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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
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Local element operations for curved simplex meshes

Summary Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post‐processing step in mesh generation procedures and in applications such as fluid simulations with severely deforming domains. In order to perform high‐order mesh optimization, these ingredients must also be extended to high‐order (curved) meshes. In this work, we present a method to perform local element operations on curved meshes. The mesh operations discussed in this work are edge/face swaps, edge collapses, and edge splitting (more generally refinement) for triangular and tetrahedral meshes. These local operations are performed by first identifying the patch of elements which contain the edge/face being acted on, performing the operation as a “straight‐sided one" by placing the high‐order nodes via an isoparametric mapping from the master element, and smoothing the high‐order nodes on the elements in the patch by minimizing a Jacobian‐based high‐order mesh distortion measure. Since the initial “straight‐sided guess” from the placement of the nodes via the isoparametric mapping frequently results in invalid elements, the distortion measure must be regularized which allows for mesh untangling for the optimization to succeed. We present several examples in 2D and 3D to demonstrate these local operations and how they can be combined with a high‐order node smoothing procedure to maintain mesh quality when faced with severe deformations.

Shi, A.↗
DOE OSTI2023

A family of independent Variable Eddington Factor methods with efficient preconditioned iterative solvers

We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A method for bounding high-order finite element functions: Applications to mesh validity and bounds-preserving limiters

We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be used to locally bound any combination of these basis functions. This approach can be applied to any element/basis type at any approximation order, can provide local (i.e., subcell) extremum bounds to a desired level of accuracy, and can be evaluated efficiently on-the-fly in simulations. Furthermore, we show that this approach generally yields more accurate bounds in comparison to traditional methods based on convex hull properties (e.g., Bernstein polynomials). Furthermore, the efficacy of this technique is shown in applications such as mesh validity checks and optimization for high-order curved meshes, where positivity of the element Jacobian determinant can be ensured throughout the entire element, and continuously bounds-preserving limiters for hyperbolic systems, which can enforce maximum principle bounds across the entire solution polynomial.

Bounding box↗
DOE OSTI2022

HLPW-4/GMGW-3: High Order Discretization Technology Focus Group Workshop Summary

This paper summarizes the High-Order Technical Focus Group (HO-TFG) submissions for the joint 4th AIAA High Lift Prediction and 3rd Geometry and Mesh Generation Workshop. The goal of the workshop was to assess the state-of-the-art in mesh generation and computational fluid dynamics software. The Common Research Model High-Lift (CRM-HL) variant served as the primary focus of the workshop, and a 2D airfoil section from the CRM-HL was used as a verification test case. The HO-TFG was tasked with generating high-order curved meshes for both geometries, and computing high-order solutions using both Reynolds Averaged Navier-Stokes and scale resolving formulations. While limited by computational resources, the final results demonstrate the potential of higher-order methods to increase solution accuracy with a lower degree of freedom count relative to second-order discretizations.

Galbraith, Marshall C.↗
DOE OSTI2023

HLPW-4/GMGW-3: High-Order Discretization Technology Focus Group Workshop Summary

This paper summarizes the High-Order Technical Focus Group (HO-TFG) submissions for the joint 4th AIAA High Lift Prediction (HLPW-4) and 3rd Geometry and Mesh Generation Workshop (GMGW-3). The goal of the workshop was to assess the state-of-the-art in mesh generation and computational fluid dynamics software. The Common Research Model High-Lift (CRM-HL) variant served as the primary focus of the workshop, and a two-dimensional airfoil section from the CRM-HL was used as a verification test case. Here, the HO-TFG was tasked with generating high-order curved meshes for both geometries, and computing high-order solutions using both Reynolds-averaged Navier–Stokes and scale-resolving formulations. While limited by computational resources, the final results demonstrate the potential of higher-order methods to increase solution accuracy with a lower degree-of-freedom count relative to second-order discretizations.

42 ENGINEERING↗
DOE OSTI2022

Mascon distribution techniques for asteroids and comets

The mass-concentration model is an approach that has been used to model the gravitational fields of irregularly shaped bodies such as asteroids and comets. By this approach, the body is treated as a collection of point masses. The method is conceptually simple, easy to program, valid down to the surface, and capable of modeling arbitrary density heterogeneities. How the mass concentrations are distributed as well as how mass is assigned to these concentrations is, however, nontrivial. These aspects significantly affect the accuracy and efficiency of the gravitational model. In this paper, we frame the distribution process in terms of numerical integration applied to finite volume meshes. We describe a new method using unstructured, curvilinear, finite volume meshes to significantly improve the accuracy of the mass-concentration model. We then compare the accuracy and efficiency of several variations of our distribution technique to those from literature using Asteroid Eros and Bennu as example bodies. Our results show that the mascon model can be as accurate as the analytic polyhedral model at the surface using an equivalent number of computational elements—i.e., mascon to surface facets. We report the improvement in the model’s performance can be mainly attributed to the volume mesh topology while mesh curving can provide modest case-dependent improvements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Local Decomposition of Hexahedral Singular Nodes into Singular Curves

Hexahedral (hex) meshing is a long studied topic in geometry processing with many challenging associated problems. Hex meshes vary from structured to unstructured depending on application or domain of interest. Fully structured meshes require that all interior mesh edges be adjacent to four hexes each. Edges failing this criteria are singular and indicate an unstructured hex mesh. Singular edges join together into singular curves that either form closed cycles, end on the mesh boundary, or end at a singular node, a complex junction of more than two singular curves. Hex meshes with more complex singular nodes tend to have more distorted elements and smaller scaled Jacobian values. In this work, we study the topology of singular nodes. We show that all eight of the most common singular nodes are decomposable into just singular curves. We further show that all singular nodes, regardless of edge valence, are locally decomposable. Finally we demonstrate these decompositions on hex meshes, thereby decreasing their distortion and converting all singular nodes into singular curves. In conclusion, with this decomposition, the enigmatic complexity of 3D singular nodes becomes effectively 2D.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Accelerating high-order mesh optimization using finite element partial assembly on GPUs

In this paper we present a new GPU-oriented mesh optimization method based on high order finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global nonlinear solve over the whole computational mesh, i.e., all mesh nodes are moved together. A key property of the method is that the mesh optimization process is recast in terms of finite element operations, which allows us to utilize recent advances in the field of GPU-accelerated high order finite element algorithms. For example, we reduce data motion by using tensor factorization and matrix-free methods, which have superior performance characteristics compared to traditional full finite element matrix assembly and offer advantages for GPU based HPC hardware. Furthermore, we describe the major mathematical components of the method along with their efficient GPU-oriented implementation. In addition, we propose an easily reproducible mesh optimization test that can serve as a performance benchmark for the mesh optimization community.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A high-order Shifted Interface Method for Lagrangian shock hydrodynamics

Here, we present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on an exact (or sharp) material interface representation, that is, it uses the precise location of the material interface. The interface is represented by the zero level-set of a continuous high-order finite element function that moves with the material velocity. This strategy allows to evolve curved material interfaces inside curved elements. By reformulating the original interface problem over a surrogate (approximate) interface, located in proximity of the true interface, the SIM avoids cut cells and the associated problematic issues regarding implementation, numerical stability, and matrix conditioning. Accuracy is maintained by modifying the original interface conditions using Taylor expansions. We demonstrate the performance of the proposed algorithms on established numerical benchmarks in one, two and three dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Incremental Interval Assignment by Integer Linear Algebra with Improvements

Interval Assignment (IA) is the problem of selecting the number of mesh edges (intervals) for each curve for conforming quad and hex meshing. The intervals x is fundamentally integer-valued. Many other approaches perform numerical optimization then convert a floating-point solution into an integer solution, which is slow and error prone. We avoid such steps: we start integer, and stay integer. Incremental Interval Assignment (IIA) uses integer linear algebra (Hermite normal form) to find an initial solution to the meshing constraints, satisfying the integer matrix equation Solving for reduced row echelon form provides integer vectors spanning the nullspace of A. Here we add vectors from the nullspace to improve the initial solution, maintaining Ax = b Heuristics find good integer linear combinations of nullspace vectors that provide strict improvement towards variable bounds or goals. IIA always produces an integer solution if one exists. In practice we usually achieve solutions close to the user goals, but there is no guarantee that the solution is optimal, nor even satisfies variable bounds, e.g. has positive intervals. We describe several algorithmic changes since first publication that tend to improve the final solution. The software is freely available.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Curvature Induced Modifications of Chirality and Magnetic Configuration in Perpendicular Films

Designing curvature in three-dimensional (3D) magnetic nanostructures enables controlled manipulation of local energy landscapes, allowing for the modification of noncollinear spin textures relevant for next-generation spintronic devices. In this study, we experimentally investigate 3D magnetization textures in a Co/Pd multilayer film, exhibiting strong perpendicular magnetic anisotropy (PMA), deposited onto curved Cu nanowire meshes with diameters as small as 50 nm and lengths of several microns. Utilizing magnetic soft X-ray nanotomography, we achieve reconstructions of 3D magnetic domain patterns at approximately 30 nm spatial resolution. This approach provides detailed information on both the orientation and magnitude of magnetization within the film. Our results reveal that interfacial anisotropy in the Co/Pd multilayers drives the magnetization toward the local surface normal. In contrast to typical labyrinth domains observed in planar films, the presence of curved nanowires significantly alters the domain structure, with domains preferentially aligning along the nanowire axis in close proximity, while adopting random orientations farther away. We report direct experimental observation of a curvature-induced Dzyaloshinskii-Moriya interaction (DMI), which is quantified to be approximately one-third of the intrinsic DMI in Co/Pd stacks. The curvature induced DMI enhances stability of Néel-type domain walls. These experimental observations are further supported by micromagnetic simulations. Altogether, our findings demonstrate that introducing curvature into magnetic nanostructures provides a powerful strategy for tailoring complex magnetic behaviors, paving the way for the design of advanced 3D racetrack memory and neuromorphic computing devices.

Raftrey, David↗
DOE OSTI2023

Remapping of Data Between One-Dimensional Meshes

In this report we present two approaches to data remapping between one-dimensional meshes implemented with the c++ programming language. Our goal was to test the performance of two search algorithms, linear and binary, and verify the accuracy of our implementations of the two methods. We first introduce the concept of data remap and meshing components, as well as their various uses. We then delve into the differences between point-wise and conservative remap, the algorithms used in the implementations, and lastly confirm the implementations work as intended when given various inputs. We expect that, after profiling, the binary search algorithm will be more efficient than the linear algorithm for sorted sets of data, the point-wise remap implementation to accurately approximate the data transfer between two meshes, and the conservative remap implementation to conserve the area underneath the curve of two distinct meshes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Interface Problem Formulation Improvements with Application to Nuclear Fuel Performance Analysis

The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation Program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. This report documents new developments and robustness improvements in mechanical and thermal (gap heat transfer) contact formulations. The improvements range from the migration of industrial level (“assessment”) nuclear fuel model setups to the usage of mortar formulations, the addition of frictional contact to one-dimensional layered representations of fuel and cladding components, and the addition of the Petrov-Galerkin approach to dual mortar, which improves performance on curved, relatively coarse meshes. In addition, the Lagrange-multiplier enforcement of mechanical mortar contact constraints has been extended to two additional types of enforcement: penalty and augmented Lagrange-Uzawa. We show that the latter approach yields the same interface results as dual mortar in the Multiphysics Object-Oriented Simulation Environment, with the advantage of not worsening the condition number of the system matrix—thereby enabling the use of some general implementations of iterative preconditioners, at the expense of additional system evaluations (i.e., augmentations).

42 ENGINEERING↗
DOE OSTI2024

Preserving Superconvergence of Spectral Elements for Curved Domains [Slides]

Finite Element Methods (FEM) and Spectral Element Methods (SEM) are crucial for solving partial differential equations (PDEs) on complex geometries. SEM offers superior accuracy due to potential superconvergence for simple domains. Challenges persist for domains with curved boundaries, restricting SEM’s advantages in real-world applications. A proposed solution is the introduction of a novel strategy to enhance accuracy and maintain superconvergence of SEM in curved domains. The strategy includes a mesh-generation procedure with geometrically refined elements near curved boundaries and a post-processing phase using the Adaptive Extended Stencil Finite Element Method (AES-FEM). The method, named AES-FEM post-processed Spectral Element Method (ApSEM), aligns the accuracy of non-tensor-product elements with superconvergent spectral elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

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.

Mathematics and Computing↗
DOE OSTI2024

mgsflib

Code for my PhD thesis that creates meshes using gmsh and code I wrote to create high-order hybrid meshes to use for testing a hybrid method between spectral element method and generalized finite differences. It also uses a tetrahedral mesh improvement method called "stellar" to improve mesh quality near a curved boundary.

Jones, Jacob↗
DOE OSTI2026

Non-conformal interface-cohesive modeling with the shifted boundary method

The accurate simulation of boundary- and interface-dominated problems on complex geometries remains challenging when boundary- or interface-fitted meshes are difficult to generate, particularly for curved boundaries, polycrystalline microstructures, and dense interface networks. The Shifted Boundary Method (SBM) alleviates this meshing burden by shifting the enforcement of boundary conditions from the true boundary to a nearby surrogate boundary and recovering the effect of the true boundary through geometric correction terms, thereby enabling standard finite element spaces on non-boundary-fitted meshes. In this report, we develop a general shiftedboundary and shifted-interface framework within the open-source MOOSE framework. We first present a general SBM implementation for complex geometries on non-boundary-fitted meshes. We then adopt the Shifted Interface Method (SIM) for internal interfaces and develop a unified shifted-interface treatment in which the interface law is enforced on a surrogate interface and the effect of the true interface is recovered through shifted jumps, fluxes, and tractions. This perspective brings scalar thermal-contact and vector-valued cohesive-zone mechanics into a single framework, the latter realized as the Shifted Cohesive Zone Method (SCZM) and coupled with history-dependent constitutive models from NEML2. We further extend the MOOSE mesh infrastructure to support cohesive-zone calculations on distributed meshes. The framework is verified and demonstrated through three progressive studies: Poisson’s equation on a smoothed starshaped domain, a manufactured thermal-contact problem on a non-interface-fitted mesh, and a two-dimensional polycrystalline representative volume element combining crystal plasticity with cohesive grain-boundary interfaces. Across these studies, the shifted formulations reproduce boundary- and interface-fitted reference solutions with high fidelity, indicating that the proposed framework provides an accurate and efficient route to boundary- and interface-dominated simulations on arbitrary geometries without requiring fitted meshes.

Yang, Cheng-Hau↗
DOE OSTI2023

CrossLink: Meshing a 3D part from a STEP file [Slides]

This example shows how to use CrossLink to create a mesh for a 3D geometry part read in from a STEP file. A STEP file (Standard for the Exchange of Product data) is a common file format used for 3D modelling that can be written out from a CAD program (e.g., Creo Parametric). Being able to read and mesh STEP file geometries is essential for meshing parts from engineering models. Creating the mesh typically involves: (1) Importing the geometry; (2) Creating geometry groups; (3) Assigning curves and surfaces to the geometry groups; (4) Building a topology; (5) Applying geometric and mesh constraints; and (6) Generating the final mesh. Current issues with this process in CrossLink include: (1) The GUI does not display trimmed surfaces; (2) The user must manually create and assign geometry groups; and (3) The user must be aware of duplicate curves and surfaces from the CAD model.

97 MATHEMATICS AND COMPUTING↗