Abstract
Abstract. When solving hydrodynamic equations in spherical or cylindrical geometry using explicit finite-difference schemes, a major difficulty is that the time step is greatly restricted by the clustering of azimuthal cells near the pole due to the Courant–Friedrichs–Lewy condition. This paper adapts the azimuthal averaging–reconstruction (ring average) technique to finite-difference schemes in order to mitigate the time step constraint in spherical and cylindrical coordinates. The finite-difference ring average technique averages physical quantities based on an effective grid and then reconstructs the solution back to the original grid in a piecewise, monotonic way. The algorithm is implemented in a community upper-atmospheric model, the Thermosphere–Ionosphere Electrodynamics General Circulation Model (TIEGCM), with a horizontal resolution up to 0.625∘×0.625∘ in geographic longitude–latitude coordinates, which enables the capability of resolving critical mesoscale structures within the TIEGCM. Numerical experiments have shown that the ring average technique introduces minimal artifacts in the polar region of general circulation model (GCM) solutions, which is a significant improvement compared to commonly used low-pass filtering techniques such as the fast Fourier transform method. Since the finite-difference adaption of the ring average technique is a post-solver type of algorithm, which requires no changes to the original computational grid and numerical algorithms, it has also been implemented in much more complicated models with extended physical–chemical modules such as the Coupled Magnetosphere–Ionosphere–Thermosphere (CMIT) model and the Whole Atmosphere Community Climate Model with thermosphere and ionosphere eXtension (WACCM-X). The implementation of ring average techniques in both models enables CMIT and WACCM-X to perform global simulations with a much higher resolution than that used in the community versions. The new technique is not only a significant improvement in space weather modeling capability, but it can also be adapted to more general finite-difference solvers for hyperbolic equations in spherical and polar geometries. Highlights. The ring average technique is adapted to solve the issue of clustered grid cells in polar and spherical coordinates with a finite-difference method. The ring average technique is applied to develop a 0.625∘×0.625∘ high-resolution TIEGCM and more complicated geoscientific models with polar and spherical coordinates as well as finite-difference numerical schemes. The high-resolution TIEGCM shows good capability in resolving mesoscale structures in the ionosphere–thermosphere (I–T) system.
Highlights
Mesoscale structures with a typical horizontal size of 100– 500 km have gained more and more attention in research on the dynamics of the upper-atmospheric system
The original ring average technique was developed for solving hyperbolic equations in spherical or polar geometry based on finite-volume schemes, which redistributes the solution azimuthally through a conservative averaging– reconstruction algorithm
The ring average technique is implemented in the Thermosphere–Ionosphere Electrodynamic General Circulation Model (TIEGCM) v2.0 to solve the issue of clustering grid cells near the poles in the development of a high-resolution version of the TIEGCM. This technique is applied as a postprocessing treatment of the fluid variables including oxygen ion density O+, neutral temperature Tn, thermospheric compositions, and meridional, zonal, and vertical winds (Un, Vn, w) at each time step, with different reconstruction methods (PPM or piecewise linear method (PLM)) for different variables (Table 1)
Summary
Mesoscale structures with a typical horizontal size of 100– 500 km have gained more and more attention in research on the dynamics of the upper-atmospheric system. A number of studies have been carried out to investigate these structures, including the formation and evolution of polar cap patches and tongues of ionization (Basu et al, 1995; Foster et al, 2005; Zhang et al, 2013), dynamics of ionospheric irregularities (Makela and Otsuka, 2012; Sun et al, 2015), variations of the polar thermospheric density anomaly (Crowley et al, 2010; Lühr et al, 2004), and the space weather effects of mesoscale electric field variability (Codrescu et al, 1995; Matsuo and Richmond, 2008; Zhu et al, 2018; Lotko and Zhang, 2018) These dynamic mesoscale structures have shown critical importance in understanding the physics of the solar–terrestrial system and in space weather predictions, which challenges the resolution and accuracy of numerical models of the upper-atmospheric system in resolving these important mesoscale signatures. The original ring average technique was developed for solving hyperbolic equations in spherical or polar geometry based on finite-volume schemes, which redistributes the solution azimuthally through a conservative averaging– reconstruction algorithm.
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