Implementation of the Novel Duo‐Grid in GFDL's FV3 Dynamical Core

Abstract

The gnomonic cubed‐sphere grid has excellent accuracy and uniformity, but the “kink” in the coordinates at the cube edges in the halo region can leave an imprint of the cube in the solution, and requires special edge handling. To reduce grid imprinting, we implement the novel “Duo‐Grid” within the Geophysical Fluid Dynamics Laboratory's (GFDL) Finite‐Volume Cubed‐Sphere Dynamical Core (FV3). The Duo‐Grid remaps a cube face's data from neighboring face from kinked to natural locations along great circle lines using 1D piecewise linear interpolation. A 2D interpolation algorithm is used to fill correct data at the eight corners of the cubed‐sphere needed for FV3's 2D advection scheme. The Duo‐Grid was tested in idealized tests using the 2D shallow water solver and the 3D hydrostatic and non‐hydrostatic solvers. We found that error norms are greatly reduced and grid imprinting is practically eliminated when employing the Duo‐Grid. These results indicate that FV3's accuracy and robustness have improved.

ExoCubed: A Riemann-solver-based Cubed-sphere Dynamic Core for Planetary Atmospheres

“…Moreover, in describing the large-scale circulation of the atmosphere, employing the hydrostatic assumption leads to "layered atmospheres" that can be solved layer by layer using the "vertically Lagrangian" approach that treats each layer as a shallow-water system (Lin 2004). Coupled with equations for tracer advection (e.g., using potential temperature for the energy tracer) on a cubed sphere (Putman & Lin 2007) and a pressure gradient solver (Lin 1997), an extended equation set based on the shallowwater equations, the vertically Lagrangian advection, and a conservative remapping scheme became the backbone of the GFDLʼs FV3 dynamic core (Harris et al 2020;Mouallem et al 2023). A similar strategy has been employed by the MITgcm (Adcroft et al 2004a), where the vector-invariant form is preferred over the conservative momentum equations.…”

“…If the left/right states are different, the result of the Riemann solver will also be different, leading to inconsistent fluxes across the panel boundary. The GFDL's FV3 model solves this issue by averaging the fluxes computed by the left and right panels (Chen 2021;Mouallem et al 2023). We take a different approach.…”

“…Yet it is a nontrivial task to work with the PDE solver on a nonorthogonal geometry. The Flexible Modeling System (FMS) developed at the Geophysical Fluid Dynamics Laboratory (GFDL) uses the gnomonic cubed-sphere grids for its atmospheric GCM (Putman & Lin 2007;Mouallem et al 2023). Both FMS-based GCMs and the MITgcm have been used to study exoplanet atmospheres (Kaspi & Showman 2015;Komacek et al 2021).…”

Analysis of finite-volume advection schemes on cubed-sphere grids and an accurate alternative for divergent winds

“…The unpublished report from Whitaker (2015) shows grid imprinting in other models, including the FV3. More recently, Mouallem et al (2023) has shown some idealized simulations using FV3 where grid imprinting appears in many simulations. Generally speaking, grid imprinting refers to the presence of artificial behaviors in the numerical solution that are associated with the grid used.…”

“…Numerical results for the advection equation on the cubed-sphere using the FV3 dynamical core were presented in Putman and Lin (2007). However, they utilized extrapolations near the cube edges instead of the duo-grid approach from Mouallem et al (2023), which affects the convergence of this method. The current solver of FV3 solves the shallow-water equation on the so-called Lagrangian surfaces.…”