A Comparison of Two Shallow-Water Models with Nonconforming Adaptive Grids

Abstract

In an effort to study the applicability of adaptive mesh refinement (AMR) techniques to atmospheric models, an interpolation-based spectral element shallow-water model on a cubed-sphere grid is compared to a block-structured finite-volume method in latitude-longitude geometry. Both models utilize a nonconforming adaptation approach that doubles the resolution at fine-coarse mesh interfaces. The underlying AMR libraries are quad-tree based and ensure that neighboring regions can only differ by one refinement level. The models are compared via selected test cases from a standard test suite for the shallow-water equations, and via a barotropic instability test. These tests comprise the passive advection of a cosine bell and slotted cylinder, a steady-state geostrophic flow, a flow over an idealized mountain, a Rossby-Haurwitz wave, and the evolution of a growing barotropic wave. Both static and dynamics adaptations are evaluated, which reveal the strengths and weaknesses of the AMR techniques. Overall, the AMR simulations show that both models successfully place static and dynamic adaptations in local regions without requiring a fine grid in the global domain. The adaptive grids reliably track features of interests without visible distortions or noise at mesh interfaces. Simple threshold adaptation criteria for the geopotential height and the relative vorticity are assessed.

Experiments with different discretizations for the shallow‐water equations on a sphere

“…For now, however, we observe that hundreds of Gaussian points are required to generate the initial conditions accurately and that the outcome depends on the alignment of the grid with the flow and how the unbalanced perturbation is sampled on the grid. Some of these points were raised in Weller et al (2009) and St-Cyr et al (2008). It is a noteworthy accomplishment that the icosahedral model successfully captures the wave with only 40 962 degrees of freedom.…”

“…Analysis of an unstable jet is also useful to evaluate the minimum grid resolution required to obtain physically meaningful solutions. In general, we use a grid with fixed resolution and the analysis of meshrefinement techniques discussed by St-Cyr et al (2008) and Weller et al (2009) is not included. We expect that the results presented here will complement recent experiments with finite-volume and discontinuous Galerkin schemes on an icosahedral grid (Läuter et al, 2008;Walko and Avissar, 2008;Bernard et al, 2009;Lee and MacDonald, 2009;Ii and Xiao, 2010), on a cubed-sphere grid Nair, 2009) and on a Yin-Yang grid (Li et al, 2008).…”

High-order central ENO finite-volume scheme for ideal MHD

“…In recent years, cubed-sphere grids have gained increasing popularity for simulating fluid flow in domains between concentric spheres, first in the area of climate and weather modelling [18,19,20,21,22,23,24], but more recently also in areas like astrophysics [25,26]. Very recently, Ivan et al [14,15] have proposed a second-order parallel solution-adaptive computational framework for solving hyperbolic conservation laws on 3D cubed-sphere grids and applied the formulation to the simulation of several magnetized and nonmagnetized space-physics problems.…”

Predicting mesh density for adaptive modelling of the global atmosphere

“…Staniforth & Mitchell 1978;Berger & Oliger 1984;Skamarock et al 1989;Dietachmayer & Droegemeier 1992;Fiedler & Trapp 1993;Skamarock & Klemp 1993) but is still mostly under research rather than operational (e.g. Jablonowski et al 2006;Läuter et al 2007;St-Cyr et al 2008), a noteworthy exception being the study of Bacon et al (2000). If adaptive meshing is to be used to resolve deep convection, mesh density requirements must be predicted before convection would be likely to break out on the refined mesh.…”

“…Bacon et al 2000;Jablonowski et al 2006;Läuter et al 2007;St-Cyr et al 2008). However, re-meshing can be expensive and have a detrimental effect on the accuracy, reducing conservation of high-moment properties of the flow and altering the partition between balanced and unbalanced flow.…”