.Furthermore, we present 3D turbulent Rayleigh–Bénard convection with low diffusion using the low-Machcorrection leading to a higher kinetic energy power spectrum. These results are very promising for future studies ofhigh Mach and highly stratified convective problems in astrophysics.
Domaines
Physique [physics]
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