A conservative discretization of the shallow-water equations on triangular grids

Korn, Peter; Linardakis, Leonidas

doi:10.1016/j.jcp.2018.09.002

Cited by 24 publications

(48 citation statements)

References 60 publications

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“…Figure 4 shows histograms of the cell's maximum angle of four different meshes. According to Korn and Linardakis (2018), an equiangular mesh offers the best numerical characteristics. Hence, the uniform grid uni03 shows something of an ideal distribution with the highest frequency in the 63°-64°i nterval and only few cells with a maximum angle above 67°.…”

Section: Grid Generationmentioning

confidence: 99%

Global tide simulations with ICON-O: testing the model performance on highly irregular meshes

et al. 2020

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The global tide is simulated with the global ocean general circulation model ICON-O using a newly developed tidal module, which computes the full tidal potential. The simulated coastal M2 amplitudes, derived by a discrete Fourier transformation of the output sea level time series, are compared with the according values derived from satellite altimetry (TPXO-8 atlas). The experiments are repeated with four uniform and sixteen irregular triangular grids. The results show that the quality of the coastal tide simulation depends primarily on the coastal resolution and that the ocean interior can be resolved up to twenty times lower without causing considerable reductions in quality. The mesh transition zones between areas of different resolutions are formed by cell bisection and subsequent local spring optimisation tolerating a triangular cell’s maximum angle up to 84°. Numerical problems with these high-grade non-equiangular cells were not encountered. The results emphasise the numerical feasibility and potential efficiency of highly irregular computational meshes used by ICON-O.

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Section: Grid Generationmentioning

confidence: 99%

Global tide simulations with ICON-O: testing the model performance on highly irregular meshes

et al. 2020

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“…The grids are symmetrized with respect to the equator by reflecting the northern hemisphere to the south. The equatorial‐symmetric grid has been tested with the ICON‐O for shallow water set‐ups and showed reduced errors (Korn & Linardakis, 2018). Local asymmetries in grids can be the cause of increased numerical errors (Weller et al., 2009).…”

Section: Model Overviewmentioning

confidence: 99%

The ICON Earth System Model Version 1.0

Jungclaus

Lorenz

Schmidt

et al. 2022

J Adv Model Earth Syst

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This work documents the ICON‐Earth System Model (ICON‐ESM V1.0), the first coupled model based on the ICON (ICOsahedral Non‐hydrostatic) framework with its unstructured, icosahedral grid concept. The ICON‐A atmosphere uses a nonhydrostatic dynamical core and the ocean model ICON‐O builds on the same ICON infrastructure, but applies the Boussinesq and hydrostatic approximation and includes a sea‐ice model. The ICON‐Land module provides a new framework for the modeling of land processes and the terrestrial carbon cycle. The oceanic carbon cycle and biogeochemistry are represented by the Hamburg Ocean Carbon Cycle module. We describe the tuning and spin‐up of a base‐line version at a resolution typical for models participating in the Coupled Model Intercomparison Project (CMIP). The performance of ICON‐ESM is assessed by means of a set of standard CMIP6 simulations. Achievements are well‐balanced top‐of‐atmosphere radiation, stable key climate quantities in the control simulation, and a good representation of the historical surface temperature evolution. The model has overall biases, which are comparable to those of other CMIP models, but ICON‐ESM performs less well than its predecessor, the Max Planck Institute Earth System Model. Problematic biases are diagnosed in ICON‐ESM in the vertical cloud distribution and the mean zonal wind field. In the ocean, sub‐surface temperature and salinity biases are of concern as is a too strong seasonal cycle of the sea‐ice cover in both hemispheres. ICON‐ESM V1.0 serves as a basis for further developments that will take advantage of ICON‐specific properties such as spatially varying resolution, and configurations at very high resolution.

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“…In addition, geometry-based methods generate periodic graphs either according to predefined geometric rules to craft the targeted periodic graphs (Friedrichs et al, 1999;Treacy et al, 2004) or simply gluing the initial fragment into periodic graphs (Le Bail, 2005). (Korn & Linardakis, 2018) As mentioned above, both domain specific-based and geometry-based generative models for periodic graphs require predefined properties that are either domain-specific or geometric-based, enabling them to usually fit well towards the properties that the predefined principles are tailored for, but usually they cannot do well for the others.…”

Section: Introductionmentioning

confidence: 99%

“…Figure 1. Examples of periodic graphs where basic units are highlighed: (a) structure of tridymite; (b) structure of graphene and (c) triangular grids(Korn & Linardakis, 2018) …”

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Deep Generative Model for Periodic Graphs

Wang¹,

Guo²,

Zhao³

2022

Preprint

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Periodic graphs are graphs consisting of repetitive local structures, such as crystal nets and polygon mesh.Their generative modeling has great potential in real-world applications such as material design and graphics synthesis. Classical models either rely on domain-specific predefined generation principles (e.g., in crystal net design), or follow geometry-based prescribed rules. Recently, deep generative models has shown great promise in automatically generating general graphs. However, their advancement into periodic graphs have not been well explored due to several key challenges in 1) maintaining graph periodicity; 2) disentangling local and global patterns; and 3) efficiency in learning repetitive patterns. To address them, this paper proposes Periodical-Graph Disentangled Variational Auto-encoder (PGD-VAE), a new deep generative models for periodic graphs that can automatically learn, disentangle, and generate local and global graph patterns. Specifically, we develop a new periodic graph encoder consisting of global-pattern encoder and localpattern encoder that ensures to disentangle the representation into global and local semantics. We then propose a new periodic graph decoder consisting of local structure decoder, neighborhood decoder, and global structure decoder, as well as the assembler of their outputs that guarantees periodicity. Moreover, we design a new model learning objective that helps ensure the invariance of local-semantic representations for the graphs with the same local structure. Comprehensive experimental evaluations have been conducted to demonstrate the effectiveness of the proposed method. The code of proposed PGD-VAE is availabe at https://github.com/shi-yu-wang/PGD-VAE.

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A conservative discretization of the shallow-water equations on triangular grids

Cited by 24 publications

References 60 publications

Global tide simulations with ICON-O: testing the model performance on highly irregular meshes

Global tide simulations with ICON-O: testing the model performance on highly irregular meshes

The ICON Earth System Model Version 1.0

Deep Generative Model for Periodic Graphs

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