Rayleigh-Bénard convection in Spherical Shells using Discrete Exterior Calculus and Finite Difference Hybrid Method

Solar convection is a highly complex phenomenon characterized by turbulent buoyant flows, differential rotation, and self-generation and sustenance of magnetic fields due to convective plasma motions. The spherical geometry and extreme lim- its of the non-dimensional numbers pose a major challenge in simulating this phe- nomenon. Given the unique features of discrete exterior calculus (DEC), for in- stance, exact discretization, ability to simulate flows on curved surfaces, coordinate independence, conservation of secondary quantities, we have developed a hybrid discrete exterior calculus and finite difference (DEC-FD) method to simulate fully three-dimensional Boussinesq convection in spherical shells. We present several test cases of Rayleigh-Bénard convection in the linear and weakly non-linear regime. In the linear regime, we quantify the kinetic energy decay, and compare with the analytical solution. In the weakly non-linear regime, for moderately thin shells, we simulate the single spiral roll state, and the steady state kinetic energies for different Prandtl numbers are in very close agreement with Li et al. (Phys. Rev. E, 2005). Furthermore, we will examine RBC for extreme regimes(Rayleigh number ≥ 10⁹).