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Results for “polygonal mesh”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records

A method for generating moving, orthogonal, area preserving polygonal meshes

A new method for generating locally orthogonal polygonal meshes from a set of generator points is presented in which polygon areas are a constraint. The area constraint property is particularly useful for particle methods where moving polygons track a discrete portion of material. Because Voronoi polygon meshes have some very attractive mathematical and numerical properties for numerical computation, a generalization of Voronoi polygon meshes was formulated that enforces a polygon area constraint. Area constrained moving polygonal meshes allow one to develop hybrid particle-mesh numerical methods that display some of the most attractive features of each approach. It is shown that this mesh construction method can continuously reconnect a moving, unstructured polygonal mesh in a pseudo-Lagrangian fashion without change in cell area/volume, and the method's ability to simulate various physical scenarios is shown. Overall, the advantages are identified for incompressible fluid flow calculations, with demonstration cases that include material discontinuities of all three phases of matter and large density jumps.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem

The virtual element method (VEM) is a Galerkin approximation method that extends the finite element method to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element method (FEM) for the numerical approximation of the Stokes problem to polygonal meshes in the framework of the virtual element method. In particular, we consider a straightforward application of the virtual element approximation space for scalar elliptic problems to the vector case and approximate the pressure variable through discontinuous polynomials. We assess the effectiveness of the numerical approximation by investigating the convergence on a manufactured solution problem and a set of representative polygonal meshes. We numerically show that this formulation is convergent with optimal convergence rates except for the lowest-order case on triangular and square meshes where the method coincides with the P 1 - P 0 Scott-Vogelius scheme, which is well-known to be unstable.

97 MATHEMATICS AND COMPUTING↗

A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem

The Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element method for the numerical approximation of the Stokes problem to polygonal meshes in the framework of the virtual element method. In particular, we consider a straightforward application of the virtual element approximation space for scalar elliptic problems to the vector case and approximate the pressure variable through discontinuous polynomials. We assess the effectiveness of the numerical approximation by investigating the convergence on a manufactured solution problem and a set of representative polygonal meshes. Finally, we numerically show that this formulation is convergent with optimal convergence rates except for the lowest-order case on triangular meshes, where the method coincides with the $\mathbb{P}_1$ – $\mathbb{P}_0$ Scott-Vogelius scheme, and on square meshes, which are situations that are well-known to be unstable.

97 MATHEMATICS AND COMPUTING↗

Conservative high-order data transfer method on generalized polygonal meshes

A conservative data transfer (remap) between two meshes is an important step of arbitrary Lagrangian-Eulerian (ALE) hydrodynamics simulations. High-order numerical methods for ALE simulations require both high-order (curvilinear) meshes and high-order remap algorithms. Here we develop a conservative and bounds-preserving method for accurate remapping of discrete fields on generalized polygonal meshes with curvilinear edges. The properties of the proposed method are studied theoretically and numerically for various (smooth and non-smooth) mesh deformations and discrete fields that represent smooth and discontinuous functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes

We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the L 2 -norm and H 1 -norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗

Generating Inviscid and Viscous Fluid-Flow Simulations over an Aircraft Surface Using a Fluid-Flow Mesh

Fluid-flow simulation over a computer-generated aircraft surface is generated using inviscid and viscous simulations. A fluid-flow mesh of fluid cells is obtained. At least one inviscid fluid property for the fluid cells is determined using an inviscid fluid simulation that does not simulate fluid viscous effects. A set of intersecting fluid cells that intersects the aircraft surface are identified. One surface mesh polygon of the surface mesh is identified for each intersecting fluid cell. A boundary-layer prediction point for each identified surface mesh polygon is determined. At least one boundary-layer fluid property for each boundary-layer prediction point is determined using the at least one inviscid fluid property of the corresponding intersecting fluid cell and a boundary-layer simulation that simulates fluid viscous effects. At least one updated fluid property for at least one fluid cell is determined using the at least one boundary-layer fluid property and the inviscid fluid simulation.

Rodriguez, David L.↗

Intersection-distribution-based remapping between arbitrary meshes for staggered multi-material arbitrary Lagrangian-Eulerian hydrodynamics

In this paper, we present a new intersection-distribution-based remapping method between arbitrary polygonal meshes for indirect staggered multi-material arbitrary Lagrangian-Eulerian hydrodynamics. All cell-centered material quantities are conservatively remapped using intersections between the Lagrangian (old, source) mesh and the rezoned (new, target) mesh. The new nodal masses are obtained by conservative distribution of all material masses in each new cell to the cell's corners and then collecting those corner masses at new nodes. This distribution is done using a local constrained optimization approach for each cell in the new mesh. In order to remap nodal momentum we first define cell-centered momentum for each cell in the old mesh, conservatively remap this to the new mesh and then conservatively distribute the new zonal momentum to each cell's bounding nodes, again using local constrained optimization. Our method also conserves total energy by applying a new nodal kinetic energy correction that relies on a process similar to that used for remapping nodal mass and momentum. Cell-centered kinetic energy is computed, conservatively remapped and then distributed to nodes. The discrepancy between this conservatively remapped and actual nodal kinetic energy is then conservatively distributed to the internal energies of the materials in the cells surrounding each node. Unlike conventional cell-based corrections of this type, this new nodal kinetic energy correction has not been observed to drive material internal energy negative in any of our testing. Unlike flux based remapping, our new intersection-distribution method can be applied to remapping between source and target meshes that are arbitrarily different, which provides superior flexibility in the rezoning strategy. Our method is accurate, essentially conservative and essentially bounds preserving.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Facilitating Staging-based Unstructured Mesh Processing to Support Hybrid In-Situ Workflows

In-situ and in-transit processing alleviate the gap between the computing and I/O capabilities by scheduling data analytics close to the data source. Hybrid in-situ processing splits data analytics into two stages: the data processing that runs in-situ aims to extract regions of interest, which are then transferred to staging services for further in-transit analytics. To facilitate this type of hybrid in-situ processing, the data staging service needs to support complex intermediate data representations generated/consumed by the in-situ tasks. Unstructured (or irregular) mesh is one such derived data representation that is typically used and bridges simulation data and analytics. However, how staging services efficiently support unstructured mesh transfer and processing remains to be explored. This paper investigates design options for transferring and processing unstructured mesh data using staging services. Using polygonal mesh data as an example, we show that hybrid in-situ workflows with staging-based unstructured mesh processing can effectively support hybrid in-situ workflows, and can significantly decrease data movement overheads.

data-driven↗

The arbitrary-order virtual element method for linear elastodynamics models. Convergence, stability and dispersion-dissipation analysis.

We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under $\textit{h}$-refinement in both the energy and the $L^2$ norms, and optimal error estimates under $\textit{p}$-refinement in the energy norm. The performance of the proposed virtual element method is assessed on a set of different computational meshes, including non-convex cells up to order four in the h-refinement setting. Exponential convergence is also experimentally observed under p-refinement. Finally, we present a dispersion-dissipation analysis for both the semi-discrete and fully-discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion-dissipation properties.

97 MATHEMATICS AND COMPUTING↗

Memory-Aware External Facelist Calculation: A Data-Parallel Atomic Hash Counting Approach

Unstructured volumetric meshes serve as fundamental data representations in various scientific simulations and analyses. They play a crucial role in representing complex computational domains and are essential for important numerical techniques, such as finite element analysis. Whenever such a mesh is read from a file, streamed in-situ, or generated by algorithms, scientific visualization libraries rely on calculating the external surface of a geometry, named “external facelist”, to produce a polygonal mesh for rendering. Consequently, external facelist calculation has become one of the most widely used algorithms in the scientific visualization domain, necessitating optimal performance. In this paper, we explore relevant work on external facelist calculation algorithms in two common visualization libraries, VTK and Viskores, assess their performance and memory constraints, and introduce a novel memory-aware external facelist calculation algorithm employing an atomic hash counting approach. This algorithm fully leverages Viskores' data-parallel primitive operations, facilitating its execution across diverse many-core architectures. Our algorithm features the lowest memory footprint on the GPU and the second-lowest on the CPU among all evaluated methods, and it also delivers the fastest performance on both CPU and GPU. It has been made available under an open-source license in the VTK and Viskores visualization systems.

Tsalikis, Spiros [Kitware] (ORCID:0000000151137195↗

The arbitrary‐order virtual element method for linear elastodynamics models: convergence, stability and dispersion‐dissipation analysis

Abstract We design the conforming virtual element method for the numerical approximation of the two‐dimensional elastodynamics problem. We prove stability and convergence of the semidiscrete approximation and derive optimal error estimates under h ‐ and p ‐refinement in both the energy and the L 2 norms. The performance of the proposed virtual element method is assessed on a set of different computational meshes, including nonconvex cells up to order four in the h ‐refinement setting. Exponential convergence is also experimentally observed under p ‐refinement. Finally, we present a dispersion‐dissipation analysis for both the semidiscrete and fully discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion‐dissipation properties.

Antonietti, Paola F.↗

Multi-Resolution Unstructured Grid-Generation for Geophysical Applications on the Sphere

An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric and ocean simulation, and numerical weather predication. Using a recently developed Frontal-Delaunay-refinement technique, a method for the construction of high-quality unstructured ellipsoidal Delaunay triangulations is introduced. A dual polygonal grid, derived from the associated Voronoi diagram, is also optionally generated as a by-product. Compared to existing techniques, it is shown that the Frontal-Delaunay approach typically produces grids with near-optimal element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a selection of uniform and non-uniform ellipsoidal grids appropriate for large-scale geophysical applications. The use of user-defined mesh-sizing functions to generate smoothly graded, non-uniform grids is discussed.

Weather↗

eFESTA: Ensemble Feature Exploration with Surface Density Estimates

We propose surface density estimate (SDE) to model the spatial distribution of surface features-isosurfaces, ridge surfaces, and streamsurfaces-in 3D ensemble simulation data. The inputs of SDE computation are surface features represented as polygon meshes, and no field datasets are required (e.g., scalar fields or vector fields). The SDE is defined as the kernel density estimate of the infinite set of points on the input surfaces and is approximated by accumulating the surface densities of triangular patches. We also propose an algorithm to guide the selection of a proper kernel bandwidth for SDE computation. An ensemble Feature Exploration method based on Surface densiTy EstimAtes (eFESTA) is then proposed to extract and visualize the major trends of ensemble surface features. For an ensemble of surface features, each surface is first transformed into a density field based on its contribution to the SDE, and the resulting density fields are organized into a hierarchical representation based on the pairwise distances between them. The hierarchical representation is then used to guide visual exploration of the density fields as well as the underlying surface features. We demonstrate the application of our method using isosurface in ensemble scalar fields, Lagrangian coherent structures in uncertain unsteady flows, and streamsurfaces in ensemble fluid flows.

Computational modeling↗

Watertight Tensor-Product Spline Reconstruction (KCNSC PDRD Technical Report)

The standard for representing geometric models in Computer Aided Design (CAD) systems is boundary representation with trimmed surfaces. However, the approximate nature of surface-surface intersections in CAD systems leaves many small gaps between mating surfaces. These gaps lead to problems for downstream analysis and manufacturing applications, requiring time consuming repair operations and further approximation of the geometry as polygonal meshes, which do not support design iteration. In this study, nVariate, Inc. evaluated its watertight reconstruction technology on a test part. The resulting watertight model has the same absolute model accuracy of the original model zero gaps, providing a representation that requires no repair and supports further design iterations in the CAD system.

42 ENGINEERING↗

Fast, Nondestructive and Precise Biomass Measurements Are Possible Using Lidar-Based Convex Hull and Voxelization Algorithms

Light detection and ranging (lidar) scanning tools are available that can make rapid digital estimations of biomass. Voxelization and convex hull are two algorithms used to calculate the volume of the scanned plant canopy, which is correlated with biomass, often the primary trait of interest. Voxelization splits the scans into regular-sized cubes, or voxels, whereas the convex hull algorithm creates a polygon mesh around the outermost points of the point cloud and calculates the volume within that mesh. In this study, digital estimates of biomass were correlated against hand-harvested biomass for field-grown corn, broom corn, and energy sorghum. Voxelization (r = 0.92) and convex hull (r = 0.95) both correlated well with plant dry biomass. Lidar data were also collected in a large breeding trial with nearly 900 genotypes of energy sorghum. In contrast to the manual harvest studies, digital biomass estimations correlated poorly with yield collected from a forage harvester for both voxel count (r = 0.32) and convex hull volume (r = 0.39). However, further analysis showed that the coefficient of variation (CV, a measure of variability) for harvester-based estimates of biomass was greater than the CV of the voxel and convex-hull-based biomass estimates, indicating that poor correlation was due to harvester imprecision, not digital estimations. Overall, results indicate that the lidar-based digital biomass estimates presented here are comparable or more precise than current approaches.

Environmental Sciences & Ecology↗

Vortex tubes in turbulent flows: Identification, representation, reconstruction

In many cases the structure of a fluid flow is well-characterized by its vortices, especially for the purpose of visualization. In this paper we present a new algorithm for identifying vortices in complex flows. The algorithm produces a skeleton line along the center of a vortex by using a two-step predictor-corrector scheme. The vorticity vector field serves as the predictor and the pressure gradient (in the perpendicular plane) serves as the corrector. We describe an economical description of the vortex tube's cross-section: a 5-term truncated Fourier series is generally sufficient, and it compresses the representation of the flow by a factor of 4000 or more. We reconstruct the vortex tubes as generalized cylinders, providing a polygonal mesh suitable for display on a graphics workstation. We show how the reconstructed geometry of vortex tubes can be enhanced to help visualize helical motion in a static image.

Banks, David C.↗

Tools for Analysis and Visualization of Large Time-Varying CFD Data Sets

In the second year, we continued to built upon and improve our scanline-based direct volume renderer that we developed in the first year of this grant. This extremely general rendering approach can handle regular or irregular grids, including overlapping multiple grids, and polygon mesh surfaces. It runs in parallel on multi-processors. It can also be used in conjunction with a k-d tree hierarchy, where approximate models and error terms are stored in the nodes of the tree, and approximate fast renderings can be created. We have extended our software to handle time-varying data where the data changes but the grid does not. We are now working on extending it to handle more general time-varying data. We have also developed a new extension of our direct volume renderer that uses automatic decimation of the 3D grid, as opposed to an explicit hierarchy. We explored this alternative approach as being more appropriate for very large data sets, where the extra expense of a tree may be unacceptable. We also describe a new approach to direct volume rendering using hardware 3D textures and incorporates lighting effects. Volume rendering using hardware 3D textures is extremely fast, and machines capable of using this technique are becoming more moderately priced. While this technique, at present, is limited to use with regular grids, we are pursuing possible algorithms extending the approach to more general grid types. We have also begun to explore a new method for determining the accuracy of approximate models based on the light field method described at ACM SIGGRAPH '96. In our initial implementation, we automatically image the volume from 32 equi-distant positions on the surface of an enclosing tessellated sphere. We then calculate differences between these images under different conditions of volume approximation or decimation. We are studying whether this will give a quantitative measure of the effects of approximation. We have created new tools for exploring the differences between images produced by various rendering methods. Images created by our software can be stored in the SGI RGB format. Our idtools software reads in pair of images and compares them using various metrics. The differences of the images using the RGB, HSV, and HSL color models can be calculated and shown. We can also calculate the auto-correlation function and the Fourier transform of the image and image differences. We will explore how these image differences compare in order to find useful metrics for quantifying the success of various visualization approaches. In general, progress was consistent with our research plan for the second year of the grant.

Wilhelms, Jane↗

Evaluation of the Anisotropic Radiative Conductivity of a Low-Density Carbon Fiber Material from Realistic Microscale Imaging

The radiative heat transfer inside a low-density carbon fiber insulator is analyzed using a three-dimensional direct simulation model. A robust procedure is presented for the numerical calculation of the geometric configuration factor to compute the radiative energy exchange processes among the small discretized surface areas of the fibrous material. The methodology is applied to a polygonal mesh of a fibrous insulator obtained from three-dimensional microscale imaging of the real material. The anisotropic values of the radiative conductivity are calculated for that geometry. The results yield both directional and thermal dependence of the radiative conductivity.

Evaluation↗