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8 records

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Centroidal Voronoi tessellation based methods for optimal rain gauge location prediction

With more satellite and model precipitation data becoming available, new analytical methods are needed that can take advantage of emerging data patterns to make well informed predictions in many hydrological applications. Herein we propose a new strategy where we extract precipitation variability patterns and use correlation map to build the resulting density map that serves as an input to centroidal Voronoi tessellation construction that optimizes placement of precipitation gauges. We provide results of numerical experiments based on the data from the Alto-Adige region in Northern Italy and Oklahoma and compare them against actual gauge locations. This method provides an automated way for choosing new gauge locations and can be generalized to include physical constraints and to tackle other types of resource allocation problems.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2018

Robust Metric-Aligned Quad-Dominant Meshing Using L(sub p) Centroidal Voronoi Tessellation

We introduce a meshing algorithm that can be used to both generate and adapt meshes for bounded domains in an anisotropic manner. This is particularly beneficial when anisotropic flow features like shock waves or contact discontinuities are present in the computational domain. The algorithm presented in this paper is based upon meshing under the imposed Riemannian metric tensor, which controls the orientation and size of the mesh elements. In this way there is no need for user intervention to recognize these features. We demonstrate that the method indeed aligns the elements with the underlying metric and produces right-angled simplices that can be recombined into quadrilateral elements. The aim is to eventually incorporate this meshing strategy in the monolithic high-order spectral element solver that is currently being developed at NASA Ames. This paper has two main contributions: First, we demonstrate that we can generate quad-dominant metric-aligned meshes for bounded domains using a generalized form of L(sub p)-Centroidal Voronoi Tessellation (L(sub p)-CVT). Unlike previous works, we do not rely on a background mesh and discretize the bounded domain in a hierarchical way by first discretizing the boundaries and then the volume using the underlying metric. Second, we present an alternative for clipping the Voronoi cells on the boundary, which is common practice in CVT-based meshing algorithms, by reconstructing the Voronoi cells using the defined metric field. In this way we avoid the geometrical complexity of the clipping procedure and we show that we evaluate the energy and its gradient correctly. We show that the reconstruction of the computational domain is consistent with the Lloyds’ algorithm that is used to compute the L(sub p)-CVT.

Centroidal↗

DOE OSTI2021

Comparing numerical accuracy and stability for different horizontal discretizations in MPAS-Ocean

This manuscript investigates the effectiveness of two possible horizontal discretizations for the global ocean model MPAS-Ocean, both applied to Spherical Centroidal Voronoi Tessellations (SCVTs). The first discretization is TRiSK, a C-grid, finite-volume method, that possesses many desirable mimetic properties, but has a low order accuracy. The second discretization was introduced for the first time by Peixoto (2016), and consists of modifications to the TRiSK scheme designed to achieve at least first-order accuracy in the L ∞ norm, with the loss of some of the mimetic properties. Tests on shallow-water and primitive-equation models show that the scheme due to Peixoto is indeed more accurate, but presents stability issues with respect to TRiSK. Here, TRiSK is indeed found to be often more stable in time and more robust with respect to errors in the geometric properties of the grid.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Multi-Sensor Optimal Motion Planning for Radiological Contamination Surveys by Using Prediction-Difference Maps

Distributed and networked mobile sensor platforms using unmanned aerial and/or ground vehicles to survey areas of interest offer a safer and more efficient method for radiological contamination mapping; however, most applications rely on uniformly sweeping of the area in a raster-type motion without utilizing the information available in a dynamic sense. We have developed a fully autonomous optimal motion planning procedure for networks with two or more mobile sensors. The procedure utilizes well-established concepts of Gaussian processes in combination with control laws based on centroidal Voronoi tessellations to achieve optimal next-iteration sensor movements. A new method of informing optimal motion planning is proposed, whereby the absolute difference between the prior and current full-map prediction, referred to as the prediction-difference map, is used as the spatial density function within each Voronoi cell, providing immediate and iterative feedback for dynamic use of available information. The Gaussian process regression model used to estimate the contamination in unvisited locations also provides prediction uncertainties, and can be used as a quantitative metric to assess the confidence in the calculated contamination map; these estimates and prediction uncertainties are unavailable for standard uniform survey routines as they can only produce maps in the vicinity of observed locations. We present through simulation the achievable performance gains from using this new method by directly comparing to a uniform survey method. Results show that using the prediction-difference maps to inform motion planning procedures offers a faster rate of producing an accurate and convergent map relative to a uniform survey route.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

MPAS-Seaice (v1.0.0): sea-ice dynamics on unstructured Voronoi meshes

Abstract. We present MPAS-Seaice, a sea-ice model which uses the Model for Prediction Across Scales (MPAS) framework and spherical centroidal Voronoi tessellation (SCVT) unstructured meshes. As well as SCVT meshes, MPAS-Seaice can run on the traditional quadrilateral grids used by sea-ice models such as CICE. The MPAS-Seaice velocity solver uses the elastic–viscous–plastic (EVP) rheology and the variational discretization of the internal stress divergence operator used by CICE, but adapted for the polygonal cells of MPAS meshes, or alternatively an integral (“finite-volume”) formulation of the stress divergence operator. An incremental remapping advection scheme is used for mass and tracer transport. We validate these formulations with idealized test cases, both planar and on the sphere. The variational scheme displays lower errors than the finite-volume formulation for the strain rate operator but higher errors for the stress divergence operator. The variational stress divergence operator displays increased errors around the pentagonal cells of a quasi-uniform mesh, which is ameliorated with an alternate formulation for the operator. MPAS-Seaice shares the sophisticated column physics and biogeochemistry of CICE and when used with quadrilateral meshes can reproduce the results of CICE. We have used global simulations with realistic forcing to validate MPAS-Seaice against similar simulations with CICE and against observations. We find very similar results compared to CICE, with differences explained by minor differences in implementation such as with interpolation between the primary and dual meshes at coastlines. We have assessed the computational performance of the model, which, because it is unstructured, runs with 70 % of the throughput of CICE for a comparison quadrilateral simulation. The SCVT meshes used by MPAS-Seaice allow removal of equatorial model cells and flexibility in domain decomposition, improving model performance. MPAS-Seaice is the current sea-ice component of the Energy Exascale Earth System Model (E3SM).

58 GEOSCIENCES↗

NASA NTRS2019

Parallel High-Order Anisotropic Meshing Using Discrete Metric Tensors

This paper presents a metric-aligned meshing algorithm that relies on the Lp-Centroidal Voronoi Tesselation approach. A prototype of this algorithm was first presented at the Scitech conference of 2018 and this work is an extension to that paper. At the end of the previously presented work, a set of problems were mentioned which we are trying to address in this paper. First, we show a significant improvement in code performance since we were limited to present relatively benign (analytical) test cases. Second, we demonstrate here that we are able to rely on discrete metric data that is delivered by a Computational Fluid Dynamics (CFD) solver. Third, we demonstrate how to generate high-order curved elements that are aligned with the underlying discrete metric field.

Ekelschot, Dirk↗

DOE OSTI2024

T RI M E ++: Multi-threaded triangular meshing in two dimensions

We present T RI M E ++, a multi-threaded software library designed for generating two-dimensional meshes for intricate geometric shapes using the Delaunay triangulation. Multi-threaded parallel computing is implemented throughout the meshing procedure, making it suitable for fast generation of large-scale meshes. Three iterative meshing algorithms are implemented: the DistMesh algorithm, the centroidal Voronoi diagram meshing, and a hybrid of the two. We compare the performance of the three meshing methods in T RI M E ++, and show that the hybrid method retains the advantages of the other two. The software library achieves significant parallel speedup when generating large-scale meshes containing between 10 4 to 10 7 points. T RI M E ++ can handle complicated geometries and generates adaptive meshes of high quality.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2000

Quantifying Void Ratio in Granular Materials Using Voronoi Tessellation

Voronoi technique was used to calculate the local void ratio distribution of granular materials. It was implemented in an application-oriented image processing and analysis algorithm capable of extracting object edges, separating adjacent particles, obtaining the centroid of each particle, generating Voronoi polygons, and calculating the local void ratio. Details of the algorithm capabilities and features are presented. Verification calculations included performing manual digitization of synthetic images using Oda's method and Voronoi polygon system. The developed algorithm yielded very accurate measurements of the local void ratio distribution. Voronoi tessellation has the advantage, compared to Oda's method, of offering a well-defined polygon generation criterion that can be implemented in an algorithm to automatically calculate local void ratio of particulate materials.

Alshibli, Khalid A.↗