JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere

An algorithm for the generation of non-uniform, locally-orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered Voronoi/Delaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally-orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a-priori bounds on element size and shape. Grid-quality is further improved through the application of hill-climbing type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution type studies is discussed in detail.Comment: Final revisions, as per: Engwirda, D.: JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere, Geosci. Model Dev., 10, 2117-2140, https://doi.org/10.5194/gmd-10-2117-2017, 201

A Comparison of Two Shallow Water Models with Non-Conforming Adaptive Grids: classical tests

In an effort to study the applicability of adaptive mesh refinement (AMR) techniques to atmospheric models an interpolation-based spectral element shallow water model on a cubed-sphere grid is compared to a block-structured finite volume method in latitude-longitude geometry. Both models utilize a non-conforming adaptation approach which doubles the resolution at fine-coarse mesh interfaces. The underlying AMR libraries are quad-tree based and ensure that neighboring regions can only differ by one refinement level. The models are compared via selected test cases from a standard test suite for the shallow water equations. They include the advection of a cosine bell, a steady-state geostrophic flow, a flow over an idealized mountain and a Rossby-Haurwitz wave. Both static and dynamics adaptations are evaluated which reveal the strengths and weaknesses of the AMR techniques. Overall, the AMR simulations show that both models successfully place static and dynamic adaptations in local regions without requiring a fine grid in the global domain. The adaptive grids reliably track features of interests without visible distortions or noise at mesh interfaces. Simple threshold adaptation criteria for the geopotential height and the relative vorticity are assessed.Comment: 25 pages, 11 figures, preprin

Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: incandecence and luminescence in arbitrary geometries

We describe a fluctuating volume--current formulation of electromagnetic fluctuations that extends our recent work on heat exchange and Casimir interactions between arbitrarily shaped homogeneous bodies [Phys. Rev. B. 88, 054305] to situations involving incandescence and luminescence problems, including thermal radiation, heat transfer, Casimir forces, spontaneous emission, fluorescence, and Raman scattering, in inhomogeneous media. Unlike previous scattering formulations based on field and/or surface unknowns, our work exploits powerful techniques from the volume--integral equation (VIE) method, in which electromagnetic scattering is described in terms of volumetric, current unknowns throughout the bodies. The resulting trace formulas (boxed equations) involve products of well-studied VIE matrices and describe power and momentum transfer between objects with spatially varying material properties and fluctuation characteristics. We demonstrate that thanks to the low-rank properties of the associatedmatrices, these formulas are susceptible to fast-trace computations based on iterative methods, making practical calculations tractable. We apply our techniques to study thermal radiation, heat transfer, and fluorescence in complicated geometries, checking our method against established techniques best suited for homogeneous bodies as well as applying it to obtain predictions of radiation from complex bodies with spatially varying permittivities and/or temperature profiles