Analysis of Discrete Shallow-Water Models on Geodesic Delaunay Grids with C-Type Staggering

Bonaventura, Luca; Ringler, Todd D.

doi:10.1175/mwr2986.1

Cited by 86 publications

(102 citation statements)

References 53 publications

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“…A partial generalization has been achieved by Bonaventura and Ringler (2005) but still lacked a discrete conservation of potential vorticity/potential enstrophy and exact discrete geostrophic equilibria, two properties tied together as discussed by Thuburn (2008). A full generalization was obtained later by Thuburn et al (2009) and Ringler et al (2010) assuming a Delaunay-Voronoi pair of primal and dual meshes, or more generally orthogonal primal and dual meshes (see Sect.…”

Section: T Dubos Et Al: Dynamico-10 An Icosahedral Hydrostatic Dymentioning

confidence: 99%

“…A number of building blocks of DYNAMICO are either directly found in the literature or are adaptations of standard methods: explicit Runge-Kutta time stepping, mimetic horizontal finite-difference operators (Bonaventura and Ringler, 2005;Thuburn et al, 2009;Ringler et al, 2010), piecewiselinear slope-limited finite-volume reconstruction (Dukowicz and Kodis, 1987;Tomita et al, 2001), swept-area calculation of scalar fluxes (Miura, 2007), and directionally split time integration of three-dimensional transport (e.g. Hourdin and Armengaud, 1999).…”

Section: Contributionsmentioning

confidence: 99%

“…(5) imitates curl grad = 0 (Bonaventura and Ringler, 2005). Notice that the generic A, B used here are unrelated to quantities A (areas) and B (Bernoulli function) defined later.…”

mentioning

confidence: 99%

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DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility

Dubos¹,

Dubey

Tort³

et al. 2015

Geosci. Model Dev.

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Abstract. The design of the icosahedral dynamical core DY-NAMICO is presented. DYNAMICO solves the multi-layer rotating shallow-water equations, a compressible variant of the same equivalent to a discretization of the hydrostatic primitive equations in a Lagrangian vertical coordinate, and the primitive equations in a hybrid mass-based vertical coordinate. The common Hamiltonian structure of these sets of equations is exploited to formulate energy-conserving spatial discretizations in a unified way.The horizontal mesh is a quasi-uniform icosahedral C-grid obtained by subdivision of a regular icosahedron. Control volumes for mass, tracers and entropy/potential temperature are the hexagonal cells of the Voronoi mesh to avoid the fast numerical modes of the triangular C-grid. The horizontal discretization is that of Ringler et al. (2010), whose discrete quasi-Hamiltonian structure is identified. The prognostic variables are arranged vertically on a Lorenz grid with all thermodynamical variables collocated with mass. The vertical discretization is obtained from the three-dimensional Hamiltonian formulation. Tracers are transported using a second-order finite-volume scheme with slope limiting for positivity. Explicit Runge-Kutta time integration is used for dynamics, and forward-in-time integration with horizontal/vertical splitting is used for tracers. Most of the model code is common to the three sets of equations solved, making it easier to develop and validate each piece of the model separately.Representative three-dimensional test cases are run and analyzed, showing correctness of the model. The design permits to consider several extensions in the near future, from higher-order transport to more general dynamics, especially deep-atmosphere and non-hydrostatic equations.

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Section: T Dubos Et Al: Dynamico-10 An Icosahedral Hydrostatic Dymentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

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DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility

Dubos¹,

Dubey

Tort³

et al. 2015

Geosci. Model Dev.

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“…where h max = 2000m, R = π/9, and d (8) is added as a forcing term to the right hand side of the PDE for the geopotential height h given in (7). Adjustment of the flow to the presence of an undifferentiable mountain results in a ringing phenomena of gravity waves whose signature echoes throughout the 15 day simulation.…”

Section: Flow Over An Isolated Mountainmentioning

confidence: 99%

“…However, the SWE can only approximate this motion, generating inherent instabilities in the flow [39]. As a result, this test has been controversial in its usefulness [7,26]. Even so, it is still commonly used as a test case for novel numerical schemes in atmospheric modeling [7,30,35,48].…”

Section: Rossby-haurwitz Wavesmentioning

confidence: 99%

A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere

Flyer

Lehto

Blaise

et al. 2012

Journal of Computational Physics

161

173

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. AbstractThe current paper establishes the computational efficiency and accuracy of the RBF-FD method for large-scale geoscience modeling with comparisons to state-of-the-art methods as high-order discontinuous Galerkin and spherical harmonics, the latter using expansions with close to 300,000 bases. The test cases are demanding fluid flow problems on the sphere that exhibit numerical challenges, such as Gibbs phenomena, sharp gradients, and complex vortical dynamics with rapid energy transfer from large to small scales over short time periods. The computations were possible as well as very competitive due to the implementation of hyperviscosity on large RBF stencil sizes (corresponding roughly to 6th to 9th order methods) with up to O(10 5 ) nodes on the sphere. The RBF-FD method scaled as O(N ) per time step, where N is the total number of nodes on the sphere. In the Appendix, guidelines are given on how to chose parameters when using RBF-FD to solve hyperbolic PDEs.

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Extending High‐Order Flux Operators on Spherical Icosahedral Grids and Their Applications in the Framework of a Shallow Water Model

Zhang

2018

J Adv Model Earth Syst

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This study extends a set of unstructured third/fourth‐order flux operators on spherical icosahedral grids from two perspectives. First, the fifth‐order and sixth‐order flux operators of this kind are further extended, and the nominally second‐order to sixth‐order operators are then compared based on the solid body rotation and deformational flow tests. Results show that increasing the nominal order generally leads to smaller absolute errors. Overall, the standard fifth‐order scheme generates the smallest errors in limited and unlimited tests, although it does not enhance the convergence rate. Even‐order operators show higher limiter sensitivity than the odd‐order operators. Second, a triangular version of these high‐order operators is repurposed for transporting the potential vorticity in a space‐time‐split shallow water framework. Results show that a class of nominally third‐order upwind‐biased operators generates better results than second‐order and fourth‐order counterparts. The increase of the potential enstrophy over time is suppressed owing to the damping effect. The grid‐scale noise in the vorticity is largely alleviated, and the total energy remains conserved. Moreover, models using high‐order operators show smaller numerical errors in the vorticity field because of a more accurate representation of the nonlinear Coriolis term. This improvement is especially evident in the Rossby‐Haurwitz wave test, in which the fluid is highly rotating. Overall, high‐order flux operators with higher damping coefficients, which essentially behave like the Anticipated Potential Vorticity Method, present better results.

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Analysis of Discrete Shallow-Water Models on Geodesic Delaunay Grids with C-Type Staggering

Cited by 86 publications

References 53 publications

DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility

DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility

A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere

Extending High‐Order Flux Operators on Spherical Icosahedral Grids and Their Applications in the Framework of a Shallow Water Model

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