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Convection is an important physical process in astrophysics well-studiedusing numerical simulations under the Boussinesq and/or anelasticapproximations. However these approaches reach their limits when compressibleeffects are important in the high Mach flow regime, e.g. in stellar atmospheresor in the presence of accretion shocks. In order to tackle these issues, wepropose a new high performance and portable code, called "ARK" with a numericalsolver well-suited for the stratified compressible Navier-Stokes equations. Wetake a finite volume approach with machine precision conservation of mass,transverse momentum and total energy. Based on previous works in appliedmathematics we propose the use of a low Mach correction to achieve a goodprecision in both low and high Mach regimes. The gravity source term isdiscretized using a well-balanced scheme in order to reach machine precisionhydrostatic balance. This new solver is implemented using the Kokkos library inorder to achieve high performance computing and portability across differentarchitectures (e.g. multi-core, many-core, and GP-GPU). We show that thelow-Mach correction allows to reach the low-Mach regime with a much betteraccuracy than a standard Godunov-type approach. The combined well-balancedproperty and the low-Mach correction allowed us to trigger Rayleigh-B\'enardconvective modes close to the critical Rayleigh number. Furthermore we present3D turbulent Rayleigh-B\'enard convection with low diffusion using the low-Machcorrection leading to a higher kinetic energy power spectrum. These results arevery promising for future studies of high Mach and highly stratified convectiveproblems in astrophysics.

A high performance and portable all-Mach regime flow solver code with well-balanced gravity. Application to compressible convection