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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↗

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↗

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↗

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↗

Learning Topological Operations on Meshes with Application to Block Decomposition of Polygons

We present a learning based framework for mesh quality improvement on unstructured triangular and quadrilateral meshes. Our model learns to improve mesh quality according to a prescribed objective function purely via self-play reinforcement learning with no prior heuristics. The actions performed on the mesh are standard local and global element operations. The goal is to minimize the deviation of the node degrees from their ideal values, which in the case of interior vertices leads to a minimization of irregular nodes.

97 MATHEMATICS AND COMPUTING↗

A cell-centered AMR-ALE framework for 3D multi-material hydrodynamics. Part I: Lagrangian and indirect Euler AMR algorithms

Many applications of physics and engineering involve wide ranges of time and spatial scales. The numerical simulation of localized small scales such as shock waves and material interfaces requires a large number of computational cells in these regions. For these applications, Lagrangian and Arbitrary-Lagrangian-Eulerian (ALE) related methods are engaging since the moving mesh feature naturally brings mesh cells on shock discontinuities and material interfaces are carefully captured. In addition, Adaptive-Mesh-Refinement (AMR) strategies aim to optimize computational resources by concentrating finer mesh cells only in areas of interest while using coarser cells elsewhere. A key but challenging AMR requirement consists in efficiently distributing the computational effort to achieve high accuracy without the prohibitive computational costs associated with uniformly fine grids. Here, in this document, the coupling of the p4est AMR library with a cell-centered Lagrangian scheme is presented with the goal to perform reliable 3D Lagrangian-AMR and indirect Euler-AMR multi-material simulations. In particular, it is shown that starting from a 3D indirect ALE code, the memory management and load balancing requirements can be delegated to an external library (here the p4est library) to unlock ALE-AMR capabilities. First, we present a strategy to transcribe the octant-based connectivity of the 3D AMR framework with that of an unstructured mesh of polygonal cells used in Lagrangian hydrodynamics. Then, we show how refinement and coarsening operations must be adapted to the particular Lagrangian framework to ensure the conservation of volume during those steps. Finally, several numerical test cases are presented that demonstrate the capabilities of the Lagrangian-AMR and indirect Euler-AMR algorithms.

3D cell-centered Lagrangian numerical scheme↗

Numerical integration in the virtual element method with the scaled boundary cubature scheme

Abstract The virtual element method (VEM) is a stabilized Galerkin method on meshes that consist of arbitrary (convex and nonconvex) polygonal and polyhedral elements. A crucial ingredient in the implementation of low‐ and high‐order VEM is the numerical integration of monomials and nonpolynomial functions over such elements. In this article, we apply the recently proposed scaled boundary cubature (SBC) scheme to compute the weak form integrals in various virtual element formulations over polygonal and polyhedral meshes. In doing so, we demonstrate the flexibility of the approach and the accuracy that it delivers on a broad suite of boundary‐value problems in 2D and 3D over polytopes with affine faces as well as on elements with curved boundaries. In addition, the use of the SBC scheme is exemplified in an enriched Poisson formulation of the VEM in which weakly singular functions are required to be integrated. This study establishes the SBC method as a simple, accurate and efficient integration scheme for use in the VEM.

Chin, Eric B.↗

From Points to Planes: A Workflow for Converting Three‐Dimensional Point Cloud Data Into Discrete Fracture Network Flow and Transport Models

We present the Point cLoud Algorithm for NEtwork Extraction of Discrete Fracture Networks (PLANE-DFN), a point cloud–based algorithm for automatic fracture network extraction designed to support discrete fracture network (DFN) modeling workflows. PLANE-DFN segments three-dimensional fracture planes from raw point cloud data using RANdom SAmple Consensus coupled with statistical outlier removal and density-based clustering to isolate individual fracture features. Each candidate plane is constrained against site-specific structural constraints based on strike and dip. After segmentation, each fracture is converted into a 2-D convex polygon suitable for meshing and simulation. The PLANE-DFN algorithm is validated by comparing geometric and flow and transport data against data from dfnWorks simulations with ensembles of plane-fit networks. We find that the flow and transport in plane-fit networks are comparable to dfnWorks-generated networks when realistic network geometry is maintained. The PLANE-DFN algorithm provides an automated and streamlined workflow to transform point clouds of data into DFN network geometry.

54 ENVIRONMENTAL SCIENCES↗

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↗

Moments-based interface reconstruction, remap and advection

Here, we present a new moment-of-fluid (MOF 2 ) interface reconstruction method. It uses the zeroth, first, and second moments of the fragment of material inside a cell of the mesh to reconstruct a convex material polygon or a union of convex polygons that approximate the respective material fragment. The new method requires information about the material moments only for the cell under consideration. The MOF 2 method allows to exactly reproduce several convex shapes: corners, filaments, and some concave shapes: cell-complements to corners and filaments. Interface reconstruction is formulated as a local (for each cell), non-linear, equality constrained optimization problem, which does not require additional communication and allows for an efficient parallel implementation. We present an extensive set of test problems, both for interface reconstruction on a single cell, and for reconstruction of a variety of shapes on a variety of meshes. We describe how to perform two-material advection using the MOF 2 method and present the results for the classical advection tests. We also show the examples of material interface remapping needed in the framework of multi-material arbitrary Lagrangian-Eulerian methods, and give a brief description of a procedure that can be used to update the material moments on the Lagrangian stage of those methods.

97 MATHEMATICS AND COMPUTING↗

Planar 2D wireframe DNA origami

Two-dimensional (2D) DNA origami is widely used for applications ranging from excitonics to single-molecule biophysics. Conventional, single-layer 2D DNA origami exhibits flexibility and curvature in solution; however, that may limit its suitability as a 2D structural template. In contrast, 2D wireframe DNA origami rendered with six-helix bundle edges offers local control over duplex orientations with enhanced in-plane rigidity. Here, we investigate the 3D structure of these assemblies using cryo–electron microscopy (cryo-EM). 3D reconstructions reveal a high degree of planarity and homogeneity in solution for polygonal objects with and without internal mesh, enabling 10-Å resolution for a triangle. Coarse-grained simulations were in agreement with cryo-EM data, offering molecular structural insight into this class of 2D DNA origami. Our results suggest that these assemblies may be valuable for 2D material applications and geometries that require high structural fidelity together with local control over duplex orientations, rather than parallel duplex assembly.

59 BASIC BIOLOGICAL SCIENCES↗

Moments-based interface reconstruction, remap and advection

We present a new moment-of-fluid (MOF 2 ) interface reconstruction method. It uses the zeroth, first, and second moments of the fragment of material inside a cell of the mesh to reconstruct a convex material polygon or a union of convex polygons that approximate the respective material fragment. The new method requires information about the material moments only for the cell under consideration. Furthermore, the MOF 2 method allows to exactly reproduce several convex shapes: corners, filaments, and some concave shapes: cell-complements to corners and filaments.

97 MATHEMATICS AND COMPUTING↗

MOOSE Framework Meshing Enhancements to Support Reactor Analysis

MOOSE-based physics codes require an input finite element mesh on which the physics solution is calculated, reported, and transferred to other physics codes. The use of difficult-touse, external licensed software is often required to generate high quality meshes for reactor geometries. High-fidelity geometry modeling also requires elaborate tracking of groups of elements for material property assignment and output reporting which can be considerably complex for the user to identify and maintain. Under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, several meshingrelated enhancements have been developed for the MOOSE framework to address user challenges in creating finite element meshes for advanced reactor geometries. MOOSE mesh generators have been developed to mesh hexagonal geometries (pins, ducted assemblies, and cores) commonly found in liquid-metal cooled fast reactor concepts. The mesh generator used for hexagonal pin cells is generic for regular polygons and therefore may also be used for Cartesian pin cells. Hexagonal pin cells can be stitched into ducted assemblies, and assemblies can be stitched together into a core. The user may specify region ids, region names, and other preferences on the mesh. This control is useful for later material mapping in the MOOSE-based physics codes input. A capability was also developed for meshing rotating control drums including determination of material volume fractions in each mesh element as a function of time. Control drum meshes may be stitched to other hexagonal assemblies to create a core configuration. Additional mesh generators were developed that wrap around the hexagonal meshing capabilities and utilize “extra element integer” ID values on each element. In regular Cartesian or hexagonal assemblies or cores, the bookkeeping of element groups for both material assignment and output reporting can now be automated through assignment of pin, assembly, core, axial and depletion id values stored as extra element integers. The extra element tags on the mesh greatly speed the reactor analyst’s efforts to map materials to meshes, track depletion zones, and parse output such as axial pin power distributions. At the highest level, pin, assembly, and core mesh generators (with this reactor terminology) have also been developed to easily generate regular Cartesian and hexagonal cores, including axial extrusion. These reactor geometry builders call upon the previously mentioned capabilities to produce analysis-ready 3D meshes including material assignments. Open source mesh triangulation capabilities were also investigated for integration into the MOOSE framework to address the need for meshing the core periphery region which extends from the irregular outer assembly border to a cylindrical boundary. Options are limited due to licensing constraints, and the recommendation is pursue building a native MOOSE Delaunay triangulator routine with full functionality. Finally, a series of verification problems were performed with NEAMS physics tools. All developed capabilities will be available in the new open-source “Reactor” module of the MOOSE framework, which is accessible to any MOOSE-based NEAMS physics tool.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Variable resolution Poisson-disk sampling for meshing discrete fracture networks

Here, we present the near-Maximal Algorithm for Poisson-disk Sampling (nMAPS) to generate point distributions for variable resolution Delaunay triangular and tetrahedral meshes in two and three-dimensions, respectively. nMAPS consists of two principal stages. In the first stage, an initial point distribution is produced using a cell-based rejection algorithm. In the second stage, holes in the sample are detected using an efficient background grid and filled in to obtain a near-maximal covering. Extensive testing shows that nMAPS generates a variable resolution mesh in linear run time with the number of accepted points. We demonstrate nMAPS capabilities by meshing three-dimensional discrete fracture networks (DFN) and the surrounding volume. The discretized boundaries of the fractures, which are represented as planar polygons, are used as the seed of 2D-nMAPS to produce a conforming Delaunay triangulation. The combined mesh of the DFN is used as the seed for 3D-nMAPS, which produces conforming Delaunay tetrahedra surrounding the network. Under a set of conditions that naturally arise in maximal Poisson-disk samples and are satisfied by nMAPS, the two-dimensional Delaunay triangulations are guaranteed to only have well-behaved triangular faces. While nMAPS does not provide triangulation quality bounds in more than two dimensions, we found that low-quality tetrahedra in 3D are infrequent, can be readily detected and removed, and a high-quality balanced mesh is produced.

97 MATHEMATICS AND COMPUTING↗

NucMesh: nuclear reactor geometry creation and mesh generation module in NEMoSys

NucMesh is a parameterized geometry and mesh generator for nuclear reactors developed within the Nuclear Energy Modeling System NEMoSys at Illinois Rocstar. NEMoSys is a platform developed for mesh generation, adaptive refinement, and solution verification. NucMesh is implemented to be generalized and extensible with a robust computer aided design engine and multiple mesh generation algorithms for unstructured triangular, quad-dominant, and structured quadrilateral meshing. In this paper, we present the geometric and meshing features of NucMesh. Geometrically objects are constructed bottom-to-top and overlaps are addressed automatically. A sophisticated object tracking algorithm prevents data from being lost for segmented objects. We discuss the primitive objects of circle and polygons that constitute the module and show how they are used with example inputs. Arrays of primitives and arrays of arrays are utilized to build large assemblies of objects. The concept of saved objects is discussed to demonstrate how repetitive objects can be reused easily and augmented in place. Three dimensional meshes can be obtained through mesh extrusion where all materials and side sets are extended to three dimensions. We show that side sets can be defined nearly anywhere within the geometry and can then be applied to the mesh. Finally, example reactor meshes are demonstrated for the Idaho National Laboratory Advanced Test Reactor and Los Alamos National Lab Empire reactor, both of which use control drums that NucMesh handles easily. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Analysis of cell-based diffusion acceleration for the slice balance approach

In this work, we perform analysis on the use of cell-based diffusion acceleration methodologies to accelerate the convergence of transport solutions discretized with the slice balance approach (SBA) on unstructured polygonal grids.We investigated both linear diffusion synthetic acceleration (DSA) and non linear diffusion acceleration (NDA), including its partial-current variant (pNDA). DSA and NDA were both shown to diverge for intermediate ranges of mesh optical thicknesses. However, pNDA and Krylov methods like GMRES and Broyden stabilized the acceleration schemes, including problems with degenerate cells formed by mesh refinement. (author)

42 ENGINEERING↗

Drying of tundra landscapes will limit subsidence-induced acceleration of permafrost thaw: Modeling Archive

This Modeling Archive is in support of a NGEE Arctic publication in review "Drying of tundra landscapes will limit subsidence-induced acceleration of permafrost thaw". The study used a cryohydrology model to assess the potential risk of abrupt permafrost thaw triggered by melting ground ice, a key open question associated with permafrost response to a warming Arctic. The spatially resolved simulations are for a small catchment 465 ice-wedge polygons in polygonal tundra near Utqiagvik, Alaska in the high-emissions RCP8.5 climate scenario. The simulations are compared to runoff, evapotranspiration and subsidence in the current climate and agree well. The study used the ATS code configured as an intermediate-scale cryohydrology model (Advanced Terrestrial Simulator, Version v2). The archive includes input files for spinup (1985 to 2005) and projections (2006 to 2100 - the manuscript reports 2006 to 2098). Three of the projections include the effects of subsidence and microtopography change with different depth profiles of ice content corresponding to the median, 20th percentile and 80th percentile. The fourth projection has subsidence turnoff and uses the reference case (median) ice content. Spatially averaged or aggregated output variables are included for the projections. Selected checkpoint files for the projections and postprocessing scripts are also included. Files included are *.xml; *.h5; *.exo; *.py; *.sh, *. nb, mesh files, and one file in the original Excel format plus *.csv and *.pdf to conserve formatting contained in the original file. The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗