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At least 307 records · Page 17

All sources NASA NTRS DOE OSTI

DOE OSTI2024

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↗

DOE OSTI2020

The distribution-based remapping of the nodal mass and momentum between arbitrary meshes for staggered arbitrary Lagrangian-Eulerian hydrodynamics

We present a new distribution-based remapping of the nodal mass and momentum between arbitrary source (Lagrangian) and arbitrary target (rezoned) meshes for indirect staggered arbitrary Lagrangian-Eulerian hydrodynamics. Here, the method is based on the following ideas: define cell-centered momentum and mass on the source mesh; conservatively remap those cell-centered quantities from source to target meshes; and use local constrained optimization for each cell of the target mesh to conservatively distribute cell mass and momentum to the nodes of the cell. This new method is efficient, conservative, accurate and bounds preserving.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Computing material volume fractions on a superimposed mesh as applied to Monte Carlo particle transport simulations

Here, we present a newly implemented ray tracing algorithm in OpenMC for efficiently computing material volume fractions on superimposed meshes in complex geometries. By firing rays along each coordinate direction through the geometry, the approach accumulates track-length data in each mesh element, thereby determining the fractional composition of each material. Scaling studies on three different models—a random tetrahedra configuration, the Frascati Neutron Generator ITER dose rate benchmark, and a stellarator design—show excellent parallel performance, with nearly linear speedup on modern multi-threaded and distributed-memory systems. An analysis of the residual error relative to high-resolution reference solutions demonstrated that under optimal conditions it decreases as 1/R, where R is the number of rays fired, making it straightforward to achieve user-prescribed accuracy. This new functionality enables practical, mesh-based approaches for detailed nuclear analyses in production Monte Carlo workflows without resorting to expensive, fully conformal or unstructured meshing.

Monte Carlo↗

DOE OSTI2018

Reducing spurious mesh motion in Lagrangian finite volume and discontinuous Galerkin hydrodynamic methods

The Lagrangian finite volume (FV) cell-centered hydrodynamic (CCH) method and the Lagrangian discontinuous Galerkin (DG) CCH method have been demonstrated to be quite stable and capable of producing very accurate solutions on many mesh topologies. However, some challenges can arise with higher-order elements and polygonal elements that have many deformational degrees of freedom. With these types of meshes, elements can deform in unphysical ways and the mesh can tangle. In this study, we present methods for obtaining more robust Lagrangian solutions on polygonal and higher-order elements. The robustness is achieved by (1) incorporating a new iterative method that modifies the velocity reconstructions in the corners of the elements, and (2) a new multidirectional approximate Riemann solver that, when coupled with the iterative method, reduces spurious mesh motion. Lastly, the details of the numerical methods are discussed and their utility is demonstrated on a diverse suite of test problems using higher-order and polygonal elements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

A high-order discontinuous Galerkin method for level set problems on polygonal meshes

We propose and analyze discontinuous Galerkin schemes for solving level set equations on polygonal meshes. For linear equations, we assume that the velocity is given only on the cell surface. Velocity inside mesh cells is approximated using virtual element projectors on polynomial spaces. For nonlinear equations, we use the Taylor expansion to approximate the normalized solution gradient. Here, we analyze the new schemes for a set of typical level set problems using square and polygonal meshes. The numerical results indicate great potential for using polygonal meshes in applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Application of mesh refinement to relativistic magnetic reconnection

During relativistic magnetic reconnection, antiparallel magnetic fields undergo a rapid change in topology, releasing a large amount of energy in the form of non-thermal particle acceleration. This work explores the application of mesh refinement to 2D reconnection simulations to efficiently model the inherent disparity in length-scales. We have systematically investigated the effects of mesh refinement and determined necessary modifications to the algorithm required to mitigate non-physical artifacts at the coarse–fine interface. We have used the ultrahigh-order pseudo-spectral analytical time-domain Maxwell solver to analyze how its use can mitigate the numerical dispersion that occurs with the finite-difference time-domain (or “Yee”) method. Absorbing layers are introduced at the coarse–fine interface to eliminate spurious effects that occur with mesh refinement. We also study how damping the electromagnetic fields and current density in the absorbing layer can help prevent the non-physical accumulation of charge and current density at the coarse–fine interface. Using a mesh refinement ratio of 8 for two-dimensional magnetic reconnection simulations, we obtained good agreement with the high-resolution baseline simulation, using only 36% of the macroparticles and 71% of the node-hours needed for the baseline. The methods presented here are especially applicable to 3D systems where higher memory savings are expected than in 2D, enabling comprehensive, computationally efficient 3D reconnection studies in the future.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Diffusion Limit–Preserving Lumped DFEMs on AMR Meshes

Here, we present sweep-compatible, novel upwinding recipes for the bilinear discontinuous (BLD) finite element method (FEM) that allows lumped BLD to be used on adaptive mesh refinement (AMR) meshes for thick transport applications without adding additional degrees of freedom at hanging nodes that exist on refinement boundaries. We analyze the properties of the upwinding and lumping that are needed for BLD to get the thick diffusion limit on such meshes, present results demonstrating locking with the wrong recipe, and present results showing error convergence and robustness properties for two diffusive problems on a variety of AMR meshes.

42 ENGINEERING↗

DOE OSTI2018

Persistent Octrees for Parallel Mesh Refinement Through Non-Volatile Byte-Addressable Memory

We report that octree-based mesh adaptation has enabled simulations of complex physical phenomena. Existing meshing algorithms were proposed with the assumption that computer memory is volatile. Consequently, for failure recovery, the in-core algorithms need to save memory states as snapshots with slow file I/Os. The out-of-core algorithms store octants on disks for persistence. However, neither of them was designed to leverage unique characteristics of non-volatile byte-addressable memory (NVBM). In this paper, we propose a novel data structure Distributed Persistent Merged octree (DPM-octree) for both meshing and in-memory storage of persistent octrees using NVBM. It is a multi-version data structure and can recover from failures using its earlier persistent version stored in NVBM. In addition, we design a feature-directed sampling approach to help dynamically transform the DPM-octree layout for reducing NVBM-induced memory write latency. DPM-octree uses parity trees which are created using erasure coding and stored in NVBM to support low-latency in-memory octant recovery after data loss. DPM-octree has been successfully integrated with Gerris software for simulation of fluid dynamics. Finally, our experimental results with real-world scientific workloads show that DPM-octree scales up to 1.1 billion mesh elements with 1000 processors on the Titan supercomputer.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

A Fully Computable A Posteriori Error Estimate for the Stokes Equations on Polytopal Meshes

Here in this paper, we present a simple a posteriori error estimate for the weak Galerkin finite element method for the Stokes equation. This residual type estimator can be applied to general meshes such as polytopal mesh or meshes with hanging nodes. The reliability and efficiency of the estimator are proved in this paper. Five numerical tests demonstrate the effectiveness and flexibility of the adaptive mesh refinement guided by the designed error estimator.

finite element methods↗

DOE OSTI2021

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↗

DOE OSTI2020

Neutronics Enhanced Meshing Operations (NEMO) Users Manual V.1.0

The is a Python framework developed at Idaho National Laboratory that uses the Cubit Python to build Cubit models and export them in EXODUS II format. These EXODUS mesh files can be used by any -based application, but NEMO is specialized for coupled neutronics calculations. Therefore, the primary purpose of NEMO is to prepare mesh files for reactor geometries and generate a homogenization overlay file for the Serpent Monte Carlo code. This homogenization overlay file ensures the consistency of the mesh with the generation of homogenized cross sections and reference fluxes for the Superhomogenization method. NEMO also supports the preparation of mesh files for thermal and thermo-mechanical models, particularly the discontinuous finite element gap heat transfer model in Griffin. This manual introduces the user to the basic capabilities in NEMO for prismatic geometries.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRSDate not supplied

Improvements to the LAURA Mesh Adaptation Algorithm

This paper describes recent improvements to the LAURA code that removes the requirementof unbroken body-normal lines when using the automated mesh adaptation algorithm inLAURA responsible for mesh alignment with shock and adjusting near-wall mesh spacing. Fornon-simple geometry, restricting block topologies such that blocks span the domain from thesurface wall boundaries to domain inflow boundary can be difficult or impossible. Removing thisrequirement enables novel block topologies that simplify the meshing workflow for LAURA users.The new adaptation algorithm implementation in LAURA is described and several examples ofthe adaptation are presented to demonstrate the efficacy of the adaptation algorithm.

LAURA↗

NASA NTRSDate not supplied

Improvements to the LAURA Mesh Adaptation Algorithm

LAURA↗

DOE OSTI2023

MATBOX, an Open-Source Microstructure Analysis Toolbox for Meshing, Generation, Segmentation, and Characterization of 3D Heterogenous Volumes

Battery performance is strongly correlated with electrode microstructural properties. To account for its impact, lithium-ion battery (LIB) models either abstract the microstructural heterogeneity of composite electrodes using effective macroscopic properties (macro- or meso- scale models) or directly solve the system of equations on the microstructure geometry or mesh (microstructure-scale models). Therefore, to be adequate, both families of models require information from the microstructure geometry, which can be provided by the numerical tool presented in this work. MATBOX is a MATLAB open-source application [1] developed by NREL for performing various microstructure-related tasks including microstructure numerical generation, image filtering and microstructure segmentation, microstructure characterization and correlation, visualization, and microstructure meshing. MATBOX was originally developed for the analysis of LIB electrode microstructures; however, the algorithms provided by the toolbox are widely applicable to other heterogeneous materials. The toolbox provides a user-friendly experience thanks to a Graphical-User Interface, requires no coding by the user, and is well documented. This presentation will illustrate various MATBOX features for the characterization of a LIB electrode, including a fully automated Representative Volume Element (RVE) analysis, the numerical generation of complex 'virtual' microstructure, including dual-layer electrodes and carbon-binder additive phase, and the meshing of a complex NMC/graphite full cell microstructure suitable for 3D finite-element modeling. Other modules (segmentation, visualization, and correlation) will be briefly presented. Thanks to its modular, open-source approach, MATBOX can easily incorporate third-party algorithms to eventually build a standard in the field that will benefit the whole scientific community. Effective diffusion coefficient [2], additive phase numerical generation [3], and meshing [4] third-party algorithms have been already integrated in the toolbox with more to come.

DIRECT ENERGY CONVERSION,MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Adaptive mesh refinement in stress-constrained topology optimization

We present a topology structural optimization framework with adaptive mesh refinement and stress-constraints. Finite element approximation and geometry representation benefit from such refinement by enabling more accurate stress field predictions and greater resolution of the optimal structural boundaries. We combine a volume fraction filter to impose a minimum design feature size, the RAMP penalization to generate “black-and-white designs” and a RAMP-like stress definition to resolve the “stress singularity problem.” Regions with stress concentrations dominate the optimized design. As such, rigorous simulations are required to accurately approximate the stress field. To achieve this goal, we invoke a threshold operation and mesh refinement during the optimization. We do so in an optimal fashion, by applying adaptive mesh refinement techniques that use error indicators to refine and coarsen the mesh as needed. In this way, we obtain more accurate simulations and greater resolution of the design domain. We present results in two dimensions to demonstrate the efficiency of our method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Thermomechanics coupling to Monte Carlo particle transport on unstructured mesh geometries using Cardinal

Geometry deformation due to thermal expansion influences neutron transport in many systems. Studying this phenomenon involves coupling models for neutronics, thermal hydraulics, and solid mechanics. To enable high fidelity modeling of these coupled physics, new capabilities were introduced in Cardinal, coupling OpenMC Monte Carlo particle transport models with MOOSE thermomechanical physics on unstructured moving-mesh geometries. In this work, we present a fully open-source capability leveraging on-the-fly mesh skinning to automatically regenerate OpenMC geometry, which allows multiphysics feedback from temperature, density, and geometry changes. The new capability is verified using an analytic benchmark slab problem, which couples S 2 neutron transport with thermal conduction, convective boundary conditions, Doppler-broadened cross sections, and nonlinear thermal expansion effects along the heated slab. Cardinal reproduces the analytic solutions for the neutron flux, heating, k eff , and temperature with demonstrated convergence in various error terms including mesh resolution and cross section temperature library spacing. For the nominal benchmark conditions and with a fine mesh, maximum relative errors for neutron flux, temperature, and heating are lower than 1%, while errors in integral quantities such as k eff and slab length are within 1 pcm and 48 µm, respectively. This work (i) presents a new numerical approach to thermomechanics coupling with OpenMC models, (ii) is the first (to our knowledge) to utilize a mechanical partial differential equation (PDE) solution to solve the (Griesheimer and Kooreman, 2022) analytic benchmark, and (iii) develops this verified capability within an open-source package.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Flow and transport in three-dimensional discrete fracture matrix models using mimetic finite difference on a conforming multi-dimensional mesh

Here, we present a comprehensive workflow to simulate single-phase flow and transport in fractured porous media using the discrete fracture matrix approach. The workflow has three primary parts: (1) a method for conforming mesh generation of and around a three-dimensional fracture network, (2) the discretization of the governing equations using a second-order mimetic finite difference method, and (3) implementation of numerical methods for high-performance computing environments. A method to create a conforming Delaunay tetrahedralization of the volume surrounding the fracture network, where the triangular cells of the fracture mesh are faces in the volume mesh, that addresses pathological cases which commonly arise and degrade mesh quality is also provided. Our open-source subsurface simulator uses a hierarchy of process kernels (one kernel per physical process) that allows for both strong and weak coupling of the fracture and matrix domains. We provide verification tests based on analytic solutions for flow and transport, as well as numerical convergence. We also provide multiple expositions of the method in complex fracture networks. In the first example, we demonstrate that the method is robust by considering two scenarios where the fracture network acts as a barrier to flow, as the primary pathway, or offers the same resistance as the surrounding matrix. In the second test, flow and transport through a three-dimensional stochastically generated network containing 257 fractures is presented.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Annular Flow Simulation Supported by Iterative In-Memory Mesh Adaptation

Various flow regimes exist in a boiling water reactor (BWR) as the steam quality increases in the uprising coolant flow, from bubbly flow, slug/churn flow, to annular flow. The annular flow is characterized by the presence of a fast-moving gas core and the surrounding liquid film flowing on the conduit wall. Additionally, entrained droplets can be observed in the gas core with ingested bubbles in the liquid film. The dynamics occurring on the wavy interface between the liquid film and gas core plays a crucial role in affecting the heat transfer rate and pressure drop within the BWR core. However, a fundamental understanding of annular flow is still lacking, partly due to the difficulty in obtaining detailed local data in annular flow experiments. In the current study, a novel simulation framework is developed for the annular flow by coupling a computational fluid dynamics flow solver with state-of-the-art meshing software. The gas-liquid interface is tracked with the level set method. Based on the computed flow solutions, the computational mesh is dynamically adapted in memory to meet the local mesh resolution requirement. This iterative simulation-adaptation framework can ensure the fine mesh resolution across the interface, which not only helps mitigate the mass conservation degradation known to level set methods but also improves the representation of dramatic interface topological changes such as wave breaking and droplet entrainment. The present investigation will shed light onto the complex interfacial processes involved in annular flow and generate much needed simulation data for annular flow modeling.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗