scholarly journals Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

2016 ◽  
Vol 144 (12) ◽  
pp. 4641-4666 ◽  
Author(s):  
Jared O. Ferguson ◽  
Christiane Jablonowski ◽  
Hans Johansen ◽  
Peter McCorquodale ◽  
Phillip Colella ◽  
...  
Keyword(s):  
Shallow Water ◽  
Adaptive Mesh Refinement ◽  
Large Scale ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
High Order ◽  
Water Model ◽  
Test Cases ◽  
Shallow Water Model ◽  
Cubed Sphere

Abstract Adaptive mesh refinement (AMR) is a technique that has been featured only sporadically in atmospheric science literature. This paper aims to demonstrate the utility of AMR for simulating atmospheric flows. Several test cases are implemented in a 2D shallow-water model on the sphere using the Chombo-AMR dynamical core. This high-order finite-volume model implements adaptive refinement in both space and time on a cubed-sphere grid using a mapped-multiblock mesh technique. The tests consist of the passive advection of a tracer around moving vortices, a steady-state geostrophic flow, an unsteady solid-body rotation, a gravity wave impinging on a mountain, and the interaction of binary vortices. Both static and dynamic refinements are analyzed to determine the strengths and weaknesses of AMR in both complex flows with small-scale features and large-scale smooth flows. The different test cases required different AMR criteria, such as vorticity or height-gradient based thresholds, in order to achieve the best accuracy for cost. The simulations show that the model can accurately resolve key local features without requiring global high-resolution grids. The adaptive grids are able to track features of interest reliably without inducing noise or visible distortions at the coarse–fine interfaces. Furthermore, the AMR grids keep any degradations of the large-scale smooth flows to a minimum.

scholarly journals Evaluation of the Utility of Static and Adaptive Mesh Refinement for Idealized Tropical Cyclone Problems in a Spectral Element Shallow-Water Model

2016 ◽  
Vol 144 (10) ◽  
pp. 3697-3724 ◽  
Author(s):  
Eric A. Hendricks ◽  
Michal A. Kopera ◽  
Francis X. Giraldo ◽  
Melinda S. Peng ◽  
James D. Doyle ◽  
...  
Keyword(s):  
Tropical Cyclone ◽  
Shallow Water ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Spectral Element ◽  
Thin Strip ◽  
Water Model ◽  
Barotropic Instability ◽  
Shallow Water Model

The utility of static and adaptive mesh refinement (SMR and AMR, respectively) are examined for idealized tropical cyclone (TC) simulations in a two-dimensional spectral element f-plane shallow-water model. The SMR simulations have varying sizes of the statically refined meshes (geometry based) while the AMR simulations use a potential vorticity (PV) threshold to adaptively refine the mesh to the evolving TC. Numerical simulations are conducted for four cases: (i) TC-like vortex advecting in a uniform flow, (ii) binary vortex interaction, (iii) barotropic instability of a PV ring, and (iv) barotropic instability of a thin strip of PV. For each case, a uniform grid high-resolution “truth” simulation is compared to two different SMR simulations and three different AMR simulations for accuracy and efficiency. The multiple SMR and AMR simulations have variations in the number of fully refined elements in the vicinity of the TC. For these idealized cases, it is found that the SMR and AMR simulations are able to resolve the vortex dynamical processes (e.g., barotropic instability, Rossby wave breaking, and filamentation) as well as the truth simulations, with no significant loss in accuracy in the refined region in the vortex vicinity and with significant speedups (factors of 4–15, depending on the total number of refined elements). The overall accuracy is enhanced by a greater area of fully refined mesh in both the SMR and AMR simulations.

Voronoi, Delaunay, and Block-Structured Mesh Refinement for Solution of the Shallow-Water Equations on the Sphere

2009 ◽  
Vol 137 (12) ◽  
pp. 4208-4224 ◽  
Author(s):  
Hilary Weller ◽  
Henry G. Weller ◽  
Aimé Fournier
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Wave Dispersion ◽  
Momentum Equation ◽  
Global Accuracy ◽  
Cubed Sphere ◽  
Block Structured

Abstract Alternative meshes of the sphere and adaptive mesh refinement could be immensely beneficial for weather and climate forecasts, but it is not clear how mesh refinement should be achieved. A finite-volume model that solves the shallow-water equations on any mesh of the surface of the sphere is presented. The accuracy and cost effectiveness of four quasi-uniform meshes of the sphere are compared: a cubed sphere, reduced latitude–longitude, hexagonal–icosahedral, and triangular–icosahedral. On some standard shallow-water tests, the hexagonal–icosahedral mesh performs best and the reduced latitude–longitude mesh performs well only when the flow is aligned with the mesh. The inclusion of a refined mesh over a disc-shaped region is achieved using either gradual Delaunay, gradual Voronoi, or abrupt 2:1 block-structured refinement. These refined regions can actually degrade global accuracy, presumably because of changes in wave dispersion where the mesh is highly nonuniform. However, using gradual refinement to resolve a mountain in an otherwise coarse mesh can improve accuracy for the same cost. The model prognostic variables are height and momentum collocated at cell centers, and (to remove grid-scale oscillations of the A grid) the mass flux between cells is advanced from the old momentum using the momentum equation. Quadratic and upwind biased cubic differencing methods are used as explicit corrections to a fast implicit solution that uses linear differencing.

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

2008 ◽  
Vol 136 (6) ◽  
pp. 1898-1922 ◽  
Author(s):  
Amik St-Cyr ◽  
Christiane Jablonowski ◽  
John M. Dennis ◽  
Henry M. Tufo ◽  
Stephen J. Thomas
Keyword(s):  
Shallow Water ◽  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
Spectral Element ◽  
Relative Vorticity ◽  
Standard Test ◽  
Water Model ◽  
Adaptive Grids ◽  
Fine Grid ◽  
Cubed Sphere

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.

Diffusion Experiments with a Global Discontinuous Galerkin Shallow-Water Model

2009 ◽  
Vol 137 (10) ◽  
pp. 3339-3350 ◽  
Author(s):  
Ramachandran D. Nair
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Water Model ◽  
Order System ◽  
Small Scale ◽  
Shallow Water Model ◽  
First Order ◽  
Advection Diffusion Equation ◽  
Diffusion Scheme ◽  
Cubed Sphere

Abstract A second-order diffusion scheme is developed for the discontinuous Galerkin (DG) global shallow-water model. The shallow-water equations are discretized on the cubed sphere tiled with quadrilateral elements relying on a nonorthogonal curvilinear coordinate system. In the viscous shallow-water model the diffusion terms (viscous fluxes) are approximated with two different approaches: 1) the element-wise localized discretization without considering the interelement contributions and 2) the discretization based on the local discontinuous Galerkin (LDG) method. In the LDG formulation the advection–diffusion equation is solved as a first-order system. All of the curvature terms resulting from the cubed-sphere geometry are incorporated into the first-order system. The effectiveness of each diffusion scheme is studied using the standard shallow-water test cases. The approach of element-wise localized discretization of the diffusion term is easy to implement but found to be less effective, and with relatively high diffusion coefficients, it can adversely affect the solution. The shallow-water tests show that the LDG scheme converges monotonically and that the rate of convergence is dependent on the coefficient of diffusion. Also the LDG scheme successfully eliminates small-scale noise, and the simulated results are smooth and comparable to the reference solution.

scholarly journals Improved moist-convective rotating shallow water model and its application to instabilities of hurricane-like vortices

2018 ◽  
Author(s):  
LMD
Keyword(s):  
Tropical Cyclone ◽  
Shallow Water ◽  
Water Vapour ◽  
Large Scale ◽  
Precipitable Water ◽  
Water Model ◽  
Moist Convection ◽  
Shallow Water Model ◽  
Atmospheric Motions ◽  
Rotating Shallow Water

We show how the two-layer moist-convective rotating shallow water model (mcRSW), which proved to be a simple and robust tool for studying effects of moist convection on large-scale atmospheric motions, can be improved by including, in addition to the water vapour, precipitable water, and the effects of vaporisation, entrainment, and precipitation. Thus improved mcRSW becomes cloud-resolving. It is applied, as an illustration, to model the development of instabilities of tropical cyclone-like vortices.

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