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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS2007

Mesh Deformation Based on Fully Stressed Design: The Method and Two-Dimensional Examples

Mesh deformation in response to redefined boundary geometry is a frequently encountered task in shape optimization and analysis of fluid-structure interaction. We propose a simple and concise method for deforming meshes defined with three-node triangular or four-node tetrahedral elements. The mesh deformation method is suitable for large boundary movement. The approach requires two consecutive linear elastic finite-element analyses of an isotropic continuum using a prescribed displacement at the mesh boundaries. The first analysis is performed with homogeneous elastic property and the second with inhomogeneous elastic property. The fully stressed design is employed with a vanishing Poisson s ratio and a proposed form of equivalent strain (modified Tresca equivalent strain) to calculate, from the strain result of the first analysis, the element-specific Young s modulus for the second analysis. The theoretical aspect of the proposed method, its convenient numerical implementation using a typical linear elastic finite-element code in conjunction with very minor extra coding for data processing, and results for examples of large deformation of two-dimensional meshes are presented in this paper. KEY WORDS: Mesh deformation, shape optimization, fluid-structure interaction, fully stressed design, finite-element analysis, linear elasticity, strain failure, equivalent strain, Tresca failure criterion

Hsu, Su-Yuen↗
NASA NTRS2014

Adaptive Shape Functions and Internal Mesh Adaptation for Modelling Progressive Failure in Adhesively Bonded Joints

Enhanced finite elements are elements with an embedded analytical solution that can capture detailed local fields, enabling more efficient, mesh independent finite element analysis. The shape functions are determined based on the analytical model rather than prescribed. This method was applied to adhesively bonded joints to model joint behavior with one element through the thickness. This study demonstrates two methods of maintaining the fidelity of such elements during adhesive non-linearity and cracking without increasing the mesh needed for an accurate solution. The first method uses adaptive shape functions, where the shape functions are recalculated at each load step based on the softening of the adhesive. The second method is internal mesh adaption, where cracking of the adhesive within an element is captured by further discretizing the element internally to represent the partially cracked geometry. By keeping mesh adaptations within an element, a finer mesh can be used during the analysis without affecting the global finite element model mesh. Examples are shown which highlight when each method is most effective in reducing the number of elements needed to capture adhesive nonlinearity and cracking. These methods are validated against analogous finite element models utilizing cohesive zone elements.

computational mechanics↗
NASA NTRS2018

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

higher-order↗
NASA NTRS2019

Adjoint-Based Anisotropic Mesh Adaptation for a Stabilized Finite-Element Flow Solver

An adjoint solver is implemented in the FUN3D stabilized finite-element flow solver. The adjoint solution is used to generate anisotropic, adapted meshes to control error in scalar out- put functionals, such as lift or drag coefficient. The inviscid and turbulent adjoints are verified with a finite-difference derivative approximation and can be used in design optimization in addition to mesh adaptation. The adjoint capability represents an extension of previous research using the FUN3D stabilized finite-element capability with metric-based mesh adaptation and interpolation-based error estimates to generate highly anisotropic adapted meshes for turbulent flows. In the present work, a metric-based approach is again utilized, where the adjoint and the primal solutions both contribute to the generation of a metric tensor field that is subsequently used to produce the required anisotropic mesh for each adaptation cycle. Adaptive results are then shown for an inviscid supersonic flow over a diamond airfoil, inviscid transonic flow over the ONERA M6 wing, and viscous laminar flow over the NACA 0012 airfoil, all using drag force as the output functional. Adjoint-based adaptation is compared with a multiscale solution-based approach that controls the L norm of Mach number interpolation error to demonstrate the effectiveness and effciency of the adjoint-based adaptive mesh technology.

Balan, Aravind↗
NASA NTRSDate not supplied

Cartesian Mesh Simulations for the Third AIAA Sonic Boom Prediction Workshop

Simulation results are presented for all cases from the Third AIAA Sonic Boom Prediction Workshop. An inviscid, embedded-boundary Cartesian-mesh flow solver is used in conjunction with adjoint-based mesh adaptation to compute nearfield pressure signatures. Specialized techniques are applied to maximize accuracy and minimize cost on Cartesian meshes. The Richardson-based error estimate highlights regions of the signatures most sensitive to mesh refinement. Timing results and coarse, medium, and fine mesh sizes for nearfield cases demonstrate that the parallel decomposition approach is efficient in both computational time and wall-clock. Pressure signals are propagated to the ground using an augmented Burgers’ equation solver to predict boom carpets. Ground signatures and loudness metrics are presented for a standard atmosphere as well as more realistic atmospheric profiles, which affect overall noise levels and can significantly widen the boom carpet. Mesh convergence studies show that high sampling frequencies, around 500 kHz, are required for propagation, and the sampling frequency increases at large off-track angles with longer acoustic ray paths and propagation times. The numerical methods yield accurate results for predicting low sonic boom signatures while being among the least computationally expensive of the workshop.

ARMD↗
NASA NTRSDate not supplied

Automation of Overset Structured Mesh Generation onBoundary Representation Geometries

A scheme is presented for the automatic generation of structured overset meshes ongeometries that are defined by Boundary Representation (BRep) solids. The surface meshsystem consists of face, edge and node meshes corresponding to the three respective basicBRep entity types. A cut-cell method is introduced to improve robustness of the on-geometrydetermination test for a face mesh grid point. A geometric component tagging scheme is utilizedto enhance local grid point distribution on a configuration with a large range of geometricscales. A cap grid topology is automatically utilized around the trailing edge of wing and tailtips to enhance mesh quality and to enable more effective surface coverage. Robustness of thehyperbolic surface marching method is improved by replacing the point projection scheme witha walking scheme. Relaxation of surface grid spacing at concave corners enables automatedhigh quality hyperbolic volume mesh creation. Domain connectivity is automatically performedon the surface mesh system. A variety of test cases are presented including a re-entry capsule,two models of the Juncture Flow Experiment wing-body, five rotorcraft concept vehicles, andvarious components of the High-Lift Common Research Model from the High-Lift PredictionWorkshop 4.

TTT↗
DOE OSTI2023

FINITE ELEMENT MODEL MESH REFINEMENT EFFECTS ON QUALIFICATION OF NUCLEAR GRADE GRAPHITE COMPONENTS

The American Society of Mechanical Engineers (ASME) provides the full and simplified design-by-analysis probabilistic assessments for determining acceptance of nuclear grade graphite core components. The assessments can be characterized by three parts: (1) a component stress distribution, often determined by a finite element (FE) model; (2) a Weibull probability density function (pdf) that characterizes the experimental tensile strength distribution; and (3) the post-processor, which combines the FE model and the Weibull strength distribution in accordance with the full and simplified assessments to determine component acceptance. It is known that the level of mesh refinement in FE models can affect the modeled component’s calculated stress distribution. Depending on the component geometry, the stress distribution may converge with sufficient refinement. It was previously unknown whether the acceptance decision resulting from the full and simplified assessments might change even with sufficient mesh refinement. This study explores that question using experimental strength results for a dog-bone geometry for two graphite grades, IG-110 and PCEA. The simplified assessment has two criteria that must be met, the first limits the combined membrane stress by the allowable stress and the second limits the peak equivalent stress by the allowable stress scaled by the ratio of flexural to tensile strength. In the application of the simplified assessment, convergence of the peak equivalent stress required extreme mesh refinement, however, the acceptance decision was not affected. It is hypothesized that more complex geometries with stress concentrations may present mesh refinement effects on the simplified assessment acceptance decision. Mesh refinement did affect the acceptance decision in the full assessment for the applied pressure loadings in this study. This work suggests component stress distribution convergence is not a sufficient criteria for POF convergence in the full assessment and that mesh refinement should continue until the POF has converged, especially where the resulting POF is bordering the SRC acceptable POF limit.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2017

Diffusion Synthetic Acceleration for High Order S{sub N} Transport on Meshes with Curved Surfaces

Thermal radiation transport is integral to multiphysics applications such as inertial confinement fusion and astrophysics. Materials in these problems can be exceptionally optically thick and diffusive. A transport solver must be capable of accurate and efficient solutions to such problems. Previously, Woods et al. established a proof-of-concept for high order (HO) discontinuous Galerkin finite element (DGFEM) transport on meshes with curved surfaces. They numerically demonstrated the spatial convergence is order p + 1. Remarkably, these convergence rates are relatively invariant to the amount of curvature of the spatial mesh. We present here an extension of this work that demonstrates a rapidly-convergent iterative solver for the FEM transport equations on meshes with curved sides. We use the modified interior penalty (MIP) diffusion synthetic acceleration (DSA) established by Wang and Ragusa. The partially consistent MIP equations stem from the symmetric interior penalty (IP) derivation of the diffusion equation. The IP method is not stable for optically thick cells so it was combined with the diffusion conforming form (DCF), a discretized diffusion equation derived from the discretized S N equations that is not stable for intermediate optical thicknesses. The MIP equations adapt a 'switch' to the IP method in optically thinner regions and the DCF method in optically thicker regions. The literature does not reveal any Fourier analyses performed for iterative transport on meshes with curved surfaces. Wang and Ragusa performed a Fourier analysis for orthogonal meshes and our results appear to be as expected. Previous literature has reported on some of the sensitivities that affect the spectral radius of DSA schemes: polynomial order, and scattering ratios. Presently, we focus on the sensitivity of the spectral radius to polynomial order, scattering ratio, the constant C, and mesh curvature for varying cell thicknesses. We also numerically study the behavior of the spectral radius to verify our DSA implementation. A sequence of problems is designed to exercise the acceleration. As the problems become more optically thick and diffusive, the accelerated solution continues to converge toward the analytic solution. We employ the Modular Finite Element Methods (MFEM) package, developed at Lawrence Livermore National Laboratory, to generate the linear algebraic system of equations for each angle in the discrete ordinates quadrature set, and use UMFPack to solve this system of equations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

An open-source hybrid unstructured mesh - CAD fusion multiphysics analysis workflow in SALAMANDER

Plasma facing components in fusion devices will endure extreme neutron and heat fluxes. To facilitate their design using simulation tools, the open-source Fusion Module, Fusion ENergy Integrated multiphys-X (FENIX) framework is being developed to model these components with a high-fidelity multi-physics multi-dimensional approach. It can iteratively resolve couplings between all the physics at play, from neutron radiation, to thermomechanics, to near-wall plasma dynamics. This framework is based on the Multiphysics Object Oriented Simulation Environment (MOOSE), which is developed by a collaboration of US National Laboratories since 2008, for advanced nuclear, geomechanics simulations and other applications. FENIX couples numerous simulation tools, including OpenMC, the Tritium Migration Analysis Program v8, the NekRS CFD software, and most MOOSE modules. For the coupling of radiation transport and other physics, FENIX supports a hybrid workflow between Computer Assisted Design (CAD) and unstructured mesh geometries. The CAD can be generated from skinning the unstructured mesh, to enable a coarse geometry for efficient particle transport, but still resolving the local material compositions and temperature gradients. Neutron transport is performed using DAGMC on the CAD, and Cardinal, integrated in FENIX, maps tallied quantities, such as the heat deposition or the tritium generation rates, from a tally volumetric mesh to the other physics’ unstructured mesh. This coupling was exercised on a simplified tokamak geometry, coupling neutron transport with the heat conduction equation, and on a monoblock divertor problem, coupling additionally with tritium migration. Mesh convergence studies highlight the importance of the mapping conservativeness. Coupling with thermo-mechanics is further enabled by the generalization of the approach to moving meshes. The presentation will include these coupled analysis as well as an update on status of the FENIX framework.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation

A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Lastly, dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Magnetic mesh generation and field line reconstruction for scrape-off layer and divertor modeling in stellarators

The design of divertor targets and baffles for optimal heat and particle exhaust from magnetically confined fusion plasmas requires a combination of fast, low-fidelity models (such as EMC3-Lite (Feng 2022 Plasma Phys. Control. Fusion 64 125012)) for scoping studies and high-fidelity ones (such as EMC3-EIRENE (Feng et al 2014 Contrib. Plasma Phys. 54 426–31)) for verification. Both of those approaches benefit from a magnetic flux tube mesh for fast interpolation and mapping of field line segments (Feng et al 2005 Phys. Plasmas 12 052505). A new automated mesh generator for unstructured quadrilateral flux tubes with adaptive refinement is presented and integrated into FLARE (Frerichs 2024 Nucl. Fusion 64 106034). For HSX with an extended first wall, it is found that several layers of flux tubes can span the entire half field period before splitting is required. This is an advantage over the traditional setup of the EMC3-EIRENE mesh where careful construction of several sub- domains is required already for the much tighter present first wall. In particular, there is no longer the need to manually construct a suitable outer boundary for the mesh. The divide and conquer paradigm with unstructured mesh layout offers a powerful alternative for fast head load approximation that is suitable for integration into optimization workflows. Further examples for W7-X and CTH demonstrate the versatile application range.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Nonconforming Mesh Refinement for High-Order Finite Elements

In this study, we propose a general algorithm for nonconforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on $h$-refinement with a fixed polynomial order. The algorithm handles triangular, quadrilateral, hexahedral, and prismatic meshes of arbitrarily high-order curvature, for any order finite element space in the de Rham sequence. We present a flexible data structure for meshes with hanging nodes and a general procedure to construct the conforming interpolation operator, both in serial and in parallel. The algorithm and data structure allow anisotropic refinement of tensor product elements in two and three dimensions and support unlimited refinement ratios of adjacent elements. We report numerical experiments verifying the correctness of the algorithms and perform a parallel scaling study to show that we can adapt meshes containing billions of elements and run efficiently on 393,000 parallel tasks. Finally, we illustrate the integration of dynamic AMR into a high-order Lagrangian hydrodynamics solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Overset meshing coupled with hybridizable discontinuous Galerkin finite elements

We introduce the use of hybridizable discontinuous Galerkin (HDG) finite element methods on overlapping (overset) meshes. Overset mesh methods are advantageous for solving problems on complex geometrical domains. We also combine geometric flexibility of overset methods with the advantages of HDG methods: arbitrarily high-order accuracy, reduced size of the global discrete problem, and the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. This approach to developing the ‘overset HDG’ method is to couple the global solution from one mesh to the local solution on the overset mesh. We present numerical examples for steady convection–diffusion and static elasticity problems. The examples demonstrate optimal order convergence in all primal fields for an arbitrary amount of overlap of the underlying meshes.

42 ENGINEERING↗
DOE OSTI2019

Circumventing mesh bias by r- and h-adaptive techniques for variational eigenfracture

This work introduces and compares mesh r- and h-adaptivity for the eigenfracture model originally proposed in Schmidt et al. (Multiscale Model Simul 7:1237–1266, 2009), Pandolfi and Ortiz (J Numer Methods Eng 92:694–714, 2012), with the goal of suppressing potential mesh bias due to the element deletion. In the r-adaptive approach, we compute the configurational force at each incremental step and move nodes near the crack tip parallel to the normalized configurational forces field such that the crack propagation direction can be captured more accurately within each incremental step. In the h-adapative approach, we introduce mesh refinement via a quad-tree algorithm to introduce more degrees of freedom within the nonlocal ϵ-neighborhood such that a more refined crack path can be reproduced with a higher mesh resolution. Our numerical examples indicate that the r-adaptive approach is able to replicate curved cracks and complex geometrical features, whereas the h-adaptive approach is advantageous in simulating sub-scale fracture when the nonlocal regions are smaller than the un-refined coarse mesh.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

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↗
DOE OSTI2019

A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables

Here, we introduce a mesh-adaption framework that employs a multi-physical configurational force and Lie algebra to capture multiphysical responses of fluid-infiltrating geological materials while maintaining the efficiency of the computational models. To resolve sharp gradients of both displacement and pore pressure, we introduce an energy-estimate-free re-meshing criterion by extending the configurational force theory to consider the energy dissipation due to the fluid diffusion and the gradient-dependent plastic flow. To establish new equilibria after remeshing, the local tensorial history-dependent variables at the integration points are first decomposed into spectral forms. Then, the principal values and directions are projected onto smooth fields interpolated by the basis function of the finite element space via the Lie-algebra mapping. Our numerical results indicate that this Lie algebra operator in general leads to a new trial state closer to the equilibrium than the ones obtained from the tensor component mapping approach. A new configurational force for dissipative fluid-infiltrating porous materials that exhibit gradient-dependent plastic flow is introduced such that the remeshing may accommodate the need to resolve the sharp pressure gradient as well as the strain localization. The predicted responses are found to be not influenced by the mesh size due to the micromorphic regularization, while the adaptive meshing enables us to capture the width of deformation bands without the necessity of employing fine mesh everywhere in the domain.

42 ENGINEERING↗
DOE OSTI2025

Stable low diffusion flux splitting schemes on unstructured meshes

Shock instabilities are shown to manifest in modern low-diffusion flux-vector splitting (FVS) schemes when used on unstructured meshes, or situations where shocks do not align with the mesh lines. These instabilities occur irrespective of the Mach number of the shock. Three types of dissipative mechanisms that suppress these instabilities are presented. These mechanisms are carefully designed in order to affect only problematic regions of the flux-splittings. The AUSM + and LDFSS schemes are stabilized using the proposed modifications. It is shown that the added dissipation improves the shock behavior of AUSM and LDFSS on unstructured meshes. It is also shown that the AUSM + -up scheme is prone to the “carbuncle” instability, a specific type of shock instability, when used on unstructured meshes. The modifications proposed in this work do not lead to carbuncle instabilities for the problems considered here. Furthermore, the modified schemes are shown to satisfy certain properties that are crucial for accurate shear layer computations, such as stationary contact preservation. Using benchmark problems, it is demonstrated that despite the diffusion added for stabilization, these schemes are not overly diffusive. Furthermore, due to these advantages, the modified FVS schemes presented here are promising candidates for high-speed compressible flow computations on unstructured meshes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Volumetric analysis and mesh generation of real and artificial microstructural geometries

Producing a viable finite element mesh of realistic microstructural structural geometry is a critical step in analyzing the thermo-mechanical behavior of complex multi-material composites. Advancements in imaging technology such as micro computed tomography have allowed modelers to access high resolution mesoscale geometries for direct numerical simulation. However, converting from voxel based 3D images to usable finite element meshes has been challenging. A robust method including algorithms and software scripts for generating finite element meshes from 3D imaged microstructures is presented in this paper. It includes a routine for inserting cohesive elements around material interfaces to enable modeling of interface properties including delamination and damage. The algorithms and procedures presented in this method leverage currently available software packages for processing surface based geometry into volume based meshes. In addition to converting real geometry from physical imaging systems, algorithms for producing numerically generated and statistically equivalent microstructural geometry are also included. These artificial microstructures can be a valuable resource for modelers when physical specimens do not exist or are limited in quantity: Method establishes a workflow from voxel data to viable finite element mesh including interface information, and Includes a method for synthetic geometry generation based on metrics from real microstructures.

36 MATERIALS SCIENCE↗