Studying 3D Spherical Shell Convection using ASPECT

ASPECT is a new convection code that uses more modern and advanced solver methods than geodynamics legacy codes. I use ASPECT to calculate 2-dimensional Cartesian as well as 2- and 3-dimensional spherical-shell convection cases. All cases use the Boussinesq approximation. The 2D cases come from Blankenbach et al. (1989), van Keken et al. (1997), and Davies et al. (in preparation). Results for 2D cases agree well with their respective benchmark papers. The time-evolutions of the root mean square velocity (Vrms) and Nusselt number agree, often to within 1%. The 3D cases come from Zhong et al. (2008). Modifications were made to the simple.cc and harmonic_perturbation.cc files in the ASPECT code in order to reproduce the initial conditions and temperature-dependence of the rheology used in the benchmark. Cases are compared using both CitcomS and ASPECT with different levels of grid spacing, as well as comparing uniform grid spacing and the ASPECT default grid spacing, which refines toward the center. Results for Vrms, average temperature, and Nusselt numbers at the top and bottom of the shell range from better than 1% agreement between CitcomS and ASPECT for cases with tetragonal planforms and 7000 Rayleigh number to as much as 44% difference for cases with cubic planforms and 10^5 Rayleigh number. For all benchmarks, the top Nusselt number from ASPECT is farthest from the reported benchmark values. The 3D planform and radially averaged quantity plots agree. I present these results, as well as recommendations and possible fixes for discrepancies in the results, specifically in the Nusselt numbers, Vrms, and average temperature.