Atmospheric and ocean modeling with an adaptive finite element solver for the shallow-water equations

Likeness, B K; Snider, Arthur David

doi:10.1016/s0168-9274(97)00090-1

Cited by 40 publications

(21 citation statements)

References 15 publications

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“…Our paper focuses on dynamically adaptive grids, which track features of interest during the model simulation by locally adding or removing grid points as needed. Adaptation criteria based on error estimates (e.g., Skamarock et al 1989;Behrens 1998;Blaise and St-Cyr 2012) or flow characteristics (e.g., Hubbard and Nikiforakis 2003;Jablonowski et al 2006Jablonowski et al , 2009St-Cyr et al 2008) can be used to determine where the high-resolution mesh should be placed. By increasing resolution only locally, dynamic refinement significantly decreases the total number of degrees of freedom for the simulation.…”

Section: Introductionmentioning

confidence: 99%

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

Ferguson

Jablonowski

Johansen

et al. 2016

Monthly Weather Review

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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.

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Section: Introductionmentioning

confidence: 99%

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

Ferguson

Jablonowski

Johansen

et al. 2016

Monthly Weather Review

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“…Dynamic mesh adaptation strategies following those structures represent a great potential in the field of ocean modelling (e.g. Behrens 1998;Heinze and Hense 2002;Nair et al 2005;Giraldo et al 2002). In this framework of a new unstructured ocean model, we believe that the DG method is a good candidate because it provides a simple and efficient error estimator for any order p, which means a simple and efficient way to deal with mesh adaptivity.…”

Section: Introductionmentioning

confidence: 99%

High-order h-adaptive discontinuous Galerkin methods for ocean modelling

et al. 2007

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In this paper, we present an h-adaptive discontinuous Galerkin formulation of the shallow water equations. For a discontinuous Galerkin scheme using polynomials up to order p, the spatial error of discretization of the method can be shown to be of the order of h pþ1 , where h is the mesh spacing. It can be shown by rigorous error analysis that the discontinuous Galerkin method discretization error can be related to the amplitude of the inter-element jumps. Therefore, we use the information contained in jumps to build error metrics and size field. Results are presented for ocean modelling problems. A first experiment shows that the theoretical convergence rate is reached with the discontinuous Galerkin high-order h-adaptive method applied to the Stommel wind-driven gyre. A second experiment shows the propagation of an anticyclonic eddy in the Gulf of Mexico.

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“…A different approach is presented in the work of Behrens [24,25], where the triangular elements indicated for refinement are subdivided making sure the conformity of the edges is preserved. The method allows for local refinement without modifying the entire domain.…”

Section: Amr In Atmospheric Simulationsmentioning

confidence: 99%

Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations

Kopera

Giraldo

2014

Journal of Computational Physics

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Atmospheric and ocean modeling with an adaptive finite element solver for the shallow-water equations

Cited by 40 publications

References 15 publications

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

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

High-order h-adaptive discontinuous Galerkin methods for ocean modelling

Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations

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