Azimuthal averaging–reconstruction filtering techniques for finite-difference general circulation models in spherical geometry

Abstract. When solving hydrodynamic equations in spherical or cylindrical geometry using explicit finite-difference schemes, a major difficulty is that the time step greatly restricted by clustering of azimuthal cells near pole due to Courant–Friedrichs–Lewy condition. This paper adapts averaging–reconstruction (ring average) technique schemes order mitigate constraint and coordinates. The ring average averages physical quantities based on an effective grid then reconstructs solution back original piecewise, monotonic way. algorithm implemented community upper-atmospheric model, Thermosphere–Ionosphere Electrodynamics General Circulation Model (TIEGCM), with horizontal resolution up 0.625∘×0.625∘ geographic longitude–latitude coordinates, which enables capability resolving critical mesoscale structures within TIEGCM. Numerical experiments have shown introduces minimal artifacts polar region general circulation model (GCM) solutions, significant improvement compared commonly used low-pass filtering techniques such as fast Fourier transform method. Since adaption post-solver type algorithm, requires no changes computational numerical algorithms, it has also been much more complicated models extended physical–chemical modules Coupled Magnetosphere–Ionosphere–Thermosphere (CMIT) Whole Atmosphere Community Climate thermosphere ionosphere eXtension (WACCM-X). implementation both CMIT WACCM-X perform global simulations higher than versions. new not only space weather modeling capability, but can be adapted solvers for hyperbolic geometries. Highlights. solve issue clustered coordinates applied develop high-resolution TIEGCM geoscientific well schemes. shows good ionosphere–thermosphere (I–T) system.