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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A face-upwinded spectral element method

Here we present a new high-order accurate discretisation on unstructured meshes of quadrilateral elements. Our Face Upwinded Spectral Element (FUSE) method uses the same node distribution as a high-order continuous Galerkin (CG) method, but with a particular choice of node locations within each element and an upwinded stencil on the face nodes. This results in a number of benefits, including fewer degrees of freedom and straight-forward integration with CG. We present the derivation of the scheme and the analysis of its properties, in particular showing stability using von Neumann analysis. We show numerical evidence for its accuracy and efficiency on multiple classes of problems including convection-dominated flows, Poisson's equation, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Study on Particle Trajectory Error in Finite-Element Particle-in-Cell Algorithms

Particle-in-cell (PIC) algorithms are widely used for the simulation of kinetic plasmas. PIC algorithms account for the interaction between charged particles in a plasma and the electromagnetic field in ambient space, including self-field interactions. The objective of this article is to study the error in charged particle trajectories present in finite-element (FE)-based PIC algorithms on unstructured meshes. We study how the trajectory error behaves according to the FE mesh resolution and the matrix solver employed in the FE algorithm. The study is performed by considering a trajectory established by a parabolic electric potential and an axial magnetic force acting on the charged particle. Under a proper choice combination of electric and magnetic field parameters, the 2-D particle trajectories comprise closed orbits. Numerical errors cause small perturbations on the trajectories, with cumulative effects. As a result, the resulting orbital trajectories exhibit distortions including spurious apsidal precession. These distortions provide a clear imprint of the numerical error. Here, we also study the numerical error in a quantitative fashion by computing the distance norm between the trajectories obtained by the exact fields and numerical fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

High-fidelity pool boiling simulations on multiple nucleation sites using interface capturing method

Boiling has proved to be one of the most efficient means for heat transfer and is a very important phenomenon during severe accident scenarios in light water reactors. High-fidelity pool boiling simulations can provide a numerical database for improving mechanistic boiling models by allowing for specific evaluation of interactions among bubbles. Previously published pool boiling simulations investigated two nucleation sites in which bubble growth at one site suppressed nucleation at the other site. Based on previous study results, more complicated interface-capturing simulations on pool boiling were conducted using PHASTA code with locally refined unstructured mesh. First, different boundary conditions (BCs) were assessed to support robustness and reproducibility of the boiling model. Then, a scale study was conducted at a larger domain with nine nucleation sites where either nine or four nucleation sites are activated. Involving more nucleation sites increased the complexity of bubble interactions from surrounding sites. Finally, bubble departure behavior influenced by wall heat flux was investigated. In this work, when heat flux was increased, the order of bubble departure changed, but diagonal bubbles always departed after one another. The departure time interval between the first and second bubble reduced as heat flux increased. The corresponding frequency was almost linearly proportional to the heat flux. In addition, bubble departure behavior was found to be greatly influenced by the nucleation site pattern. Multiple nucleation sites resulted in superimposed inhibitive effects from surrounding sites to each bubble, which extensively delayed the departure. This new observation was not discussed in previously published works. The work presented here provides new insight on the fundamental understanding of boiling phenomena, contributes to the development of a 3D multiphase computational fluid dynamics (M-CFD) model, and provides a more comprehensive database for data-driven pool boiling studies.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Athena-I CUBIT Journal Files

The Monte Carlo N-Particle (MCNP)1 transport code version 6 (also known as MCNP6) has the capability for tracking particles on unstructured mesh (UM) geometry models embedded into con structive solid geometry (CSG) cells. This feature has been developed for performing calculations of complex geometry models because manually creating CSG models is a time-consuming and error prone process as the complexities of geometries increase. The UM capability was originally designed to work with UM models created with the Abaqus software and ASCII input files that it generates. The MCNP code version 6.0 and later can process UM models formatted as Abaqus input files. Starting with version 6.3, MCNP can also process HDF5 mesh input files. External codes must be used to generate Abaqus input files for MCNP UM calculations. CUBIT, the Sandia National Laboratory automated mesh generation toolkit, can generate a UM model formatted as an Abaqus input file. However, the Abaqus input files exported from CUBIT cannot be used for MCNP simulations because it lacks the proper syntax. A Python script was developed to convert an Abaqus file created by CUBIT to an Abaqus file format that MCNP can process. Creating UM models for complex geometries is not an easy task. The process of creating UM models in CUBIT for MCNP simulations is detailed in. CUBIT provides several user interface options including a graphical user interface (GUI) and a command line interface. A GUI provides an easy way to use CUBIT without learning the CUBIT command syntax. When using CUBIT with either interface option, command lines are written into an ASCII file known as a journal file; this journal file can be edited and archived so that it can be played back in CUBIT to automatically generate a UM model. This report describes the CUBIT journal files of the UM models developed for Athena-I. The Athena platform, an energy-tuning assembly, was developed to spectrally shape the National Ignition Facility (NIF) deuterium-tritium fusion neutron source to a thermonuclear (fusion) plus prompt fission neutron spectrum with capability to act as a short-pulse neutron source. MCNP6 was used for the Athena experiment design analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Decay Dose Shielding Analysis with Hybrid Unstructured Mesh/Constructive Solid Geometry Monte Carlo Calculation and ADVANTG Acceleration

Here, the target segments of the Oak Ridge National Laboratory Second Target Station (STS) neutron production facility become highly activated due to spallation reactions or nuclei transmutation by primary protons and emitted neutrons. Once the target segments are removed from their location within the core vessel, decay dose rates must be accurately quantified to determine the shielding configurations of remote-handling tools and transport casks and to aid in planning maintenance activities. For this analysis, we utilized a hybrid unstructured mesh (UM)/constructive solid geometry approach for calculating spallation products and neutron fluxes, activation calculations using the AARE package that includes the CINDER2008 activation code to calculate the decay photon source at different cooling times, and the ADVANTG code to accelerate the final decay photon transport calculation. Both Type 316 stainless steel (SS-316) and lead were investigated as candidates for shielding materials. The decay photon transport calculation through the thick SS-316 or lead shields exhibited between 25 and 30 orders-of-magnitude attenuations in the radial direction, depending on the shield. Such a difficult shielding calculation required advanced variance reduction. ADVANTG has some missing features, which limits its usability in spallation neutron source applications. It does not support volumetric sources created for MCNP6.2 UM capability. An approximate source was created for this problem. Not only was this approximate source needed for running the ADVANTG calculation to generate the weight windows, but also it was essential to develop source biasing (SB) parameters that were crucial for dramatically accelerating the decay photon transport in this problem. With this approximate source, the analysis was completed in a very reasonable computational time, and the design of the STS remote-handling equipment was finalized. This paper compares the efficiency of Monte Carlo simulations with different weight window and SB parameters calculated using different approximate ADVANTG calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Voronoi Meshing to Accurately Capture Geological Structure in Subsurface Simulations

Mesh generation lies at the interface of geological modeling and reservoir simulation. Highly skewed or very small grid cells may be necessary to accurately capture the geometry of geological features, but the resulting poorly scaled or small grid cells can have a substantial negative impact on simulator accuracy and speed. One way to minimize numerical errors caused by gridding complex structures is to simulate on high-quality Voronoi meshes, which reduce grid orientation effects in fluid flow. This work presents a complete methodology to create Voronoi simulation grids, model fluid flow in complex geological systems, and visualize the results. A recently developed Voronoi meshing method that can automatically generate provably good unstructured meshes that conform to input surfaces creating closed volumes is used. Initially an analytical benchmark simulation is presented to validate the quality of the meshes and simulation results and demonstrate the superiority of simulation results using Voronoi meshes over flexed-hexahedral meshes on a domain with internal features. Next, meshes are created for test structures representing four of the most common geological features in the subsurface: layering, pinch-out, an interior lens that tapers to zero thickness on all sides and a fault with offset. Two benchmark flow simulations are run for each test structure. Finally, a realistic geological example for CO 2 injection into an anticline is simulated. Three realizations of the Voronoi mesh at the same resolution are generated for the simulations. Each mesh is highly refined near the injection wells and coarse in areas of less interest. These three meshes are used to model the CO 2 plume in the subsurface as it migrates to the top of the structure and then fills downward. Simulations on the meshes with randomly generated elements inside the input volumes each give slightly different fingering patterns for the viscous-unstable buoyant gas flow. The results presented in this work show a promising step towards utilizing fully automated Voronoi meshing for subsurface flow simulations in complex geology.

58 GEOSCIENCES↗
NASA NTRS1987

Approaches to the automatic generation and control of finite element meshes

The algorithmic approaches being taken to the development of finite element mesh generators capable of automatically discretizing general domains without the need for user intervention are discussed. It is demonstrated that because of the modeling demands placed on a automatic mesh generator, all the approaches taken to date produce unstructured meshes. Consideration is also given to both a priori and a posteriori mesh control devices for automatic mesh generators as well as their integration with geometric modeling and adaptive analysis procedures.

Shephard, Mark S.↗
NASA NTRS1995

Multigrid solution strategies for adaptive meshing problems

This paper discusses the issues which arise when combining multigrid strategies with adaptive meshing techniques for solving steady-state problems on unstructured meshes. A basic strategy is described, and demonstrated by solving several inviscid and viscous flow cases. Potential inefficiencies in this basic strategy are exposed, and various alternate approaches are discussed, some of which are demonstrated with an example. Although each particular approach exhibits certain advantages, all methods have particular drawbacks, and the formulation of a completely optimal strategy is considered to be an open problem.

Mavriplis, Dimitri J.↗
NASA NTRS1995

Multigrid solution strategies for adaptive meshing problems

This paper discusses the issues which arise when combining multigrid strategies with adaptive meshing techniques for solving steady-state problems on unstructured meshes. A basic strategy is described, and demonstrated by solving several inviscid and viscous flow cases. Potential inefficiencies in this basic strategy are exposed, and various alternate approaches are discussed, some of which are demonstrated with an example. Although each particular approach exhibits certain advantages, all methods have particular drawbacks, and the formulation of a completely optimal strategy is considered to be an open problem.

Mavriplis, Dimitri J.↗
NASA NTRS1987

Three dimensional mesh generation by triangulation of arbitrary point sets

A method for generating an unstructured mesh is described. The approach is quite general and joins an arbitrary set of points to produce a covering of three dimensional space by tetrahedra. After removing the tetrahedra that connect surface points, a mesh suitable for a finite element based flow solver is obtained. Details of the triangulation algorithm are provided together with an analysis of the algorithm efficiency and validity.

Baker, Timothy J.↗
NASA NTRS2013

Recent Development in the CESE Method for the Solution of the Navier-Stokes Equations Using Unstructured Triangular or Tetrahedral Meshes With High Aspect Ratio

In the multidimensional CESE development, triangles and tetrahedra turn out to be the most natural building blocks for 2D and 3D spatial meshes. As such the CESE method is compatible with the simplest unstructured meshes and thus can be easily applied to solve problems with complex geometries. However, because the method uses space-time staggered stencils, solution decoupling may become a real nuisance in applications involving unstructured meshes. In this paper we will describe a simple and general remedy which, according to numerical experiments, has removed any possibility of solution decoupling. Moreover, in a real-world viscous flow simulation near a solid wall, one often encounters a case where a boundary with high curvature or sharp corner is surrounded by triangular/tetrahedral meshes of extremely high aspect ratio (up to 106). For such an extreme case, the spatial projection of a space-time compounded conservation element constructed using the original CESE design may become highly concave and thus its centroid (referred to as a spatial solution point) may lie far outside of the spatial projection. It could even be embedded beyond a solid wall boundary and causes serious numerical difficulties. In this paper we will also present a new procedure for constructing conservation elements and solution elements which effectively overcomes the difficulties associated with the original design. Another difficulty issue which was addressed more recently is the wellknown fact that accuracy of gradient computations involving triangular/tetrahedral grids deteriorates rapidly as the aspect ratio of grid cells increases. The root cause of this difficulty was clearly identified and several remedies to overcome it were found through a rigorous mathematical analysis. However, because of the length of the current paper and the complexity of mathematics involved, this new work will be presented in another paper.

Chang, Sin-Chung↗
DOE OSTI2021

FIERRO V.X

FIERRO is a modern C++ code intended to simulate quasi-static solid mechanics problems and transient, compressible material dynamic problems with Lagrangian methods, which have meshes with constant mass elements that move with the material. FIERRO is designed to aid a) material model research that has historically been done using commercial implicit and explicit finite element codes, b) numerical methods research, and c) computer science research. FIERRO supports user developed material models that adhere to several industry standard formats by using a C++ to Fortran interface to couple the model to the numerical solvers. FIERRO is built on the ELEMENTS library that supports a diverse suite of element types, including high-order elements, and quadrature rules. The mesh class within the ELEMENTS library is designed for efficient calculations on unstructured meshes and to minimize memory usage. FIERRO is designed to readily accommodate a range of numerical methods including continuous finite element, finite volume, and discontinuous Galerkin methods. FIERRO is designed to support explicit and implicit time integration methods. FIERRO only supports a single material in an element. No physical data exists within the code.

Morgan, Nathaniel↗
DOE OSTI2022

$χ$-$MeRA$: 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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1993

Line relaxation methods for the solution of 2D and 3D compressible flows

An implicit finite element based algorithm for the compressible Navier-Stokes equations is outlined, and the solution of the resulting equation by a line relaxation on general meshes of triangles or tetrahedra is described. The problem of generating and adapting unstructured meshes for viscous flows is reexamined, and an approach for both 2D and 3D simulations is proposed. An efficient approach appears to be the use of an implicit/explicit procedure, with the implicit treatment being restricted to those regions of the mesh where viscous effects are known to be dominant. Numerical examples demonstrating the computational performance of the proposed techniques are given.

Hassan, O.↗
NASA NTRS1995

A unified multigrid solver for the Navier-Stokes equations on mixed element meshes

A unified multigrid solution technique is presented for solving the Euler and Reynolds-averaged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms, and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the formulation of a complete solution technique which can handle structured grids, block structured grids, and unstructured grids of tetrahedra or mixed elements without any modification. This is achieved by discretizing the full Navier-Stokes equations on tetrahedral elements, and the thin layer version of these equations on other types of elements, while using a single edge-based data-structure to construct the discretization over all element types. An agglomeration multigrid algorithm, which naturally handles meshes of any types of elements, is employed to accelerate convergence. An automatic algorithm which reduces the complexity of a given triangular or tetrahedral mesh by merging candidate triangular or tetrahedral elements into quadrilateral or prismatic elements is also described. The gains in computational efficiency afforded by the use of non-simplicial meshes over fully tetrahedral meshes are demonstrated through several examples.

Mavriplis, D. J.↗
DOE OSTI2022

Multiphysics analysis system for heat pipe cooled micro-reactors employing PRAGMA-OpenFOAM-ANLHTP

A multiphysics analysis system for neutronics/thermo-mechanical/heat-pipe analysis of heat pipe cooled micro-reactors was developed using the PRAGMA code as the neutronics engine. PRAGMA, which used to be a GPU-based continuous-energy MC code for power reactor applications, now has an extended geometry package to handle geometries with unstructured meshes generated by the ANSYS Design-Modeler and Meshing. The NVIDIA ray tracing engine OptiX was exploited for efficient neutron transport on unstructured geometry. On the multiphysics side, the open-source CFD tool OpenFOAM and one-dimensional heat pipe analysis code ANLHTP were adopted. The manager-worker system based on the MPI dynamic process management (DPM) model enables efficient coupling of codes employing different parallelization schemes. With all the features, the multiphysics analysis of the one-sixth symmetrical MegaPower 2D core was performed and it demonstrated the benefit of the tight integration of the three-way coupling system and one-to-one geometry coupling strategy. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1993

Looking for O(N) Navier-Stokes solutions on non-structured meshes

Multigrid methods are good candidates for the resolution of the system arising in numerical fluid dynamics. However, the question is to know if those algorithms which are efficient for the Poisson equation on structured meshes will still apply well to the Euler and Navier-Stokes equations on unstructured meshes. The study of elliptic problems leads us to define the conditions where a full multigrid strategy has O(N) complexity. The aim of this paper is to build a comparison between the elliptic theory and practical CFD problems. First, as an introduction, we will recall some basic definitions and theorems applied to a model problem. The goal of this section is to point out the different properties that we need to produce an FMG algorithm with O(N) complexity. Then, we will show how we can apply this theory to the fluid dynamics equations such as Euler and Navier-Stokes equations. At last, we present some results which are 2nd-order accurate and some explanations about the behavior of the FMG process.

Morano, Eric↗
NASA NTRS1993

Looking for O(N) Navier-Stokes solutions on non-structured meshes

Multigrid methods are good candidates for the resolution of the system arising in Numerical Fluid Dynamics. However, the question is to know if those algorithms which are efficient for the Poissan equation on structured meshes will still apply well to the Euler and Navier-Stokes equations on unstructured meshes. The study of elliptic problems leads us to define the conditions where a Full Multigrid strategy has O(N) complexity. The aim of this paper is to build a comparison between the elliptic theory and practical CFD problems. First, as an introduction, we will recall some basic definitions and theorems applied to a model problem. The goal of this section is to point out the different properties that we need to produce an FMG algorithm with O(N) complexity. Then, we will show how we can apply this theory to the fluid dynamics equations such as Euler and Navier-Stokes equations. At last, we present some results which are 2nd-order accurate and some explanations about the behavior of the FMG process.

Morano, Eric↗