Pierre Arrial, Ph.D. & Professor Louise Kellogg
University of Davis, California

3-D numerical simulations of thermal convection in a spherical shell have become a standard for studying the dynamics of pattern formation and its stability under perturbations to various parameter values. The question arises as to how the discretization of the governing equations affects the outcome and thus, any physical interpretation. Motivated by numerical simulations of convection in the Earth’s mantle, we consider isoviscous Rayleigh–Bénard convection at infinite Prandtl number. We show that the subtleties involved in developing mantle convection models are considerably more delicate than has been previously appreciated, due to the rich dynamical behavior of the system. Two codes with different numerical discretization schemes – an established, community developed, and benchmarked finite-element code (CitcomS) and a novel spectral method that combines Chebyshev polynomials with radial basis functions (RBF) – are fully compared. A third code (ASPECT), using finite-element, is also tested for the comparison and reproduces partially results with other methods. This work demonstrates the impact of numerical discretization on the observed patterns, the value at which symmetry is broken, and how stability and stationary behavior is dependent upon it.

[All 2014-15 webinars] [YouTube]

1. Arrial
2. Kellogg
3. webinar
4. 2015