Automatic spectral methods for non-radial structure and stability problems

Non-radial boundary-value and eigenvalue problems in spherical geometries frequently arise in stellar and planetary science. Common applications include solving for background structures, computing oscillation modes, and studying tidal and convective instabilities. These problems are multidimensional and highly coupled, requiring complex numerical methods that are difficult to develop and modify. Here we will describe recent additions to the Dedalus code that support general non-radial boundary value and eigenvalue problems in spherical shells and full balls. We will briefly describe the underlying numerical methods which support general tensorial PDEs with non-constant coefficients in these geometries. We will then describe several example applications to rotating structure and stability problems in stars and giant planets.