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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
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DOE OSTI2017

Universal Method of Modeling Linear Stationary Physical Fields

The aim of this paper is to develop a method, described earlier, of solving quantum-mechanical problems into a universal numerical method of modeling fields of various physical nature. This method is based on reducing the initial equation of mathematical physics describing a given physical field to a simpler inhomogeneous equation with a known fundamental solution. This equation is then transformed into an inhomogeneous integral equation with a kernel expressed in terms of the known fundamental solution. The obtained integral equation with boundary conditions is solved numerically. To confirm the efficiency of the proposed numerical method, a two-dimensional and a three-dimensional boundary value problem with known solutions have been solved. Another important illustration of the efficiency of the proposed method is the solution of quantum-mechanical problems for one-dimensional and two-dimensional quantum oscillators. It is shown that the considered method allows one to find the energy eigenvalues and the eigenfunctions with acceptable accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves

We model liquid–gas flows with cavitation by a variant of the six-equation single-velocity two-phase model with stiff mechanical relaxation of Saurel–Petitpas–Berry (Saurel et al., 2009) [9]. In our approach we employ phasic total energy equations instead of the phasic internal energy equations of the classical six-equation system. This alternative formulation allows us to easily design a simple numerical method that ensures consistency with mixture total energy conservation at the discrete level and agreement of the relaxed pressure at equilibrium with the correct mixture equation of state. Temperature and Gibbs free energy exchange terms are included in the equations as relaxation terms to model heat and mass transfer and hence liquid–vapor transition. The algorithm uses a high-resolution wave propagation method for the numerical approximation of the homogeneous hyperbolic portion of the model. In two dimensions a fully-discretized scheme based on a hybrid HLLC/Roe Riemann solver is employed. Thermo-chemical terms are handled numerically via a stiff relaxation solver that forces thermodynamic equilibrium at liquid–vapor interfaces under metastable conditions. We present numerical results of sample tests in one and two space dimensions that show the ability of the proposed model to describe cavitation mechanisms and evaporation wave dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A boundary integral method for numerical computation of radar cross section of 3D targets using hybrid BEM/FEM with edge elements

This contribution presents the boundary integral formulation for numerical computation of time-harmonic radar cross section for 3D targets. Method relies on hybrid edge element BEM/FEM to compute near field edge element coefficients that are associated with near electric and magnetic fields at the boundary of the computational domain. Special boundary integral formulation is presented that computes radar cross section directly from these edge element coefficients. Consequently, there is no need for near-to-far field transformation (NTFFT) which is common step in RCS computations. By the end of the paper it is demonstrated that the formulation yields accurate results for canonical models such as spheres, cubes, cones and pyramids. Method has demonstrated accuracy even in the case of dielectrically coated PEC sphere at interior resonance frequency which is common problem for computational electromagnetic codes. - Graphical abstract: - Highlights: • Hybrid edge element BEM/FEM is used to find edge element coefficients. • New formulation for RCS computation directly from edge element coefficients is presented. • Formulation is tested on canonical cases and on coated dielectric sphere at interior resonance frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Verification and Demonstration of One-Dimensional Freezing Model in SAM for Salt-Cooled Reactor Analysis Applications

This work presented the development and implementation of the one-dimensional freezing model in system analysis code, SAM, as well as code verification, and code demonstration during a postulated overcooling transient, for fluoride salt-cooled high-temperature reactor (FHR) system and safety analysis applications. The paper at first summarized the freezing model, finite element numerical method, and special numerical treatment for handling phase appearance/disappearance. Analytical solutions were derived for two cases (with and without solid walls) for code verifications purpose. As expected, numerical results predicted by the SAM code agreed very well with the analytical solution. A code demonstration was then performed on a postulated protected overcooling event transient of a generic reference PB-FHR design. The code was found to successfully predict salt freezing during such a postulated event. However, due to lack of salt freezing testing data, code validation has not been performed in this work, which will be pursued in later studies when such data becomes available.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Comparing the MELCOR Aerosol Deposition Model with Exact Analytical Solutions

Exact analytical solutions are presented for the evolution of the aerosol particle mass density function in a control volume for particle deposition due to gravitational settling, thermophoresis, and diffusion. The solutions are for arbitrary initial mass density functions and are applied for an initial lognormal density function. Integration of these solutions provides the suspended mass in the control volume as a function of time. These solutions serve as an exact benchmark to assess the accuracy of numerical methods. For the numerical algorithm used in MELCOR, excellent agreement is obtained for gravitational settling, diffusive deposition, and thermophoretic deposition for the suspended aerosol mass. In all cases, the default number of discrete particle size bins of 10 is shown to converge, with hardly any advantage to using 20 size bins.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

The First Tri-Lab Workshop on Formal Verification: Capabilities, Challenges, Research Opportunities, and Exemplars

The First Tri-Lab Workshop on Formal Verification was held in Santa Fe, New Mexico, on December 5th, 2023. This workshop gathered staff from Sandia, Los Alamos, and Lawrence Livermore National Laboratories and NASA’s Jet Propulsion Laboratory. This report summarizes and expands on the presentations given and discussion had at this workshop. In this report, we describe the current capabilities and research needs related to formal methods at the NNSA labs. In particular, we identify medium-term and long-term research gaps in programming languages, formalization efforts of complex systems, embedded systems verification, hardware verification, cybersecurity, formal methods usability, workflows, numerical methods, the use of formal methods for artificial intelligence (and its converse, artificial intelligence for formal methods), and collaboration opportunities and considerations on these topics. We conclude with a small number of exemplar research problems related to these topics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Numerical integration method for triple integrals using the second kind Chebyshev wavelets and Gauss–Legendre quadrature

In this paper, a computational method combining the second kind Chebyshev wavelets and Gauss–Legendre quadrature is proposed for numerical integrations of arbitrary functions over regions like cuboid, tetrahedron, cylinder, cone, paraboloid and ellipsoid. Gauss–Legendre quadrature is used to convert a triple integral into a double integral and integral regions are transformed to the standard integration region by linear and nonlinear transformation. Moreover, convergence and accuracy estimation of the second kind Chebyshev wavelets expansion of two dimensions is given. Illustrative examples have been demonstrated to show the applicability and accuracy of the present method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On One Numerical-Analytic Method for the Solution of One-Dimensional Quasistatic Problems of Thermoelasticity for Thermosensitive Bodies of Simple Geometry

We propose a procedure for the numerical-analytic solution of one-dimensional problems of thermoelasticity for bodies of simple geometry based on the representation of temperature dependences of the physicomechanical characteristics of materials in the form of piecewise constant functions of temperature and the application of the Kirchhoff substitution and the methods of generalized functions. This procedure enables us to study one-dimensional nonstationary thermal and quasistatic stress-strain states under the combined thermal and force action with controlled reliability.

36 MATERIALS SCIENCE↗
DOE OSTI2014

TH-E-BRE-01: A 3D Solver of Linear Boltzmann Transport Equation Based On a New Angular Discretization Method with Positivity for Photon Dose Calculation Benchmarked with Geant4

Purpose: The Linear Boltzmann Transport Equation (LBTE) solved through statistical Monte Carlo (MC) method provides the accurate dose calculation in radiotherapy. This work is to investigate the alternative way for accurately solving LBTE using deterministic numerical method due to its possible advantage in computational speed from MC. Methods: Instead of using traditional spherical harmonics to approximate angular scattering kernel, our deterministic numerical method directly computes angular scattering weights, based on a new angular discretization method that utilizes linear finite element method on the local triangulation of unit angular sphere. As a Result, our angular discretization method has the unique advantage in positivity, i.e., to maintain all scattering weights nonnegative all the time, which is physically correct. Moreover, our method is local in angular space, and therefore handles the anisotropic scattering well, such as the forward-peaking scattering. To be compatible with image-guided radiotherapy, the spatial variables are discretized on the structured grid with the standard diamond scheme. After discretization, the improved sourceiteration method is utilized for solving the linear system without saving the linear system to memory. The accuracy of our 3D solver is validated using analytic solutions and benchmarked with Geant4, a popular MC solver. Results: The differences between Geant4 solutions and our solutions were less than 1.5% for various testing cases that mimic the practical cases. More details are available in the supporting document. Conclusion: We have developed a 3D LBTE solver based on a new angular discretization method that guarantees the positivity of scattering weights for physical correctness, and it has been benchmarked with Geant4 for photon dose calculation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Application of Jacobian-free Newton–Krylov method in implicitly solving two-fluid six-equation two-phase flow problems: Implementation, validation and benchmark

This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3D code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. As a result, this in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.

42 ENGINEERING↗
DOE OSTI2015

A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elastic wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.

58 GEOSCIENCES↗
DOE OSTI2024

DG-IMEX method for a two-moment model for radiation transport in the $\mathscr{O}$($v$/$c$) limit

Here, we consider neutral particle systems described by moments of a phase-space density and propose a realizability-preserving numerical method to evolve a spectral two-moment model for particles interacting with a background fluid moving with nonrelativistic velocities. The system of nonlinear moment equations, with special relativistic corrections to $\mathscr{O}$($v$/$c$), expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. The model is conservative for the correct $\mathscr{O}$($v$/$c$) Eulerian-frame number density and is consistent, to $\mathscr{O}$($v$/$c$), with Eulerian-frame energy and momentum conservation. This model is closely related to the one promoted by Lowrie et al. and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The proposed numerical method is designed to preserve moment realizability, which guarantees that the moments correspond to a nonnegative phase-space density. The realizability-preserving scheme consists of the following key components: (i) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (ii) a discontinuous Galerkin (DG) phase-space discretization with carefully constructed numerical uxes; (iii) a realizability-preserving implicit collision update; and(iv) a realizability-enforcing limiter. In time integration, nonlinearity of the moment model necessitates solution of nonlinear equations, which we formulate as fixed-point problems and solve with tailored iterative solvers that preserve moment realizability with guaranteed global convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose a "spectral redistribution" scheme that promotes Eulerian-frame energy conservation. Through numerical experiments, we demonstrate the accuracy and robustness of this DG-IMEX method and investigate its Eulerian-frame energy conservation properties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

KiT-RT: An Extendable Framework for Radiative Transfer and Therapy

Here, in this article, we present Kinetic Transport Solver for Radiation Therapy (KiT-RT), an open-source C++-based framework for solving kinetic equations in therapy applications available at https://github.com/CSMMLab/KiT-RT . This software framework aims to provide a collection of classical deterministic solvers for unstructured meshes that allow for easy extendability. Therefore, KiT-RT is a convenient base to test new numerical methods in various applications and compare them against conventional solvers. The implementation includes spherical harmonics, minimal entropy, neural minimal entropy, and discrete ordinates methods. Solution characteristics and efficiency are presented through several test cases ranging from radiation transport to electron radiation therapy. Due to the variety of included numerical methods and easy extendability, the presented open-source code is attractive for both developers, who want a basis to build their numerical solvers, and users or application engineers, who want to gain experimental insights without directly interfering with the codebase.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Energy spectra of finite temperature superfluid helium-4 turbulence

A mesoscopic model of finite temperature superfluid helium-4 based on coupled Langevin-Navier-Stokes dynamics is proposed. Drawing upon scaling arguments and available numerical results, a numerical method for designing well resolved, mesoscopic calculations of finite temperature superfluid turbulence is developed. The application of model and numerical method to the problem of fully developed turbulence decay in helium II, indicates that the spectral structure of normal-fluid and superfluid turbulence is significantly more complex than that of turbulence in simple-fluids. Analysis based on a forced flow of helium-4 at 1.3 K, where viscous dissipation in the normal-fluid is compensated by the Lundgren force, indicate three scaling regimes in the normal-fluid, that include the inertial, low wavenumber, Kolmogorov k{sup −5/3} regime, a sub-turbulence, low Reynolds number, fluctuating k{sup −2.2} regime, and an intermediate, viscous k{sup −6} range that connects the two. The k{sup −2.2} regime is due to normal-fluid forcing by superfluid vortices at high wavenumbers. There are also three scaling regimes in the superfluid, that include a k{sup −3} range that corresponds to the growth of superfluid vortex instabilities due to mutual-friction action, and an adjacent, low wavenumber, k{sup −5/3} regime that emerges during the termination of this growth, as superfluid vortices agglomerate between intense normal-fluid vorticity regions, and weakly polarized bundles are formed. There is also evidence of a high wavenumber k{sup −1} range that corresponds to the probing of individual-vortex velocity fields. The Kelvin waves cascade (the main dynamical effect in zero temperature superfluids) appears to be damped at the intervortex space scale.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Polarized Line Formation in Arbitrary Strength Magnetic Fields Angle-averaged and Angle-dependent Partial Frequency Redistribution

Magnetic fields in the solar atmosphere leave their fingerprints in the polarized spectrum of the Sun via the Hanle and Zeeman effects. While the Hanle and Zeeman effects dominate, respectively, in the weak and strong field regimes, both these effects jointly operate in the intermediate field strength regime. Therefore, it is necessary to solve the polarized line transfer equation, including the combined influence of Hanle and Zeeman effects. Furthermore, it is required to take into account the effects of partial frequency redistribution (PRD) in scattering when dealing with strong chromospheric lines with broad damping wings. In this paper, we present a numerical method to solve the problem of polarized PRD line formation in magnetic fields of arbitrary strength and orientation. This numerical method is based on the concept of operator perturbation. For our studies, we consider a two-level atom model without hyperfine structure and lower-level polarization. We compare the PRD idealization of angle-averaged Hanle–Zeeman redistribution matrices with the full treatment of angle-dependent PRD, to indicate when the idealized treatment is inadequate and what kind of polarization effects are specific to angle-dependent PRD. Because the angle-dependent treatment is presently computationally prohibitive when applied to realistic model atmospheres, we present the computed emergent Stokes profiles for a range of magnetic fields, with the assumption of an isothermal one-dimensional medium.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Fluctuating Hydrodynamic Methods for Fluid-Structure Interactions in Confined Channel Geometries

Computational methods are developed for the study of fluid-structure interactions subject to thermal fluctuations when conned within channels having slit-like geometry. The methods take into account the hydrodynamic coupling and diusivity of microstructures when influenced by their proximity to no-slip walls. We develop stochastic numerical methods subject to no-slip boundary conditions using a staggered nite volume discretization. We show that by imposing an exact fluctuation-dissipation condition to discretize the stochastic driving elds combined with using an exact projection method to enforce incompressibility is sucient to ensure results consistent with statistical mechanics. We demonstrate our methods by investigating how the proximity of ellipsoidal colloids to the channel wall eects their active hydrodynamic responses and passive diusivity. We also study the collective dynamics of a large number of particles by considering the intermediate scattering functions for the relaxation of density fluctuations. We expect our introduced stochastic computational methods to be applicable broadly to applications in which confinement effects play an important role in the dynamics of microstructures subject to hydrodynamic coupling and thermal fluctuations. uctuations.

Wang, Yaohong↗
DOE OSTI2015

Novel comparison of microscopy and diffraction techniques on the structure of iron oxide nanoparticle monolayers transferred by Langmuir-Schaefer method

Iron oxide nanoparticles undergo self-assembly into well-ordered monolayer films of macroscopic size at the air-water interface. This self-assembly process is the result of the van der Waals forces between the constituent particles. For roughly spherical particles, this monolayer is a 2D hexagonal close packed lattice. With Grazing Incidence X-Ray Diffraction (GID), one can obtain global statistical information about the film’s spacing and correlation length. Herein, we demonstrate that comparable structural information can be obtained by a novel Fourier transform analysis method applied to Scanning Electron Microscopy (SEM) images taken of the film after it has been transferred to a silicon substrate. This consists of using numerical methods to isolate the lattice structure of the monolayer in the SEM image to which a 2D discrete Fourier Transform is applied and the result integrated. This results in Bragg peak information akin to that obtained from GID, whose structure shows the same hexagonal close packed lattice with similar spacing and of greater peak contrast. Furthermore, this analysis technique may prove to be a suitable alternative or compliment to GID for many applications.

36 MATERIALS SCIENCE↗