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The present work develops, verifies, and benchmarks a hybrid discreteexterior calculus and finite difference (DEC-FD) method for density-stratifiedthermal convection in spherical shells. Discrete exterior calculus (DEC) isnotable for its coordinate independence and structure preservation properties.The hybrid DEC-FD method for Boussinesq convection has been developed byMantravadi et al. (Mantravadi, B., Jagad, P., & Samtaney, R. (2023). A hybriddiscrete exterior calculus and finite difference method for Boussinesqconvection in spherical shells. Journal of Computational Physics, 491, 112397).Motivated by astrophysics problems, we extend this method assuming anelasticconvection, which retains density stratification; this has been widely used fordecades to understand thermal convection in stars and giant planets. In thepresent work, the governing equations are splitted into surface and radialcomponents and discrete anelastic equations are derived by replacing sphericalsurface operators with DEC and radial operators with FD operators. The novelfeature of this work is the discretization of anelastic equations with theDEC-FD method and the assessment of a hybrid solver for density-stratifiedthermal convection in spherical shells. The discretized anelastic equations areverified using the method of manufactured solution (MMS). We performed a seriesof three-dimensional convection simulations in a spherical shell geometry andexamined the effect of density ratio on convective flow structures and energydynamics. The present observations are in agreement with the benchmark models.

A hybrid discrete exterior calculus and finite difference method for anelastic convection in spherical shells