Assessing the Accuracy of 2-D Planetary Evolution Models Against the 3-D Sphere

Kurzfassung

Regardless of the steady increase of computing power during the last decades, numerical models in a 3D spherical shell are only used in specific setups to investigate the thermochemical convection in planetary interiors, while 2D geometries are typically favored in most exploratory studies involving a broad range of parameters. The 2D cylindrical and the more recent 2D spherical annulus geometries are predominantly used in this context, but the extent to how well they reproduce the 3D spherical shell results in comparison to each other and in which setup has not yet been extensively investigated. Here we performed a thorough and systematic study in order to assess which 2D geometry reproduces best the 3D spherical shell. In a first set of models, we investigated the effects of the geometry on thermal convection in steady-state setups while varying a broad range of parameters. Additional thermal evolution models of three terrestrial bodies, namely Mercury, the Moon, and Mars, which have different interior structures, were used to compare the 2D and 3D geometries. Our investigations show that the 2D spherical annulus geometry provides results closer to models in a 3D spherical shell compared to the 2D cylindrical geometry. Our study indicates where acceptable differences can be expected when using a 2D instead of a 3D geometry and where to be cautious when interpreting the results.