Adaptive Atmospheric Modeling: Key Techniques in Grid by Jörn Behrens

By Jörn Behrens

This ebook supplies an summary and suggestions within the improvement of adaptive thoughts for atmospheric modeling. Written in an instructional sort and that includes an exhaustive checklist of references, it's a place to begin for everybody who's attracted to adaptive modeling, no longer constrained to atmospheric sciences. It covers paradigms of adaptive suggestions, equivalent to blunders estimation and version standards. Mesh new release tools are offered for triangular/tetrahedral and quadrilateral/hexahedral meshes, with a distinct part on preliminary meshes for the field. potency concerns are mentioned together with options for accelerating unstructured mesh computations in addition to parallelization. contemplating functions, the booklet demonstrates a number of suggestions for discretizing suitable conservation legislation from atmospheric modeling. Finite quantity, discontinuous Galerkin and conservative Semi-Lagrangian tools are brought and utilized in simplified genuine lifestyles simulations. it's the author's goal to encourage the reader to get entangled with adaptive modeling concepts.

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Hanging node 1. 2. Fig. 10. Closures for avoiding hanging nodes in quadrilateral patch refinement. 3 Refinement Strategies in 2D 35 hanging node 1. 2. Fig. 11. 16 For uneven numbers of sub-cells in each patch cell, a convenient closure method can be derived that avoids triangular closures. 15 that can easily be generalized to higher uneven numbers. It should be mentioned, however, that for high numbers ν = 2k + 1, k ∈ N very thin quadrilaterals can occur which might degrade numerical stability. See fig.

For purely advection modeling, Kessler showed that a gradient based criterion results in even better approximation quality than a truncation error estimate [240, 393]. In general, proxy criteria often interleave with physics based criteria. A gradient or a curvature of a constituent is only a proxy, since not the gradient of the constituent causes the real problem but the low approximation quality of a numerical scheme. Karni and coworkers use a smoothness indicator for adaptive refinement control in a solver for hyperbolic systems [230].

1. e. vn = (v1 + v2 )/2. 2. Define new cells τ1 and τ2 by: τ1 = {v1 , vn , v3 }, τ2 = {vn , v2 , v3 }. 3. e. eτm1 = {v1 , v3 }, and eτm2 = {v2 , v3 }. This algorithm is depicted in fig. 2. Note that the order of vertices is important to maintain the orientation of triangles. The above definition maintains orientation in the daughter elements. 1, called bisection of longest edge. It differs from the above given algorithm in that it refines the longest edge only. When starting with a sufficiently regular initial triangle, both algorithms are equivalent.

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