Adaptive Atmospheric Modeling: Key Techniques in Grid by Jörn Behrens

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By Jörn Behrens

This is an summary of the advance of adaptive suggestions for atmospheric modeling. Written in an academic kind, it features as a place to begin for readers attracted to adaptive modeling, in atmospheric sciences and past. assurance comprises paradigms of adaptive suggestions, equivalent to blunders estimation and edition standards. Mesh iteration equipment are offered for triangular/tetrahedral and quadrilateral/hexahedral meshes, with a distinct part on preliminary meshes for the sphere.

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Extra resources for Adaptive Atmospheric Modeling: Key Techniques in Grid Generation, Data Structures, and Numerical Operations with Applications (Lecture Notes in Computational Science and Engineering)

Example text

For example the 850 hPa relative vorticity extreme values have been used to track cyclones. Successful approaches applied geopotential or temperature extremes as well as sea level pressure (see [221] for a review of methods). L¨auter uses the direct values of vorticity and divergence to derive an efficient and accurate refinement criterion. More precisely, the refinement criterion ητ in each cell τ of the triangulation is computed from vorticity ζ and divergence δ by 2 ζ 2 + δ 2 dx ητ = = ζ +δ τ L2 (τ ) .

The error estimator is based on the energy norm χ τ . These error estimators were originally proposed by Bank and Weiser [22] 4. e. D = −∆. The method tries to construct an approximation σ (2) to the true ∆ρ, by applying the following scheme for the gradient operator twice. Let σ be the weighted average of the gradients corresponding to one node patch: |τi | · ∇ρh |τi . σ= {i:τi ∈ patch of node i} As usual, |τ | denotes the area of τ . Extend σ to the whole element τ by linear interpolation. The error estimator is derived from |σ (2) − ∆ρh |.

D Note that since hb,τ < he,τ < hB,τ < Cϑ hb,τ , where Cϑ is a constant that depends only on the smallest inner angle, all mesh width parameters are equivalent to each other. Therefore, we often just use the notation h for mesh width, without specifying which specific measure is to be used. 8 implies that ϑ is close to π3 . For quadrilateral triangulations a similar remark holds with ϑ close to π2 . −1 hb Note that the regularity condition is equivalent to 0 hB = Cϑ < 1. 2 Grid Types In this section different grid types are classified.

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