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

• Published in: Journal of computational physics Vol. 491; p. 112397
• Main Authors: Mantravadi, Bhargav, Jagad, Pankaj, Samtaney, Ravi
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.10.2023
• Subjects: Boussinesq convection; Discrete exterior calculus; Finite difference method; Flow in spherical shell; Operator splitting; PETSc; Boussinesq convection; Operator splitting; PETSc; Flow in spherical shell; Discrete exterior calculus; Finite difference method
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2023.112397

We present a new hybrid discrete exterior calculus (DEC) and finite difference (FD) method to simulate fully three-dimensional Boussinesq convection in spherical shells subject to internal heating and basal heating, relevant in the planetary and stellar phenomenon. We employ DEC to compute the surface spherical flows, taking advantage of its unique features including coordinate system independence to preserve the spherical geometry, while we discretize the radial direction using FD method. The grid employed for this novel method is free of problems like the coordinate singularity, grid non-convergence near the poles, and the overlap regions. We have developed a parallel in-house code using the PETSc framework to verify the hybrid DEC-FD formulation and demonstrate convergence. We have performed a series of numerical tests which include quantification of the critical Rayleigh numbers for spherical shells characterized by aspect ratios ranging from 0.2 to 0.8, simulation of robust convective patterns in addition to stationary giant spiral roll covering all the spherical surface in moderately thin shells near the weakly nonlinear regime, and the quantification of Nusselt and Reynolds numbers for basally heated spherical shells. •Boussinesq convection in spherical shells.•Hybrid discrete exterior calculus and finite difference (DEC-FD) discretization.•Surface and radial operators are approximated by DEC and FD, respectively.•No coordinate singularity and grid non-convergence near poles, and overlap regions.•A plethora of robust convective patterns and resolving high wavenumber features.