40 research outputs found
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
Conforming restricted Delaunay mesh generation for piecewise smooth complexes
A Frontal-Delaunay refinement algorithm for mesh generation in piecewise
smooth domains is described. Built using a restricted Delaunay framework, this
new algorithm combines a number of novel features, including: (i) an
unweighted, conforming restricted Delaunay representation for domains specified
as a (non-manifold) collection of piecewise smooth surface patches and curve
segments, (ii) a protection strategy for domains containing curve segments that
subtend sharply acute angles, and (iii) a new class of off-centre refinement
rules designed to achieve high-quality point-placement along embedded curve
features. Experimental comparisons show that the new Frontal-Delaunay algorithm
outperforms a classical (statically weighted) restricted Delaunay-refinement
technique for a number of three-dimensional benchmark problems.Comment: To appear at the 25th International Meshing Roundtabl
Locally optimal Delaunay-refinement and optimisation-based mesh generation
The field of mesh generation concerns the development of efficient algorithmic techniques to construct high-quality tessellations of complex geometrical objects. In this thesis, I investigate the problem of unstructured simplicial mesh generation for problems in two- and three-dimensional spaces, in which meshes consist of collections of triangular and tetrahedral elements. I focus on the development of efficient algorithms and computer programs to produce high-quality meshes for planar, surface and volumetric objects of arbitrary complexity. I develop and implement a number of new algorithms for mesh construction based on the Frontal-Delaunay paradigm - a hybridisation of conventional Delaunay-refinement and advancing-front techniques. I show that the proposed algorithms are a significant improvement on existing approaches, typically outperforming the Delaunay-refinement technique in terms of both element shape- and size-quality, while offering significantly improved theoretical robustness compared to advancing-front techniques. I verify experimentally that the proposed methods achieve the same element shape- and size-guarantees that are typically associated with conventional Delaunay-refinement techniques. In addition to mesh construction, methods for mesh improvement are also investigated. I develop and implement a family of techniques designed to improve the element shape quality of existing simplicial meshes, using a combination of optimisation-based vertex smoothing, local topological transformation and vertex insertion techniques. These operations are interleaved according to a new priority-based schedule, and I show that the resulting algorithms are competitive with existing state-of-the-art approaches in terms of mesh quality, while offering significant improvements in computational efficiency. Optimised C++ implementations for the proposed mesh generation and mesh optimisation algorithms are provided in the JIGSAW and JITTERBUG software libraries
Using Power Diagrams to Build Optimal Unstructured Meshes for C-Grid Models
The Model for Prediction Across Scales (MPAS) for Ocean (-O), Sea-Ice (-SI) and Land-Ice (-LI), in addition to the Coastal Ocean Marine Prediction Across Scales (COMPAS) are two novel general circulation models designed to resolve coupled ocean-ice dynamics over variable spatial scales using non-uniform unstructured grids. Both models are based on a conservative mimetic finite-difference/volume formulation (TRiSK), in which staggered momentum, vorticity and mass-based degrees- of-freedom are distributed over an orthogonal 'primal-dual' mesh
High-order Accurate Finite-Volume Formulations for the Pressure Gradient Force in Layered Ocean Models
Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the contact pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates andor terrain-following representations
MPAS - Ocean Simulation Quality for Variable-Resolution North American Coastal Meshes
Climate model components utilizing unstructured meshes enable variableresolution, regionally enhanced simulations within global domains. Here we investigate the relationship between mesh quality and simulation statistics using the JIGSAW unstructured meshing library and the Model for Prediction Across ScalesOcean (MPASOcean) with a focus on Gulf Stream dynamics. In the base configuration, the refined region employs 8 km cells that extend 400 km from the coast of North America. This coastal refined region is embedded within a lowresolution global domain, with cell size varying latitudinally between 30 and 60 km. The resolution transition region between the refined region and background mesh is 600 km wide. Three sensitivity tests are conducted: 1) the quality of meshes is intentionally degraded so that horizontal cells are progressively more distorted; 2) the transition region from high to low resolution is steepened; and 3) resolution of the coastal refinement region is varied from 30 km to 8 km. Overall, the ocean simulations are shown to be robust to mesh resolution and quality alterations. Meshes that are substantially degraded still produce realistic currents, with Southern Ocean transports within 0.4% and Gulf Stream transports within 12% of highquality mesh results. The narrowest transition case of 100 km did not produce any spurious effects. Refined regions with high resolution produce eddy kinetic energy and sea surface height variability that are similar to the highresolution reference simulation. These results provide heuristics for the design criteria of variableresolution climate model domains
Fast Mapping onto Census Blocks
Pandemic measures such as social distancing and contact tracing can be
enhanced by rapidly integrating dynamic location data and demographic data.
Projecting billions of longitude and latitude locations onto hundreds of
thousands of highly irregular demographic census block polygons is
computationally challenging in both research and deployment contexts. This
paper describes two approaches labeled "simple" and "fast". The simple approach
can be implemented in any scripting language (Matlab/Octave, Python, Julia, R)
and is easily integrated and customized to a variety of research goals. This
simple approach uses a novel combination of hierarchy, sparse bounding boxes,
polygon crossing-number, vectorization, and parallel processing to achieve
100,000,000+ projections per second on 100 servers. The simple approach is
compact, does not increase data storage requirements, and is applicable to any
country or region. The fast approach exploits the thread, vector, and memory
optimizations that are possible using a low-level language (C++) and achieves
similar performance on a single server. This paper details these approaches
with the goal of enabling the broader community to quickly integrate location
and demographic data.Comment: 8 pages, 7 figures, 55 references; accepted to IEEE HPEC 202