Search NASA⌕ Search

SEARCH · Search NASA

Results for “finite difference method”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

THERMAL/STRUCTURAL ANALYSIS OF THE AXION QUANTUM METROLOGY CAVITY AND ITS COMPONENTS

This research was centered around maximizing the capability to cool dielectric material within a containment unit, or Photonic Band Gap (PBG) cavity, designed for detecting axion dark matter and identifying the unit’s thermal properties. There are multiple types of PBG cavities, but the latest version that axion researchers wish to use has been theorized to contain possible issues related to its thermal properties. Thermal conductivity is an issue with the dielectric material because it is made from alumina which is highly insulative. This is important since the research is being done in a cryogenic environment and the thermal noise affects the quantum bit used for detecting the axion to photon conversion process. Therefore, any improvements to this unit should be justified and implemented but are not entirely limited to thermal contact related aspects of PBG cavities. A prospect of using sapphire in place of alumina also exists, but this is a more expensive, less tested, and more elusive material to justify the creation of a full dielectric structure out of sapphire. Thermal aspects of the cavity were analyzed using finite element method (FEM) and an experiment designed to test different thermal joint materials. FEM was used to check the contraction of the cavity during cooling, the contact quality between the dielectric material and cavity wall, theheat flow rate through the assembly, and helps visualize the cavity’s reaction to different design changes. A simple comparison between thermal conductivity curves justified the usage of sapphire over alumina from a thermal property point of view. Thus, the method of experimentation had an additional dielectric material, sapphire, to test with and compare to alumina. The thermal test identified which material is best to use for a thermal joint but also simultaneously found the conductance of the joint and dielectric material as well as an estimate for what the temperature is inside the larger scale cavity since a thermometer cannot be placed inside the PBG when it cools. Initially, the cavity simulation was tested for structural deformation properties and stress distribution since it is made of copper which contracts heavily in comparison to most other materials. The reduction in volume of the cavity was less than anticipated which gave more room for a possible usage of a modified thermal joint for additional contact area and higher conductivity.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

A sixth order Mehrstellen scheme with an application to the Method of Local Corrections for the 3D Poisson equation

We present a sixth order finite difference scheme for Poisson’s equation when discretized with the compact 27-point stencil based on Mehrstellen corrections of the forcing function term f. Our approach results in a sixth order accurate solution error as opposed to a fourth-order error imposed by the classical Mehrstellen correction for the 19-point and 27-point stencils. The present study is a continuation of former work of Spotz and Carey (1996) on compact finite difference schemes for Poisson’s equation where sixth order convergence may be obtained under the assumption that the fourth order derivatives of f are determined analytically. Specifically, we show that sixth order convergence can still be attained when only values of f at grid points are available. The sixth order Mehrstellen scheme is further coupled with a Method of Local Corrections (MLC) 3D Poisson solver improving to sixth order accuracy the results reported in Kavouklis and Colella (2019). The MLC test case considered involves an adaptive grid that comprises 7.5 billion cells.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Comparison of three state-of-the-art crystal plasticity based deformation twinning models for magnesium alloys

In magnesium alloys, deformation twinning and its interactions with dislocation slip are responsible for a sigmoidal shape stress–strain behavior and an asymmetrical tension–compression yield strength in magnesium alloys. The sensitivity of twinning to the underlying microstructure renders the crystal plasticity method the most commonly adopted modeling approach for magnesium-twinning. This paper compares three state-of-the-art crystal plasticity-based twinning models from the literature, namely the elastic-viscoplastic self-consistent twinning-detwinning (EVPSC-TDT) model, crystal plasticity finite element model based on enhanced predominate twin reorientation approach (CPFE-ePTR), and the crystal plasticity finite element model based on “discrete twinning” approach (CPFE-DT). A polycrystalline microstructure is simulated with all three methods to compare the resulting stress–strain curves and lattice strains to those from the experimentally measured data. All three methods showed the capability of capturing the experimental results with different levels of accuracy. Additionally, the EVPSC-TDT method avoids solving the finite element matrices and showed the highest computational efficiency. The CPFE-ePTR model shows a higher accuracy in capturing the lattice strain. The CPFE-DT relies on high-resolution finite element mesh and is much slower than the other two methods, but it captured the local deformation concentration and stress reversal phenomena near the twin band, which was not possible with the other two methods. Based on the comparison, guidance for the selection of the appropriate model based on the specific modeling target is provided in this paper.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Instrument design optimization with computational methods

Using Finite Element Analysis to approximate the solution of differential equations, two different instruments in experimental Hall C at the Thomas Jefferson National Accelerator Facility are analyzed. The time dependence of density uctuations from the liquid hydrogen (LH2) target used in the Q wea k experiment (2011-2012) are studied with Computational Fluid Dynamics (CFD) and the simulation results compared to data from the experiment. The 2.5 kW liquid hydrogen target was the highest power LH2 target in the world and the first to be designed with CFD at Jefferson Lab. The first complete magnetic field simulation of the Super High Momentum Spectrometer (SHMS) is presented with a focus on primary electron beam deflection downstream of the target. The SHMS consists of a superconducting horizontal bending magnet (HB) and three superconducting quadrupole magnets. The HB allows particles scattered at an angle of 5:5 deg to the beam line to be steered into the quadrupole magnets which make up the optics of the spectrometer. Without mitigation, remnant fields from the SHMS may steer the unscattered beam outside of the acceptable envelope on the beam dump and limit beam operations at small scattering angles. A solution is proposed using optimal placement of a minimal amount of shielding iron around the beam line.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Neutron transport methods for multiphysics heterogeneous reactor core simulation in Griffin

Griffin is a reactor physics application based on the Multiphysics Object-Oriented Simulation Environment (MOOSE). This work discloses the methods, algorithms, and implementation for simulating heterogeneous reactor dynamics models. Griffin utilizes a discontinuous finite-element method with discrete ordinates (DFEM-S ) to discretize the field variable of the multigroup neutron transport equation. Multiphysics feedback is handled using two-step tabulated cross-section methodology. Feedback quantities are evaluated using the MOOSE-MultiApp system to couple various engineering phenomena, such as heat conduction and thermal fluids. The multiphysics DFEM-S system is solved using fixed-point iteration with a fully asynchronous parallel sweeper, unstructured coarse-mesh finite difference acceleration, and a multi-timescale improved quasi-static method scheme. The implementation is applied to a multiphysics microreactor model, with two transients: one initiated by a single heat-pipe failure and another by control drum rotation. Importantly, these examples demonstrate the ability of Griffin to tractably solve the neutron transport equation considering seven independent variables and feedback.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Comparative analysis of plasticity-based GND density estimation methods in crystal plasticity finite element models

In crystal plasticity finite element (CPFE) simulations, accurately quantifying geometrically necessary dislocations (GNDs) is critical for capturing strain gradients in polycrystals. We compare different methods for quantifying GNDs, all of which originate from the Nye tensor, which is computed as the curl of the plastic deformation gradient. The projection technique directly decomposes the Nye tensor onto individual screw and edge dislocation components to compute GNDs. This approach requires converting a nine-component Nye tensor into densities for a larger number of dislocation systems, a fundamentally underdetermined (non-unique) process, which is resolved using L2 minimization. In contrast, when employing CPFE analysis, one could directly compute dislocation densities on each slip system using shear gradients. Projection and slip gradient methods are compared with respect to their prediction of GNDs with changing grain size, strain, and grain neighborhoods, including multigrain junctions. Although these techniques match analytical GND densities for single slip, single crystal deformation, and are consistent with anticipated overall GND trends, we find that the GND densities from projection techniques are significantly lower than those predicted from CPFE-based slip gradients in polycrystals. A suggested improvement of only using the active dislocation systems in the projection technique almost entirely resolved this mismatch.

Crystal plasticity↗
DOE OSTI2022

An immersed interface method for the 2D vorticity-velocity Navier-Stokes equations with multiple bodies

We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by nonconvex immersed bodies, multiply connected domains, and the calculation of force distributions on immersed surfaces. The immersed interface method is re-interpreted as a polynomial extrapolation of flow quantities and boundary conditions into the immersed solid bodies, reducing computational cost and enabling simulations with nonconvex bodies that could not be discretized with previous immersed interface methods. In the flow, the vorticity transport equation is discretized using a conservative finite difference scheme and explicit Runge-Kutta time integration. The velocity reconstruction problem is transformed to a scalar Poisson equation that is discretized with conservative finite differences, and solved using an FFT-accelerated iterative algorithm. The use of conservative differencing throughout leads to exact enforcement of a discrete Kelvin's theorem, allowing for simulations with multiply connected domains and outflow boundaries that have challenged other immersed interface vortex methods. We also explore novel methods for recovering time-dependent pressure distributions on immersed bodies within a vorticity-based method and present a novel control volume formulation for recovering aerodynamic moments from only the vorticity and velocity fields. The method achieves second order spatial accuracy and third order temporal accuracy, and is validated on a variety of 2D flows in internal and free-space domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Examination of Mean Stress Calculation Approaches in Rock Mechanics

The mean stress, as a fundamental statistical property of a group of stress data, is essential for stress variability characterisation. However, currently in rock mechanics, the mean stress is customarily and erroneously calculated by separately averaging the principal stress magnitudes and orientations. In order to draw the attention of our community to the appropriate approach for stress variability characterisation, here we compare the customary scalar/vector mean with that obtained by the mathematically rigorous tensorial approach—the Euclidean mean. Calculation of mean stress using both a small group of actual in situ stress measurement results and a large group of simulated stress data (obtained using the combined finite– discrete element method, FEMDEM) demonstrates that the two approaches yield different results. Further investigation of these results shows that the scalar/vector approach may yield non-unique and non-orthogonal mean principal stresses, and these may deviate significantly from those of the Euclidean mean. Our calculations and comparisons reveal that the scalar/ vector approach is deficient because it processes the principal stress magnitudes and orientations separately as independent quantities and ignores the connection between them. Conversely, the tensorial approach appropriately averages the tensors that simultaneously carry not only the information of stress magnitudes and orientations, but also the inherent relations between them. Therefore, arbitrarily using scalar/vector mean stress of in situ stress measurements as input in further rock engineering analyses may yield significantly erroneous results. Finally, we advise that stress data should be statistically processed in a tensorial manner using tensors referred to a common Cartesian coordinate system.

58 GEOSCIENCES↗
DOE OSTI2020

A matrix-free hyperviscosity formulation for high-order ALE hydrodynamics

The numerical approximation of compressible hydrodynamics is at the core of high-energy density (HED) multiphysics simulations as shocks are the driving force in experiments like inertial confinement fusion (ICF). In this work, we describe our extension of the hyperviscosity technique, originally developed for shock treatment in finite difference simulations, for use in arbitrarily high-order finite element methods for Lagrangian hydrodynamics. Hyperviscosity enables shock capturing while preserving the high-order properties of the underlying discretization away from the shock region. Specifically, we compute a high-order term based on a product of the mesh length scale to a high power scaled by a hyper-Laplacian operator applied to a scalar field. We then form the total artificial viscosity by taking a non-linear blend of this term and a traditional artificial viscosity term. We also present a matrix-free formulation for computing the finite element based hyper-Laplacian operator. Such matrix-free methods have superior performance characteristics compared to traditional full matrix assembly approaches and offer advantages for GPU based HPC hardware. We demonstrate the numerical convergence of our method and its application to complex, multi-material ALE simulations on high-order (curved) meshes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Monte Carlo/CFD Coupling for Accurate Modeling of the Delayed Neutron Precursors and Compressibility Effects in Molten Salt Reactors

Multiphysics reactor analysis has become one of the leading activities of most nuclear engineering research groups. Coupled neutronics and thermal/hydraulics (T/H) simulations have traditionally been performed by adopting deterministic transport tools and reactor system T/H codes. The main reason for avoiding higher fidelity numerical methods like continuous-energy Monte Carlo analysis has been the high computational cost of coupled, full-scale simulations. Nowadays, high fidelity multiphysics simulations represent a hot research topic, with several applications involving advanced nuclear systems. Liquid fuel Molten Salt Reactors (MSRs) feature peculiar physical phenomena that are not present in solid fuel reactors. Some of these phenomena are not correctly resolved by legacy reactor physics tools, and require specific treatments. This work focuses in particular on the analysis of the effect of the delayed neutron precursors drift and the impact of liquid fluid thermal expansion and compressibility in postulated criticality excursion transients in fast-spectrum MSRs. A new modeling tool based on a Monte Carlo approach for neutronics (Serpent code) coupled to a Computational Fluid Dynamic (CFD) analysis (OpenFOAM) was developed to obtain accurate modeling and simulation of these phenomena. The development of the Serpent Monte Carlo code [1] at VTT in the past few years has made this code particularly attractive for performing multiphysics studies. The availability of a flexible multiphysics interface, on-the-fly Doppler broadening and density-based collision rejection, and Delta-tracking, proved of paramount importance for the computationally efficient performance of coupled Monte Carlo/CFD calculations [2]. OpenFOAM is a C++ multiphysics toolkit featured by automatic matrix construction and solution capabilities for scalar and vector partial differential equations (PDEs), adopting several possible differencing and interpolation schemes, based on the Finite-Volume method. The ease of implementing the constitutive equations of different physical phenomena makes OpenFOAM particularly suitable for the modeling of complex coupled phenomena. In the past, several research activities proposed the adoption of both Serpent and OpenFOAM for the modeling and simulation of MSRs and the associated fuel cycles. In this work, these tools have been internally coupled for the steady-state and transient analysis of fast-spectrum systems, accounting for the effect of delayed neutron precursors transport and the salt thermal expansion and compressibility.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2018

Comparative Study of Finite Element Methods Using the Time-Accuracy-Size(TAS) Spectrum Analysis

We present a performance analysis appropriate for comparing algorithms using different numerical discretizations. By taking into account the total time-to-solution, numerical accuracy with respect to an error norm, and the computation rate, a cost-benefit analysis can be performed to determine which algorithm and discretization are particularly suited for an application. This work extends the performance spectrum model in for interpretation of hardware and algorithmic tradeoffs in numerical PDE simulation. As a proof-of-concept, popular finite element software packages are used to illustrate this analysis for Poisson’s equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Method and apparatus for shape-based energy analysis of solids

A method of evaluating response of a physical structure to external stimulus includes defining a mesh of finite elements, each defined by edges, for a model of the physical structure. The method includes identifying a governing differential equation and associated complementary functions, which are each associated with a scalar multiplier. The method includes generating an energy optimization model that minimizes a difference between internal and external energies of the finite elements. The internal energy is based on strain energy in a volume defined by the edges of the finite element and resulting from deformations by the complementary functions. The external energy of each finite element is based on external work done by the external stimulus acting on the finite element as deformed by the complementary functions. The method includes solving the energy optimization model for the scalar multipliers and calculating a resulting parameter of interest of the physical structure.

42 ENGINEERING↗
DOE OSTI2018

Finite element solution of MHD power-law fluid with slip velocity effect and non-uniform heat source/sink

The laminar steady boundary layer flow of an incompressible MHD Power-law fluid past a continuously moving surface is investigated numerically. The study involves the influence of surface slip and non-uniform heat source/sink on the flow and heat transfer. The governing boundary layer flow equations are transformed into non-dimensional, non-linear coupled ordinary differential equations with the help of suitable similarity transformations. The Galerkin finite element method is implemented to crack the resulting system. The impact of different involved physical parameters is exhibited on the dimensionless velocity profile, temperature distributions and rate of heat transfer in graphical and tabular forms for pseudoplastic and dilatant fluids. The local Nusselt number is found to be the decreasing function of slip parameter, temperature and space-dependent heat sink parameter whereas it increases with increasing values of temperature and space dependent heat source parameter. The problem has important application in attaining the sustainable heat transfer rate for the cooling of fluids, especially in heat exchangers used frequently in chemical industry, in order to increase the trustworthiness of a system, as it removes high heat loads from these systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Thermal Test Suite for Code Maintenance and Validation of Diablo

This document describes a series of test problems that ensure that the Thermal capabilities of Diablo are working correctly. Diablo utilizes the Finite Element Method to discretize the problem in space and a trapezoidal rule finite difference scheme to discretize the problem in time. This suite will test the codes capabilities to handle various boundary conditions, source terms, and initial conditions. It will also test the coupling between thermal and solid effects, and the use of various linear and nonlinear solvers.

42 ENGINEERING↗
DOE OSTI2019

Experimental Study of the 3 He and Neutron Spin Structure at Low Q 2 and The Upgrade of the JLab Polarized 3 He Target

In the scattering process off a nuclear or nucleon target, the Gerasimov-Drell-Hearn (GDH) sum rule for real photons (Q 2 =0 where Q 2 &equiv; -q 2 with q the photon's 4-momentum) relates static properties of the target particle's ground state to dynamic properties of all its excited states. On the other side of the Q 2 spectrum, the Bjorken sum rule holds in the Bjorken limit Q 2 &rarr; &infin;. Bjorken sum rule relates the final structure functions of the proton and neutron to the nucleon axial coupling constant in weak decay. These two sum rules belong to domains where calculations are achievable but use different degrees of freedom: hadronic degrees of freedom at low Q 2 versus partonic degrees of freedom at intermediate Q 2 . Meanwhile, different methods have been used to connect the two sum rules at finite Q 2 values: Chiral Perturbation Theory is used to expand the GDH sum rule while Operator Product Expansion is used to expand the Bjorken sum rule. In recent decades, improvements in polarized beam and polarized target techniques have made it possible to test theoretical predictions in the intermediate Q 2 region. During the Jefferson Lab (JLab) Hall A E97110 experiment, a precise measurement of polarized cross sections was performed at 0.02 < Q 2 < 0.3 GeV 2 using a polarized 3 He target as an effective polarized neutron target. The measured data allowed us to test predictions of Chiral Perturbation Theory at very low Q 2 . Furthermore, an extrapolation to the real photon point Q 2 =0 tests the GDH sum rule on the neutron. In order to reach the small angles necessary for the low Q 2 range, a new septum magnet was installed in Hall A for this experiment. Unfortunately, the magnet was mis-wired during initial running. There were therefore two periods for this experiment: the first period had the defective magnet due to mis-wiring; while in the second period, the magnet had been fixed and was working properly. The cross sections and the asymmetries for the first period must be extracted using a difficult and unusual method employing focal plane variables in the spectrometer. In the work described in this thesis, the target-plane and focal-plane method will be established first and confirmed by elastic scattering cross section measurements from carbon foil and 3 He targets. Cross sections and asymmetries of inelastic scattering were then extracted using the same method, which constitute the main physics results of this thesis. Preliminary results on ITT , the integral of the polarized cross section, were also extracted and are presented in this thesis. In addition to the data analysis of E97110, this thesis includes instrumentation work performed on the polarized 3 He target at JLab. For the 12 GeV program of JLab, the polarized 3 He target is being upgraded to satisfy new experimental requirements. The new target is a convection-based cell with two transfer tubes rather than a single transfer tube as in the former 6 GeV design. The first stage of the target upgrade aims to produce a 40 cm long, 10 amg target that can withstand 30 &mu;A of electron beam current with an in-beam polarization of 55%, doubling the figure-of-merit from the 6 GeV time. Several studies were conducted at the Test Lab of JLab on the new convection cell. Work and improvement done on the Pulse Nuclear Magnetic Resonance (NMR) polarimetry and its test results will be presented. As this thesis is written, the target is being installed in Hall C of JLab in preparation for a 6-month long running from November 2019 to May 2020.

Ton, Nguyen↗
DOE OSTI2017

Extension of the DIF3D Code for Molten Salt Reactor Analysis

The molten salt reactor (MSR) with the fuel dissolved into the liquid salt has been selected as one of the six Generation-IV reactors due to its excellent characteristics in the aspects of sustainability, economy, passive safety, and resource utilization. In a MSR, the fuel salt is circulated throughout the whole system and thus some of delayed neutron precursors generated in the core decay in position of low importance or even out of the core. As a result, the multiplication factor (k-eff) of MSR is smaller than that of a reactor of stationary fuel when all the other conditions are same. Therefore, the neutronics code developed for stationary fuel cannot be applied directly to MSR analysis. In this paper, we describe the extension and application of the DIF3D code to MSR neutronics analysis. The DIF3D code system is a multi-group steady-state neutron diffusion and transport theory solver. It provides three flux solution options: finite-difference diffusion theory, nodal diffusion theory, and variational nodal transport theory methods. Eigenvalue, adjoint, fixed source and criticality (concentration) search problems are permitted. The DIF3D code has recently been modified to model the flowing fuel. To verify the new capability of DIF3D, the MSFR [4] core was analyzed with a wide range of velocity field of fuel salt and time spent outside of the core.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2019

Robust Approaches to Handling Complex Geometries with Galerkin Difference Methods

The Galerkin difference (GD) basis is a set of continuous, piecewise polynomials defined using a finite-difference-like grid of degrees of freedom. The one dimensional GD basis functions are naturally extended to multiple dimensions using a tensor product construction on quadrilateral elements. The GD basis can be used to define the solution space for a discontinuous Galerkin finite element discretization of partial differential equations. In this work we propose two approaches to handling complex geometries within this setting: (1) using nonconforming, curvilinear GD elements and (2) coupling affine GD elements with curvilinear simplicial elements. In both cases the (semidiscrete) discontinuous Galerkin method is provably energy stable even when variational crimes are committed. Additionally, for both element types a weight-adjusted mass matrix is used, which ensures that only the reference mass matrix must be inverted. We also present sufficient conditions on the treatment of metric terms for the curvilinear, nonconforming GD elements to ensure that the scheme is both constant preserving and conservative. Numerical experiments confirm the stability results and demonstrate the accuracy of the coupled schemes.

97 MATHEMATICS AND COMPUTING↗