Measurement Challenges in Atmospheric Chemistry by Newman L. (ed.)

By Newman L. (ed.)

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8 for the first four cases): 1. One hanging node: connect hanging node with both vertices of opposite edge, obtaining 3 new triangular cells; 2. two hanging nodes on opposite edges: connect both hanging nodes, obtaining 2 new quadrilateral cells; 3. 3 Refinement Strategies in 2D 33 hanging node 1. 3. 2. 4. Fig. 8. Closures for avoiding hanging nodes in quadrilateral grid refinement. Four cases are shown, as described in the text 4. three hanging nodes: insert new vertex at cell center, connect new vertex nodes with all hanging, and with vertices of unrefined edge, obtaining 2 new quadrilateral and 3 new triangular cells; 5.

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.

C represents the coarsest mesh level used in computations, and f is the finest grid level. Extending the above naming convetion with this pair, we have a ONSH[3 : 6]-grid in [221], while in [39] the finest mesh is of type CNT[4 : 19]. If we have uniform grids, then we can omit one of the entries, obtaining CNT[15] ≡ CNT[15 : 15]. If refinement levels are inadequate or not available for the classification, we could consider resolutions of the coarsest grid cells and the finest grid cells. Thus, CNT[4 : 19] ≡ CNT(230 : 5)[km] .

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