Anelastic thermal convection in spherical shells using hybrid discrete exterior calculus and finite difference method

Thermal convection is a significant transport mechanism that transfers energy across stellar interiors. The convective regions in stars feature density stratification. The flow is subsonic in the sun, resulting in a small change in density from equilibrium. Anelastic thermal convection, a paradigm for solar/stellar convection, filters out the sound waves from the fully compressible flow. There is a dearth of literature investigating anelastic thermal convection using spherical geometry as compared to cylindrical and planar geometry.

The present work verifies and benchmarks an in-house developed hybrid solver for anelastic thermal convection in spherical shells. The solver utilizes a hybrid discrete exterior calculus and finite difference (DEC-FD) method. The hybrid DEC-FD method is notable for its coordinate independence and structure preservation properties. The solver has been developed and parallelized using the PETSc framework (Mantravadi, B., Jagad, P., & Samtaney, R. (2022). A hybrid discrete exterior calculus and finite difference method for Boussinesq convection in spherical shells. arXiv preprint arXiv:2210.00861). The discrete exterior calculus (DEC) is used to compute the spherical surface flows. In contrast, the finite difference computes the flow in the radial direction. The novelty of the present work is to split the anelastic continuity, momentum, and entropy equations in spherical and radial operators. The modified equation is derived by replacing spherical surface operators with DEC operators and radial operators using the FD operators. Further, the hybrid DEC-FD solver assessment for anelastic approximation is demonstrated through the simulation of convection in spherical shells subject to internal and basal heating.

Acknowledgements

This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award URF/1/4342-01. For computer time, this research used the Cray XC40, Shaheen II, of the Supercomputing Laboratory at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia.