Analytical solutions for mantle flow in cylindrical and spherical shells

Abstract. Computational models of mantle convection must accurately represent curved boundaries and the associated boundary conditions a 3-D spherical shell, bounded by Earth's surface core–mantle boundary. This is also true for comparable in simplified 2-D cylindrical geometry. It fundamental importance that codes underlying these are carefully verified prior to their application geodynamical context, which comparisons against analytical solutions an indispensable tool. However, Stokes equations geometries, based upon simple source terms adhere physically realistic conditions, often complex difficult derive. In this paper, we present smooth polynomial delta-function forcing, combination with free-slip zero-slip both cylindrical- spherical-shell domains. We study convergence Taylor–Hood (P2–P1) discretisation respect solutions, within finite element computational modelling framework Fluidity, discuss issue suboptimal presence discontinuities. To facilitate verification numerical across wider community, provide Python package, Assess, evaluates at arbitrary points domain.