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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 595 records · Page 33
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DOE OSTI2021

A Butterfly-Accelerated Volume Integral Equation Solver for Broad Permittivity and Large-Scale Electromagnetic Analysis

In this work, a butterfly-accelerated volume integral equation (VIE) solver is proposed for fast and accurate electromagnetic (EM) analysis of scattering from heterogeneous objects. The proposed solver leverages the hierarchical off-diagonal butterfly (HOD-BF) scheme to construct the system matrix and obtain its approximate inverse, used as a preconditioner. Complexity analysis and numerical experiments validate the O(N log 2 N) construction cost of the HOD-BF-compressed system matrix and O(N log 1.5 N) inversion cost for the preconditioner, where N is the number of unknowns in the high-frequency EM scattering problem. For many practical scenarios, the proposed VIE solver requires less memory and computational time to construct the system matrix and obtain its approximate inverse compared to a H matrix-accelerated VIE solver. The accuracy and efficiency of the proposed solver have been demonstrated via its application to the EM analysis of large-scale canonical and real-world structures comprising of broad permittivity values and involving millions of unknowns.

42 ENGINEERING↗
DOE OSTI2025

Influence of helium bubbles on the bulk equation of state of gold under static compression

Nuclear materials often evolve into two-phase systems comprising a bulk matrix with dispersed inert-gas bubbles. The presence of these bubbles can have consequences to the thermomechanical response of materials and is a key life-limiting factor in some nuclear fuel forms. Understanding the behavior of these two-phase, bubble-matrix systems is, thus, important to improved predictive models and frameworks for many nuclear materials applications. While temperature excursions of these two-phase systems have been characterized, fewer studies have focused on the evolution of inert-gas bubbles under pressure. Here, in this paper, we use x-ray tools to interrogate a He-implanted gold foil to determine the pressure-dependent evolution of the individual components (Au matrix + bubbles), and we compare that total pressure dependence to theoretical equation-of-state descriptions based on mixing rules.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

A Fast Solver for the Fractional Helmholtz Equation

The purpose of this paper is to study a Helmholtz problem with a spectral fractional Laplacian, instead of the standard Laplacian. Recently, it has been established that such a fractional Helmholtz problem better captures the underlying behavior in Geophysical Electromagnetics. In this work, we establish the well-posedness and regularity of this problem. We introduce a hybrid spectral-finite element approach to discretize it and show well-posedness of the discrete system. In addition, we derive a priori discretization error estimates. Finally, we introduce an efficient solver that scales aswell as the best possible solver for the classical integer-order Helmholtz equation. We conclude withseveral illustrative examples that confirm our theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

An Efficient High-Order Solver for Diffusion Equations with Strong Anisotropy on Non-Anisotropy-Aligned Meshes

This paper concerns numerical solution of the diffusion equation with strong anisotropy on meshes not aligned with the anisotropic vector field. In order to resolve the numerical pollution for simulations on a non-anisotropy-aligned mesh and reduce the associated high computational cost we propose an effective preconditioner, extending our previous work. Similar to the anisotropy-aligned mesh case, we apply the auxiliary space preconditioning framework to design a preconditioner where a continuous finite element space is used as the auxiliary space for the discontinuous finite element space. The key component is an effective line smoother that can mitigate the high-frequency errors perpendicular to the magnetic field. We design a graph-based approach to find such a line smoother that is approximately perpendicular to the vector fields when the mesh does not align with the anisotropy. Finally, numerical experiments for several benchmark problems are presented, demonstrating the effectiveness and robustness of the proposed preconditioner when applied to Krylov iterative methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Fourth-Order Embedded Boundary Finite Volume Method for the Unsteady Stokes Equations with Complex Geometries

A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the ``small cut-cell"" problem without mesh modifications, cell merging, or state redistribution. Spatial discretizations are based on a weighted least-squares technique that has been extended to fourth-order operators and boundary conditions, including an approximate projection to enforce the divergence-free constraint. Solutions are advanced in time using a fourth-order additive implicit-explicit Runge-Kutta method, with the viscous and source terms treated implicitly and explicitly, respectively. Formal accuracy of the method is demonstrated with several grid convergence studies, and results are shown for an application with a complex bio-inspired material. In conclusion, the developed method achieves fourth-order accuracy and is stable despite the pervasive small cells arising from complex geometries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Temperature effects on the neutron matter equation of state obtained from chiral effective field theory

Temperature effects on the neutron matter equation of state (EoS) are investigated in the framework of chiral effective field theory. Recently, state-of-the-art chiral two-nucleon forces are applied from third to fifth order in the chiral expansion together with chiral three-nucleon forces, allowing for a determination of the truncation error of the theoretical predictions. The thermodynamic quantities considered include the chemical potential, the internal energy, the entropy, and the free energy. In general, good order-by-order convergence of all predictions is observed. As to be expected, temperature effects are largest at low density. Finally, the temperature dependence of the chiral three-nucleon force turns out to be weak.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

A unified framework of stabilized finite element method for solving the Boltzmann transport equation

This paper presents a unified framework of stabilized finite element method for solving the Boltzmann transport equation. Unlike the traditional Petrov-Galerkin finite element method which modifies the test function to construct the stabilization term, we derive the stabilization methods from the standard Galerkin weak form with Sub-grid scale model. The basic idea of this method is to decompose the unknowns into its numerical solution and residual, with an approximation for the residual and embeds it in the Galerkin weak form to yield a stabilized variational formula. Different approximations of the residual lead to different stabilization methods, all the frequently used stabilized methods, including the Streamline Upwinding Petrov-Galerkin (SUPG) method, Galerkin/Least-Square (GLS) method, and Algebraic Sub-Grid Scale (ASGS) method can be obtained from this framework. The similarities and differences of the different approximations are compared in this paper. The numerical results show that the behaviors of the different methods area similar with the same stabilization parameter, and all these stabilized techniques can obtain a correct and stable solution. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Equations of State in Computational Physics: What, Why, and How

Summary: 1. Equations of state furnish thermodynamic properties of a material. 2. Usually involve P, p (or V), and T, or P, r, and E 3. Necessary ingredient to solve compressible flow problems. 4. Varieties: i. Analytical expressions (ideal gas, Grüneisen) – fast, convenient for verification and test problems ii. Graphs and charts – good for hand calculations iii. Tables and databases – generally most accurate, require interpolation i. Steam tables ii. NIST database iii. SESAME EOS Library 5. Constructed by using semi-empirical models from Statistical Mechanics and fitting to available data

36 MATERIALS SCIENCE↗
DOE OSTI2020

Understanding machine learning approaches for partial differential equations

Recent works in computational physics have been successful in the super-resolution of numerical solutions of partial differential equations (PDEs) via neural networks. In this paper we explore the possibilities and limitations of the data-driven discretization approach implemented by Bar-Sinai et. al., while contrasting it with a simpler yet weaker approach utilizing the nangs Python library. The results demonstrate what neural network parameters optimize accuracy and performance, as well as what conditions on PDEs are necessary to maintain convergence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Combining DPG in space with DPG time-marching scheme for the transient advection-reaction equation

In this article, we present a general methodology to combine the Discontinuous PetrovGalerkin (DPG) method in space and time in the context of methods of lines for transient advection-reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). We also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection-reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Sesame Equation of State for Kel F-800

I describe the construction of new equations of state for Kel F-800, as both linear and quadratic fits to shock data and Sesame 97200. This is the first SESAME table for Kel F-800 of which I’m aware. The SESAME table recovers shock data by construction and does reasonably well with thermal data, but differs with Brillouin scattering results for sound speed and density under static compression.

42 ENGINEERING↗
DOE OSTI2023

Reactive Flow Characteristic Equations

The characteristic equations are derived for the reactive flow PDEs in 1-dimension with 1 irreversible reaction. They differ from the non-reacting case only by source terms proportional to the reaction rate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

The extended Vinet analytical equations of state

When testing new materials models, it is often not possible to use tabulated Equations of States (EOS) since the model might only be available in a smaller specialized research code without capability to read in tables. In such cases a versatile and easy to implement analytical EOS is needed. In this report I derive, give, and discuss all formulas necessary for implementing the thermodynamically complete extended Vinet EOS 3 into codes. While similar to a Mie-Grüneisen (MG) EOS, this Vinet EOS is based on an isotherm and substantially easier to correctly implement than a MG EOS. In the extended Vinet the isotherm’s density dependence is given as a power series in density to accommodate for higher density behavior which normally requires the Hugoniot based MG.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Parameterization of the β and γ phases of Tin using the Vinet and Mie-Grüneisen Equations of State

When testing new phase aware materials models, it is often not possible to use tabulated Equations of States for the phases since the model might only be available in a smaller specialized research code without capability to read in tables. These EOS parameterizations for two of the solid phases of Tin were developed for testing the Kinetic Phase Transition model by Carl Greeff, LANL. They are based on two isotherms per phase obtained from work in progress by Carl Greeff, and their phase boundary corresponds fairly well to SESAME 2162. A full machinery is applied for the parameterization of the Vinet EOSs while the Mie-Grüneisen parameterizations are translated from the Vinet EOSs.

36 MATERIALS SCIENCE↗
DOE OSTI2023

New Sesame Equations of State for Polypropylene, Polyvinylchloride (PVC), and Nylon 66

I built new Sesame equations of state (EOS) for polypropylene (PP), polyvinylchloride (PVC), and nylon 66. PP has the same stoichiometry as polyethylene and TPX but with a density intermediate between the two. Nylon is a polyamide manufactured chiefly in the form of fibers. PP and PVC are the second- and third-most widely produced polymers in the world. All three are thermoplastics. Their monomer units are depicted in Figure 1. I discuss the theory on which the EOS are based in the following section, then compare results to thermal and shock compression data in Section III.

36 MATERIALS SCIENCE↗
DOE OSTI2025

SESAME: The Los Alamos National Laboratory’s Tabulated Equation of State Database Description with Extensions for Multi-phase Representations

Modeling of the thermodynamic equation of state (EOS) of various materials has had a long storied tradition at LANL. As early as 1949 Feynman, Metropolis, and Teller published a paper presenting EOS values for some elements and a methodology for calculating the EOS at high compression [1]. Cowan and Ashkin made notable methodology improvements for compressed materials throughout the 1950’s and beyond [2]. In 1971 Jack Barnes and Jerry Rood created the SESAME database and by 1972 the database became publicly available.

36 MATERIALS SCIENCE↗
DOE OSTI2026

GEOSH: Ideal Gas Chemical Equation of State

We present the framework and methodology for the new Los Alamos National Laboratory (LANL) G as chemical E quation O f S tate at H igher temperatures code (GEOSH) which aims to accurately model the behavior of chemically complex gaseous mixtures in equilibrium. Assuming the ideal gas approximation, GEOSH leverages the recursive nature of the Saha ionization and molecular equations in order to eliminate the molecular and ionic degrees of freedom, thereby reducing the problem size to the number of atomic species plus one for the free electrons if ions are included. This approach allows the chemical species, both molecular and ionic, of the mixture to be expressed in terms of the abundances of the elemental species. As a result, the GEOSH framework achieves a reduction in computational expense, increased processing speed, and the capability to efficiently model large-scale chemical networks. This report provides the necessary physical background and theoretical foundations for the GEOSH code, accompanied by benchmarking studies.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

General features of the stellar matter equation of state from microscopic theory, new maximum-mass constraints, and causality

The profile of a neutron star probes a very large range of densities, from the density of iron up to several times the density of saturated nuclear matter, and thus no theory of hadrons can be considered reliable if extended to those regions. We emphasize the importance of taking contemporary ab initio theories of nuclear and neutron matter as the baseline for any extension method, which will unavoidably involve some degree of phenomenology. We discuss how microscopic theory, on the one end, with causality and maximum-mass constraints, on the other, set strong boundaries to the high-density equation of state. We present our latest neutron star predictions where we combine polytropic extensions and parametrizations guided by speed of sound considerations. The predictions we show include our baseline neutron star cooling curves.

chiral effective field theory↗