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Spectral Element Applications in Complex Nuclear Reactor Geometries: Tet-to-Hex Meshing
The spectral element code Nek5000 is an open-source, higher-order computational fluid dynamics code developed at Argonne National Laboratory. It is designed to solve incompressible Navier-Stokes equations, but it also has a low-Mach-number approximation feature available. Large eddy simulation is approached by explicit filtering of the velocity field (and other fields) to mimic the effect of dissipation due to the unresolved scale. The computational domain is decomposed into second-order hexahedral elements that conform to the boundaries. However, generating a high-quality pure-hexahedral mesh can be challenging for some problems. For simple geometries, traditional blocking methods can be used to decompose the domain into smaller blocks to generate a so-called structural mesh. A structural mesh can maintain good orthogonality but can have a highly skewed mesh to conform to the geometry, as well as unnecessary refinement in the far field. Moreover, for geometries with relative complexity, blocking the geometry becomes impossible. To address these issues, we adopted a let-to-hex strategy to generate a pure hexahedral mesh for Nek5000. First, we generate a pure tetrahedral mesh for the geometry; then we divide one tetrahedral element into four hexahedral elements. A pure tetrahedral mesh could be easily generated for complex geometries by using many current meshing codes. In this paper, we use the commercial codes ANSYS meshing and ANSYSICEM to generate the pure tetrahedral mesh and then convert it to a pure hexahedral mesh. Boundary layers are extruded in ANSYSICEM to maintain near-wall resolution.
Automatic Mesh Generation of Hybrid Mesh on Valves in Multiple Positions in Feedline Systems
Fluid flow simulations through a valve often require evaluation of the valve in multiple opening positions. A mesh has to be generated for the valve for each position and compounding. The problem is the fact that the valve is typically part of a larger feedline system. In this paper, we propose to develop a system to create meshes for feedline systems with parametrically controlled valve openings. Herein we outline two approaches to generate the meshes for a valve in a feedline system at multiple positions. There are two issues that must be addressed. The first is the creation of the mesh on the valve for multiple positions. The second is the generation of the mesh for the total feedline system including the valve. For generation of the mesh on the valve, we will describe the use of topology matching and mesh generation parameter transfer. For generation of the total feedline system, we will describe two solutions that we have implemented. In both cases the valve is treated as a component in the feedline system. In the first method the geometry of the valve in the feedline system is replaced with a valve at a different opening position. Geometry is created to connect the valve to the feedline system. Then topology for the valve is created and the portion of the topology for the valve is topology matched to the standard valve in a different position. The mesh generation parameters are transferred and then the volume mesh for the whole feedline system is generated. The second method enables the user to generate the volume mesh on the valve in multiple open positions external to the feedline system, to insert it into the volume mesh of the feedline system, and to reduce the amount of computer time required for mesh generation because only two small volume meshes connecting the valve to the feedline mesh need to be updated.
Transparent, High‐Charge Capacity Metal Mesh Electrode for Reversible Metal Electrodeposition Dynamic Windows with Dark‐State Transmission <0.1%
Abstract Dynamic windows allow user control over light and heat flow to save energy and maximize comfort. Reversible metal electrodeposition (RME) dynamic windows can uniquely tint to a color‐neutral privacy state (0.1% visible light transmission). The design parameters of transparent metal mesh counter electrodes for high‐contrast RME dynamic windows: high transparency, charge capacity and surface area with low haze, sheet resistance and cost are discussed, concluding that woven metal meshes meet these design parameters. Electroplated current is measured on an indium tin oxide electrode and two meshes with different wire spacings, showing the meshes’ cylindrical geometry enable them to draw more current per square area. The mesh material composition is analyzed to ensure cycling durability in a CuBi electrolyte by developing a transparent mesh with an inert core (stainless steel, SS), a thin Au coating, and a high charge‐capacity (1.5 C cm −2 ) CuBi outer coating. The study demonstrates that the films maintain a consistent Cu:Bi ratio and optical properties after 250 privacy cycles or 1500 cycles to 10% transmission, showing that the Cu and Bi coating is effective in keeping the films from becoming Cu rich with cycling. Finally, a 100 cm 2 device with excellent uniformity and color neutrality is demonstrated.
PUMIPic: A mesh-based approach to unstructured mesh Particle-In-Cell on GPUs
Unstructured mesh particle-in-cell, PIC, simulations executing on the current and next generation of massively parallel systems require new methods for both the mesh and particles to achieve performance and scalability on GPUs. The traditional approach to implementing PIC simulations defines data structures and algorithms in terms of particles with a full copy of the unstructured mesh on every process. To effectively scale the unstructured mesh and particles, mesh-based PIC uses the unstructured mesh as the predominant data structure with the particles stored in terms of the mesh entities. Here, this paper details the PUMIPic library, a framework for developing efficient and performance-portable mesh-based PIC simulations on GPU systems. A pseudo physics simulation based on a five-dimensional gyro-kinetic code for modeling plasma physics is used to examine the performance of PUMIPic. Scaling studies of the unstructured mesh partition and number of particles are performed up to 4096 nodes of the Summit system at Oak Ridge National Laboratory. The studies show that mesh-based PIC can utilize a partitioned mesh and maintain scaling up to system limitations.
A Qualitative Study on the Effects of Mesh Guideline Modification for Unstructured Mesh Generation of the NASA High Lift Common Research Model (HL-CRM)
As part of the 1st Geometry and Mesh Generation Workshop, unstructured tetrahedral and unstructured hybrid Computational Fluid Dynamics meshes were generated according to the meshing guidelines supplied by the 3rd High Lift Prediction Workshop. During this process, it was noted that application of some meshing guidelines became a bottleneck in the process and negatively impacted the quality of the meshes. A study is performed to compare the FUN3D simulation from the baseline medium-resolution workshop unstructured mesh with those on meshes resulting from guideline variations to the baseline. Recommendations on the elimination or reduction of meshing guidelines for high lift aerodynamic cases like the High Lift Common Research Model are based on the resulting data.
Investigating mesh sensitivity and polycrystalline RVEs in crystal plasticity finite element simulations.
Abstract not provided.
$χ$-$MeRA$: Computationally efficient adaptive mesh refinement of Monte Carlo mesh based tallies
Here, the reactor physics community is always focused on reducing the computational time and memory required for simulations. $χ$-$MeRA$, which stands for flux-based-($χ$)-Mesh tally Refinement Adaptively, was built to reduce the computational time and memory required to solve the neutronics side of a multiphysics problem when compared to traditional methods for mesh based tallies in Monte Carlo (MC) simulations. $χ$-$MeRA$ couples a MC code with an adaptive mesh refinement (AMR) algorithm to take advantage of the accuracy of a MC code and the efficiency of an AMR algorithm. Also developed within $χ$-$MeRA$ was a set of metrics to assess the effects of the refinement on various parameters in the simulation space. For a plutonium sphere, $χ$-$MeRA$ shows a reduction in memory usage and computation time when compared to a fully refined mesh by a factor of 14.7 and 6.7, respectively. When compared to an unstructured mesh, improvement of 1.3 and 4.8 was achieved for memory usage and computation time. The development of $χ$-$MeRA$ helps solve the neutronics side of a multiphysics problem in a faster, more computationally efficient manner than traditional methods, and the final mesh created contains accurate results that can be passed onto the next physics code.
Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes
This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on an embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.
High-Order Mesh r-Adaptivity with Tangential Relaxation and Guaranteed Mesh Validity
High-order meshes are crucial for achieving optimal convergence rates in curvilinear domains, preserving symmetry, and aligning with key flow features in moving mesh simulations [1], but their quality is challenging to control. In prior work, we have developed techniques based on Target-Matrix Optimization Paradigm (TMOP) to adapt a given high-order mesh to the geometry and solution of the partial differential equation (PDE) [2, 3]. Here, we extend this framework to address two key gaps in the literature for highorder mesh 𝑟-adaptivity. First, we introduce tangential relaxation on curved surfaces using solely the discrete mesh representation, eliminating the need for access to underlying geometry (e.g., CAD model). Second, we ensure a continuously positive Jacobian determinant throughout the domain. This determinant positivity is essential for using the high-order mesh resulting from 𝑟-adaptivity with arbitrary quadrature schemes in simulations. The proposed approach is demonstrated to be robust using a variety of numerical experiments.
Model Data for the Mesh Convergence Study Demonstrating Benefits of Mixed-polyhedral Mesh in Integrated Hydrology Simulations
This archived model data is related to a study introducing a unique method that employs a stream-aligned mixed-polyhedral mesh to effectively and accurately represent river valleys, stream corridors, and narrow engineered channels in integrated hydrology simulations. The study finds that utilizing stream-aligned mixed-polyhedral meshes in integrated hydrology simulations achieves accuracy on par with a finely refined TIN-based mesh while markedly diminishing computational costs. This archive contains scripts and data files needed to generate the ATS model input, including mesh and ATS input files, for all mesh scenarios using the Watershed Workflow package. Additionally, this archive also provides key outputs from the model simulations that are used in the analysis and post-processing scripts to reproduce figures in the manuscript. The Watershed Workflow package is implemented in Python3. The Jupyter notebooks can be executed through multiple open-source tools, for example, Anaconda Jupyter Lab, VS Studio Code, etc. Other data files include CSV and HDF5 files, which can be read through Python scripts. The input files for the ATS model, open-source integrated hydrology, and transport model are in XML format and can be edited in any commonly used text editors.
A Framework for Mesh-Geometry Associativity during Mesh Adaptation
A framework has been developed for describing how a computational mesh is associated to the geometry model it discretizes. The target application of this framework is surface mesh adaptation in a CFD flow solver. The framework, called MeshLink, consists of two components. First, a schema has been defined for describing the one-to-many associativity of a surface mesh to the geometry model entities to which it is attached. Second, a high-level library provides a kernel-agnostic wrapper for providing the necessary geometry queries to an application (e.g., mesher, flow solver). Both the schema and library are provided freely and openly. MeshLink’s ability to support solution mesh adaptation on linear and curved meshes for a high-order flow solution is demonstrated on several test cases relevant to the aerospace and automotive industries.
Output-based mesh optimization for hybridized and embedded discontinuous Galerkin methods
Not provided.
Fast Mesh-to-Mesh Remaps Using Hash Algorithms
Here, we explore the potential uses of hash-based algorithms in the remap operation, mapping one computational mesh onto another. We implement and test optimizations designed to reduce memory operations and compare these optimizations in order to evaluate the performance impact across different meshes. In particular, we created a new remap method that creates a structured hierarchy of hashes. Tests were run on 2D meshes on up to 14 levels of mesh refinement and hundreds of millions of cells to measure the algorithms' relative speeds under differing circumstances. We show that our methods perform two orders of magnitude better than the standard kD-tree algorithm and that on different meshes different hash methods can be optimal. We explore these algorithms on serial CPUs, GPUs using OpenCL, and multi-core CPUs using OpenMP.
Adaptive Meshing Techniques for Viscous Flow Calculations on Mixed Element Unstructured Meshes
An adaptive refinement strategy based on hierarchical element subdivision is formulated and implemented for meshes containing arbitrary mixtures of tetrahendra, hexahendra, prisms and pyramids. Special attention is given to keeping memory overheads as low as possible. This procedure is coupled with an algebraic multigrid flow solver which operates on mixed-element meshes. Inviscid flows as well as viscous flows are computed an adaptively refined tetrahedral, hexahedral, and hybrid meshes. The efficiency of the method is demonstrated by generating an adapted hexahedral mesh containing 3 million vertices on a relatively inexpensive workstation.
Improving Unstructured Mesh Partitions for Multiple Criteria Using Mesh Adjacencies
The scalability of unstructured mesh based applications depends on partitioning methods that quickly balance the computational work while reducing communication costs. Zhou et al. [SIAM J. Sci. Comput., 32 (2010), pp. 3201{3227; J. Supercomput., 59 (2012), pp. 1218{1228] demonstrated the combination of (hyper)graph methods with vertex and element partition improvement for PHASTA CFD scaling to hundreds of thousands of processes. Our work generalizes partition improvement to support balancing combinations of all the mesh entity dimensions (vertices, edges, faces, regions) in partitions with imbalances exceeding 70%. Improvement results are then presented for multiple entity dimensions on up to one million processes on meshes with over 12 billion tetrahedral elements.
Conservative finite‐volume schemes for the quasi‐geostrophic equation on coastal‐conforming unstructured primal–dual meshes
In this article we propose finite‐volume schemes for solving the inviscid and viscous quasi‐geostrophic equations on coastal‐conforming unstructured primal–dual meshes. Several approaches for enforcing the boundary conditions are also explored along with these schemes. The pure transport parts in these schemes are shown to conserve the potential vorticity along fluid paths in an averaged sense, and conserve the potential enstrophy up to the time truncation errors. Numerical tests based on the centroidal Voronoi–Delaunay meshes are performed to confirm these properties, and to distinguish the dynamical behaviours of these schemes. Finally some potential applications of these schemes in different situations are discussed.
SERPENT validation and optimization with mesh adaptive search on stereolithography geometry models
Not Available