Search NASA⌕ Search

SEARCH · Search NASA

Results for “Infinite Medium”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Analytic Sensitivity Coefficients for General Multigroup Infinite Medium k-Eigenvalue Problems

The general multigroup infinite medium k-eigenvalue neutron transport equation is used to derive analytic expressions for the infinite medium k-eigenvalue, the scalar neutron flux and adjoint, and the sensitivity of $k$ ∞ to perturbations in the multigroup nuclear data of a single species isotropic elastic scattering material. In the appendix, we present the multigroup nuclear data for U-235 and U-238 along with the corresponding k-eigenvalue, flux, adjoint, and sensitivity profiles, which include the sensitivity of $k$ ∞ to the total, fission, capture, and scattering macroscopic cross sections as well as to the group-to-group scattering cross section matrix, group neutron production, and the unconstrained and constrained fission neutron energy distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Analytic Sensitivity Coefficients for General Multigroup Infinite Medium k-Eigenvalue Problems

This work presents a general set of equations that can be used to rapidly generate new benchmarks to verify nuclear data sensitivity calculations. The general multigroup infinite medium k-eigenvalue neutron transport equation is used to derive analytic expressions for the infinite medium k-eigenvalue, the scalar neutron flux and adjoint flux, and the sensitivity of k∞ to perturbations in the multigroup nuclear data of a single species, isotropic and elastic scattering, material. The multigroup nuclear data for U-235 and U-238 is presented along with their corresponding k-eigenvalues, forward flux, adjoint flux, and sensitivity profiles, which include the sensitivity of k∞ to the total, fission, capture, and scattering macroscopic cross sections as well as to the group-to-group scattering cross section matrix, group-wise fission neutron production, and the unconstrained and constrained fission neutron energy distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2012

Calculating alpha Eigenvalues in a Continuous-Energy Infinite Medium with Monte Carlo

The α eigenvalue has implications for time-dependent problems where the system is sub- or supercritical. We present methods and results from calculating the α-eigenvalue spectrum for a continuous-energy infinite medium with a simplified Monte Carlo transport code. We formulate the α-eigenvalue problem, detail the Monte Carlo code physics, and provide verification and results. We have a method for calculating the α-eigenvalue spectrum in a continuous-energy infinite-medium. The continuous-time Markov process described by the transition rate matrix provides a way of obtaining the α-eigenvalue spectrum and kinetic modes. These are useful for the approximation of the time dependence of the system.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Calculating infinite-medium {alpha}-eigenvalue spectra with a transition rate matrix method

The time-dependent behavior of the energy spectrum in neutron transport was investigated with a formulation, based on continuous-time Markov processes, for computing {alpha}-eigenvalues and eigenvectors in an infinite medium. For this, a research Monte Carlo code called TORTE was created and used to estimate elements of a transition rate matrix. TORTE is capable of using both multigroup and continuous-energy nuclear data, and verification was performed. Eigenvalue spectra for infinite homogeneous mixtures were obtained and an eigenfunction expansion was used to investigate transient behavior of the neutron energy spectrum. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Calculating infinite-medium α-eigenvalue spectra with Monte Carlo using a transition rate matrix method

The time-dependent behavior of the energy spectrum in neutron transport was investigated with a formulation, based on continuous-time Markov processes, for computing α eigenvalues and eigenvectors in an infinite medium. In this study, a research Monte Carlo code called “TORTE” (To Obtain Real Time Eigenvalues) was created and used to estimate elements of a transition rate matrix. TORTE is capable of using both multigroup and continuous-energy nuclear data, and verification was performed. Eigenvalue spectra for infinite homogeneous mixtures were obtained, and an eigenfunction expansion was used to investigate transient behavior of the neutron energy spectrum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2012

Application of the discrete generalized multigroup method to ultra-fine energy mesh in infinite medium calculations

The Discrete Generalized Multigroup (DGM) method uses discrete Legendre orthogonal polynomials to expand the energy dependence of the multigroup neutron transport equation. This allows a solution on a fine energy mesh to be approximated for a cost comparable to a solution on a coarse energy mesh. The DGM method is applied to an ultra-fine energy mesh (14,767 groups) to avoid using self-shielding methodologies without introducing the cost usually associated with such energy discretization. Results show DGM to converge to the reference ultra-fine solution after a small number of recondensation steps for multiple infinite medium compositions. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2014

Explicit solutions of the radiative transport equation in the P{sub 3} approximation

Purpose: Explicit solutions of the monoenergetic radiative transport equation in the P{sub 3} approximation have been derived which can be evaluated with nearly the same computational effort as needed for solving the standard diffusion equation (DE). In detail, the authors considered the important case of a semi-infinite medium which is illuminated by a collimated beam of light. Methods: A combination of the classic spherical harmonics method and the recently developed method of rotated reference frames is used for solving the P{sub 3} equations in closed form. Results: The derived solutions are illustrated and compared to exact solutions of the radiative transport equation obtained via the Monte Carlo (MC) method as well as with other approximated analytical solutions. It is shown that for the considered cases which are relevant for biomedical optics applications, the P{sub 3} approximation is close to the exact solution of the radiative transport equation. Conclusions: The authors derived exact analytical solutions of the P{sub 3} equations under consideration of boundary conditions for defining a semi-infinite medium. The good agreement to Monte Carlo simulations in the investigated domains, for example, in the steady-state and time domains, as well as the short evaluation time needed suggests that the derived equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Here, we study convergence of the integral transport matrix method (ITMM) based on a parallel block Jacobi (PBJ) iterative strategy for solving particle transport problems. The ITMM is a spatial domain decomposition method proposed for massively parallel computations. AFourier analysis of the PBJ-based iterations applied to SN diamond-difference equations in 1D slab and 2D Cartesian geometries is performed. It is carried out for infinite-medium problems with homogeneous material properties. To analyze the performance of the ITMM with the PBJ algorithm and evaluate its potential in scalability we consider a limiting case of one spatial cell per subdomain. The analysis shows that in such limit the spectral radius of the iteration method is one without regard to values of the scattering ratio and optical thickness of the spatial cells. This implies lack of convergence in infinite medium. Numerical results of finite-medium problems are presented. They demonstrate effects of finite size of spatial domain on the performance of the iteration algorithm as well as its asymptotic behavior when the extent of the spatial domain increases. Finally, these numerical experiments also show that for finite domains iterative convergence to a finite criterion is achievable in a multiple of the sum of number of cells in each dimension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Celeritas: Accelerating Geant4 with GPUs

Celeritas [1] is a new Monte Carlo (MC) detector simulation code designed for computationally intensive applications (specifically, High Lumi- nosity Large Hadron Collider (HL-LHC) simulation) on high-performance heterogeneous architectures. In the past two years Celeritas has advanced from prototyping a GPU-based single physics model in infinite medium to implementing a full set of electromagnetic (EM) physics processes in complex geometries. The current release of Celeritas, version 0.3, has incorporated full device-based navigation, an event loop in the presence of magnetic fields, and detector hit scoring. New functionality incorporates a scheduler to offload electromagnetic physics to the GPU within a Geant4-driven simulation, enabling integration of Celeritas into high energy physics (HEP) experimental frameworks such as CMSSW. On the Summit supercomputer, Celeritas performs EM physics between 6 and 32 faster using the machine’s Nvidia GPUs compared to using only CPUs. When running a multithreaded Geant4 ATLAS test beam application with full hadronic physics, using Celeritas to accelerate the EM physics results in an overall simulation speedup of 1.8–2.3× on GPU and 1.2× on CPU.

Johnson, Seth R.↗
DOE OSTI2019

Optical-property coefficient estimation of bulky medium in experiments with a succinctly analytical calculation

Diffuse optical imaging enables to reconstruct distribution of optical properties, absorption and scattering coefficients, in tissue for breast cancer detection based on diffusion equation with the help of the initial guess obtained from measured data. To estimate the initial guess of the optical-property coefficients, an analytical solution of diffusion equation can be used and compared with the measured data. The analytical solution for a homogeneous infinite medium can be obtained in the frequency domain, expressing that the photon intensity and the phase lag relative to the distance between source and detector in a linear relationship. In this study, a succinct calculation using the trigonometric relation is proposed to estimate the optical-property coefficients. A tank-type and a cylinder Lipovenoes phantoms with two concentrations of 1.25% and 2.5% are employed and measured for verification. It is found that the method proposed here shows better results and results in estimation errors of 0–14.81% for μ{sub a} and 20–42% for μ{sub s}′.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Design of Phosphor Thermometry System for Transient High Heat Flux Surface Thermometry

Abstract: A transformative calibration methodology is presented for predicting transient surface temperatures in a thermally conducting medium from in-depth, time-varying temperature measurements. The surface temperature is resolved using two experimental runs and a newly devised first-kind Volterra integral equation. The first experimental run involves calibration with known surface temperature while the second run involves resolving the surface temperature of interest through the ill-posed integral equation. This paper presents the concept genesis and numerically demonstrates the concept for feasibility, robustness, stability and accuracy. From this demonstration, we propose to implement surface placed thermographic phosphors in the calibration stage of the inverse method for estimating the required surface temperature. As a preliminary study, we consider transient, constant property, onedimensional heat conduction in a semi-infinite medium. It is mathematically demonstrated that a Volterra integral equation of the first kind is developed for estimating the surface temperature using a calibrated system (host material and sensor). Sensor characterization, explicit sensor positioning and thermophysical properties are implicitly contained in the new calibration integral equation. The calibration integral equation displays only four terms; namely, the measured front surface temperature and corresponding measured in-depth temperature response associated with the calibration run; and, the unknown surface temperature and its measured in-depth temperature response associated with the second run. Preliminary numerical results indicate the merit of the concept. This paper suggests using thermographic phosphors for estimating the surface temperature in the calibration portion of the process owing to their rapid thermal response, good surface thermal contact characteristics and lack of capacitance for assuring minimal delay. Though the present paper describes the theoretical basis for resolving such problems, it is intended for near-term application using the UTK s high-heat flux laser facility which is presently under development

Fluorescence thermometry↗
DOE OSTI2018

A mesh-independent method for planar three-dimensional crack growth in finite domains: A mesh-independent method for crack growth in 3D finite domains

The discrete crack mechanics (DCM) method is a dislocation-based crack modeling technique where cracks are constructed using Volterra dislocation loops. The method allows for the natural introduction of displacement discontinuities, avoiding numerically expensive techniques. Mesh dependence in existing computational modeling of crack growth is eliminated by utilizing a superposition procedure. The elastic field of cracks in finite bodies is separated into two parts: the infinite-medium solution of discrete dislocations and an finite element method solution of a correction problem that satisfies external boundary conditions. In the DCM, a crack is represented by a dislocation array with a fixed outer loop determining the crack tip position encompassing additional concentric loops free to expand or contract. Solving for the equilibrium positions of the inner loops gives the crack shape and stress field. The equation of motion governing the crack tip is developed for quasi-static growth problems. Additionally, convergence and accuracy of the DCM method are verified with two- and three-dimensional problems with well-known solutions. Crack growth is simulated under load and displacement (rotation) control. In the latter case, a semicircular surface crack in a bent prismatic beam is shown to change shape as it propagates inward, stopping as the imposed rotation is accommodated.

42 ENGINEERING↗
DOE OSTI2013

Numerical solution of the time dependent neutron transport equation by the method of the characteristics

This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2014

The iterative thermal emission method: A more implicit modification of IMC

For over 40 years, the Implicit Monte Carlo (IMC) method has been used to solve challenging problems in thermal radiative transfer. These problems typically contain regions that are optically thick and diffusive, as a consequence of the high degree of “pseudo-scattering” introduced to model the absorption and reemission of photons from a tightly-coupled, radiating material. IMC has several well-known features that could be improved: a) it can be prohibitively computationally expensive, b) it introduces statistical noise into the material and radiation temperatures, which may be problematic in multiphysics simulations, and c) under certain conditions, solutions can be nonphysical, in that they violate a maximum principle, where IMC-calculated temperatures can be greater than the maximum temperature used to drive the problem. We have developed a variant of IMC called iterative thermal emission IMC, which is designed to have a reduced parameter space in which the maximum principle is violated. ITE IMC is a more implicit version of IMC in that it uses the information obtained from a series of IMC photon histories to improve the estimate for the end of time step material temperature during a time step. A better estimate of the end of time step material temperature allows for a more implicit estimate of other temperature-dependent quantities: opacity, heat capacity, Fleck factor (probability that a photon absorbed during a time step is not reemitted) and the Planckian emission source. We have verified the ITE IMC method against 0-D and 1-D analytic solutions and problems from the literature. These results are compared with traditional IMC. We perform an infinite medium stability analysis of ITE IMC and show that it is slightly more numerically stable than traditional IMC. We find that significantly larger time steps can be used with ITE IMC without violating the maximum principle, especially in problems with non-linear material properties. The ITE IMC method does however yield solutions with larger variance because each sub-step uses a different Fleck factor (even at equilibrium)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Stability analysis of nonlinear two-grid method for multigroup neutron diffusion problems

We present theoretical analysis of a nonlinear acceleration method for solving multigroup neutron diffusion problems. This method is formulated with two energy grids that are defined by (i) fine-energy groups structure and (ii) coarse grid with just a single energy group. The coarse-grid equations are derived by averaging of the multigroup diffusion equations over energy. The method uses a nonlinear prolongation operator. We perform stability analysis of iteration algorithms for inhomogeneous (fixed-source) and eigenvalue neutron diffusion problems. To apply Fourier analysis the equations of the method are linearized about solutions of infinite-medium problems. The developed analysis enables us to predict convergence properties of this two-grid method in different types of problems. Numerical results of problems in 2D Cartesian geometry are presented to confirm theoretical predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Formulations and analysis of Compton scattering for deterministic thermal radiation transport

In high-energy-density physics at low densities and high temperatures, Compton scattering can be the dominant interaction mechanism between thermal radiation and the material. Boson statistics leads to induced scattering, where the rate of scattering is proportional to the square of the photon intensity. To explore the importance of this nonlinear effect in the context of thermal radiative transfer, in this work we formulate several linear approximations to the scattering rate and compare them to the proper nonlinear rate in an infinite-medium setting. With the goal of implementing Compton scattering in a radiation transport code, we study heating-rate accuracy and iterative convergence properties for the linear methods as we vary the fidelity of the discretization in photon frequency. We find the equilibrium out-scattering formulation to be the most accurate linear method, with heating rate errors around 15% when the radiation is heating the material and up to 50% when the radiation is cooling the material.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Efficient smoothed particle radiation hydrodynamics I: Thermal radiative transfer

This work presents efficient solution techniques for radiative transfer in the smoothed particle hydrodynamics discretization. Two choices that impact efficiency are how the material and radiation energy are coupled, which determines the number of iterations needed to converge the emission source, and how the radiation diffusion equation is solved, which must be done in each iteration. The coupled material and radiation energy equations are solved using an inexact Newton iteration scheme based on nonlinear elimination, which reduces the number of Newton iterations needed to converge within each time step. During each Newton iteration, the radiation diffusion equation is solved using Krylov iterative methods with a multigrid preconditioner, which abstracts and optimizes much of the communication when running in parallel. The code is verified for an infinite medium problem, a one-dimensional Marshak wave, and a two and three-dimensional manufactured problem, and exhibits first-order convergence in time and second-order convergence in space. For these problems, the number of iterations needed to converge the inexact Newton scheme and the diffusion equation is independent of the number of spatial points and the number of processors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗