  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-B\'enard
convective modes close to the critical Rayleigh number. Furthermore we present
3D turbulent Rayleigh-B\'enard 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.
