Two-Dimensional Evaluation of ATHAM-Fluidity, a Nonhydrostatic Atmospheric Model Using Mixed Continuous/Discontinuous Finite Elements and Anisotropic Grid Optimization

Abstract

This paper presents the first attempt to apply the compressible nonhydrostatic Active Tracer High-Resolution Atmospheric Model-Fluidity (ATHAM-Fluidity) solver to a series of idealized atmospheric test cases. ATHAMFluidity uses a hybrid finite-element discretization where pressure is solved on a continuous second-order grid while momentum and scalars are computed on a first-order discontinuous grid (also known as P 1DG 2 P 2 ). ATHAMFluidity operates on two-and three-dimensional unstructured meshes, using triangular or tetrahedral elements, respectively, with the possibility to employ an anisotropic mesh optimization algorithm for automatic grid refinement and coarsening during run time. The solver is evaluated using two-dimensional-only dry idealized test cases covering a wide range of atmospheric applications. The first three cases, representative of atmospheric convection, reveal the ability of ATHAM-Fluidity to accurately simulate the evolution of large-scale flow features in neutral atmospheres at rest. Grid convergence without adaptivity as well as the performances of the Hermite-Weighted Essentially Nonoscillatory (Hermite-WENO) slope limiter are discussed. These cases are also used to test the grid optimization algorithm implemented in ATHAM-Fluidity. Adaptivity can result in up to a sixfold decrease in computational time and a fivefold decrease in total element number for the same finest resolution. However, substantial discrepancies are found between the uniform and adapted grid results, thus suggesting the necessity to improve the reliability of the approach. In the last three cases, corresponding to atmospheric gravity waves with and without orography, the model ability to capture the amplitude and propagation of weak stationary waves is demonstrated. This work constitutes the first step toward the development of a new comprehensive limited area atmospheric model.

微分可能な流束表現を用いたo2o3局所ガラーキン法

“…The inaccuracies and noise for this problem, as seen for some non-Galerkin treatments, are absent; o2o3 is able to advect a structure along a straight line without generating noise. This result is consistent with that for the first-order Galerkin approach and with that obtained by Savre et al (2016), who reported fewer numerical boundary-related errors for the classic Galerkin method. These results indicate that cut cells may be applicable with polynomial representations higher than one.…”

“…Nevertheless, existing atmospheric Galerkin models often do not take advantage of such suitability for good surface approximations, because grids that are not horizontally aligned are typically used. A notable exception is the atmospheric model called Active Tracer High-resolution Atmospheric Model-Fluidity (ATHAM-Fluidity) that uses horizontally aligned cells and achieves good results in the generation of mountain-induced waves (Savre et al 2016).…”

Demonstration of a three-dimensional dynamically adaptive atmospheric dynamic framework for the simulation of mountain waves

“…Marras 4 / 40 et al (2016) pointed out that element-based Galerkin methods might perform well in next-generation atmospheric and climate models competing with finite difference and spectral transform methods. Savre et al (2016) first introduced the anisotropic adaptive mesh technique into atmospheric modeling in both horizontal and vertical directions and evaluated it with 2D idealized test cases.…”

“…In this study, we develop a new 3D dynamically adaptive atmospheric model (Fluidity-Atmosphere) based on the dynamic framework of Fluidity, a computational fluid dynamic (CFD) model developed by the Applied Modeling and Computation Group (AMCG), Imperial College London (ICL) (Pain et al 2001(Pain et al , 2005Piggott et al 2009). Its accuracy and conservation properties have been validated by a series of idealized simulations using a uniform mesh, and the computational cost has been decreased by mesh adaptivity in rising bubble, density current and interacting warm and cold bubble tests (Pain et al 2001(Pain et al , 2005Piggott et al 2009;Savre et al 2016;Zheng et al 2015;2020). Fluidity-Atmosphere applies dynamically tetrahedral adaptive meshes in 3D space and time so that regions of steep topography, high dynamic activity or specific interest can be modeled with high horizontal and vertical resolutions.…”

“…The performance of Fluidity, including the approximation accuracy, numerical stability, mesh convergence and conservation properties, has been demonstrated by Pain et al (2001Pain et al ( ), (2005; Farrell et al (2009); Piggott et al (2009); Savre et al (2016); Li et al (2018); and Zheng et al (2015Zheng et al ( ), (2020. One important unanswered question is whether Fluidity-Atmosphere can accurately represent the underlying terrain and simulate mountain waves, which have a dominant effect on atmospheric motions as the horizontal resolution approaches or exceeds O(10 1 ) km (Gallus and Klemp 2000).…”