Kore : A spectral anelastic MHD eigenvalue code for rotating fluids in spherical geometries

We present a new open source spectral code to compute the eigenmodes or the linear forced response of a rotating fluid contained in a sphere or a spherical shell. Kore supports any combination of the Navier-Stokes equation, magnetic induction, thermal transport and compositional transport equations. Kore uses a spherical harmonic expansion in the angular directions. For radial functions and derivatives, it makes use of the numerical method by Olver and Townsend (2013) using Chebyshev polynomials to expand the functions and using different Gegenbauer polynomial bases for radial derivatives. This method produces sparse matrices and thus allows the use of tools such as PETSc and SLEPc for the solve stage. Kore has already been used for studies of mechanical forcings in planets (Rekier et al., 2019) and the study of viscous and Ohmic dissipation in the Earth's core (Triana et al., 2021). We now present the latest version of the code with capabilities to deal with compressible systems with an equation of state and variable transport properties. This can have potential applications for study of waves and onset of convection in gas giant planets, hot Jupiters as well as stars.