  The accurate prediction of aerodynamic drag on satellites orbiting in the
upper atmosphere is critical to the operational success of modern space
technologies, such as satellite-based communication or navigation systems,
which have become increasingly popular in the last few years due to the
deployment of constellations of satellites in low-Earth orbit. As a result,
physics-based models of the ionosphere and thermosphere have emerged as a
necessary tool for the prediction of atmospheric outputs under highly variable
space weather conditions.
  This paper proposes a high-fidelity approach for physics-based space weather
modeling based on the solution of the Navier-Stokes equations using a
high-order discontinuous Galerkin method, combined with a matrix-free strategy
suitable for high-performance computing on GPU architectures. The approach
consists of a thermospheric model that describes a chemically frozen neutral
atmosphere in non-hydrostatic equilibrium driven by the external excitation of
the Sun. A novel set of variables is considered to treat the low densities
present in the upper atmosphere and to accommodate the wide range of scales
present in the problem. At the same time, and unlike most existing approaches,
radial and angular directions are treated in a non-segregated approach.
  The study presents a set of numerical examples that demonstrate the accuracy
of the approximation and validate the current approach against observational
data along a satellite orbit, including estimates of established empirical and
physics-based models of the ionosphere-thermosphere system. Finally, a 1D
radial derivation of the physics-based model is presented and utilized for
conducting a parametric study of the main thermal quantities under various
solar conditions.

Space Physics;Computational Engineering, Finance, and Science;Numerical Analysis;Numerical Analysis;Fluid Dynamics