Analysis of finite-volume advection schemes on cubed-sphere grids and an accurate alternative for divergent winds - Santos, Luan da Fonseca (2024)
The finite-volume dynamical core developed by GFDL-NOAA-USA, originally designed for latitude-longitude grids, was adapted to the cubed-sphere to enhance scalability on massively parallel supercomputers, resulting in the creation of the FV3 dynamical core. FV3 serves as the dynamical core for many models worldwide, and in 2019, it was officially designated as the dynamical core for the new Global Forecast System of the National Weather Service in the USA, replacing the spectral model. The finite-volume approach employed by FV3 to solve horizontal dynamics involves applying advection fluxes for different variables; thus, the advection scheme plays a key role in the model. Therefore, in this thesis, we propose to investigate the details of the advection scheme of FV3. We were able to suggest modifications to the FV3 advection scheme that significantly improved advection for divergent winds with only a small extra computational effort and of simple implementation in the existing codes. We conducted several numerical simulations using the advection and shallow-water equations. Since the FV3 advection scheme utilizes a splitting strategy, combining 1D finite-volume flux operators, our improvements were obtained by improving the departure point computation for the 1D flux operators and modifying the way the metric term of the cubed-sphere is treated when computing the 1D fluxes. Through simulations, we demonstrate that the current FV3 advection scheme is only first-order accurate for divergent winds, while our scheme is second-order accurate. For divergence-free winds, both schemes are second-order, with our scheme being slightly more accurate. One major difficulty in working on the cubed-sphere is handling coordinate discontinuity along the cube faces, which may lead to larger errors in these regions. However, we demonstrate through numerical simulations that the proposed advection scheme exhibits slightly reduced sensitivity to the cube corners. In conclusion, this thesis offers a comprehensive examination of the FV3 discretization of horizontal dynamics, providing valuable insights into enhancing the accuracy of the FV3 dynamical core, particularly for divergent winds.