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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Error analysis of numerical methods for thick diffusive neutron transport problems on Shishkin mesh

A thin layer will develop at the boundary if the incoming angular flux is anisotropic in thick diffusive neutron transport problems. Solving such singularly perturbed problems, which have non-smooth solutions with singularity near the boundary, is computationally challenging. Standard finite difference schemes on a uniform mesh cannot yield ε-uniform convergence, where ε is a small parameter, while it can be achieved on a suitable piecewise-uniform Shishkin mesh. We present a formal error analysis of the diamond difference (DD) method and step difference (SD) method for solving the S{sub N} neutron transport equation. The analysis can be extended to other finite difference methods. Numerical results are presented to confirm the error estimates and the advantages of the Shishkin mesh. (author)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

MOCMC: Method of Characteristics Moment Closure, a Numerical Method for Covariant Radiation Magnetohydrodynamics

In this work, we present a conservative numerical method for radiation magnetohydrodynamics with frequency-dependent full transport in stationary spacetimes. This method is stable and accurate for both large and small optical depths and radiation pressures. The radiation stress–energy tensor is evolved in flux-conservative form, and closed with a swarm of samples that each transport a multigroup representation of the invariant specific intensity along a null geodesic. In each zone, the enclosed samples are used to efficiently construct a Delaunay triangulation of the unit sphere in the comoving frame, which in turn is used to calculate the Eddington tensor, average source terms, and adaptively refine the sample swarm. Furthermore, radiation four-forces are evaluated in the moment sector in a semi-implicit fashion. The radiative transfer equation is solved in invariant form deterministically for each sample. Since each sample carries a discrete representation of the full spectrum, the cost of evaluating the transport operator is independent of the number of frequency groups, representing a significant reduction of algorithmic complexity for transport in frequency-dependent problems. The major approximation we make in this work is performing scattering in an angle-averaged way. Local adaptivity in samples also makes this scheme more amenable to nonuniform meshes than a traditional Monte Carlo method. We describe the method and present results on a suite of test problems. We find that Method of Characteristics Moment Closure converges at least as ~N -1 , rather than the canonical Monte Carlo N -1/2 , where N is the number of samples per zone.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Numerical methods and hypoexponential approximations for gamma distributed delay differential equations

Abstract Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic gamma distributed DDEs have not previously been implemented. Modellers have therefore resorted to approximating the gamma distribution with an Erlang distribution and using the linear chain technique to derive an equivalent system of ordinary differential equations (ODEs). In this work, we address the lack of appropriate numerical tools for gamma distributed DDEs in two ways. First, we develop a functional continuous Runge–Kutta (FCRK) method to numerically integrate the gamma distributed DDE without resorting to Erlang approximation. We prove the fourth-order convergence of the FCRK method and perform numerical tests to demonstrate the accuracy of the new numerical method. Nevertheless, FCRK methods for infinite delay DDEs are not widely available in existing scientific software packages. As an alternative approach to solving gamma distributed DDEs, we also derive a hypoexponential approximation of the gamma distributed DDE. This hypoexponential approach is a more accurate approximation of the true gamma distributed DDE than the common Erlang approximation but, like the Erlang approximation, can be formulated as a system of ODEs and solved numerically using standard ODE software. Using our FCRK method to provide reference solutions, we show that the common Erlang approximation may produce solutions that are qualitatively different from the underlying gamma distributed DDE. However, the proposed hypoexponential approximations do not have this limitation. Finally, we apply our hypoexponential approximations to perform statistical inference on synthetic epidemiological data to illustrate the utility of the hypoexponential approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Final report of activities for the LDRD-express project #223796 titled: “Fluid models of charged species transport: numerical methods with mathematically guaranteed properties”, PI: Ignacio Tomas, Co-PI: John Shadid

This report summarizes the findings and outcomes of the LDRD-express project with title “Fluid models of charged species transport: numerical methods with mathematically guaranteed properties”. The primary motivation of this project was the computational/mathematical exploration of the ideas advanced aiming to improve the state-of-the-art on numerical methods for the one-fluid Euler-Poisson models and gain some understanding on the Euler-Maxwell model. Euler-Poisson and Euler-Maxwell, by themselves are not the most technically relevant PDE plasma-models. However, both of them are elementary building blocks of PDE-models used in actual technical applications and include most (if not all) of their mathematical difficulties. Outside the classical ideal MHD models, rigorous mathematical and numerical understanding of one-fluid models is still a quite undeveloped research area, and the treatment/understanding of boundary conditions is minimal (borderline non-existent) at this point in time. This report focuses primarily on bulk-behaviour of Euler-Poisson’s model, touching boundary conditions only tangentially.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Numerical Methods to Evaluate Hyperelastic Transducers: Hexagonal Distributed Embedded Energy Converters

Hexagonal distributed embedded energy converters, also known as hexDEECs, are centimeter-scale energy transducers that leverage variable capacitance to generate electricity when their hyperelastic structure is dynamically deformed. To better understand, characterize, and optimize hexDEEC designs, a series of numerical methods and techniques were developed to model the hyperelastic mechanics of hexDEECs, electrostatic properties, and electricity generation characteristics. The numerical methods developed for the hyperelastic structural analysis were corroborated by empirical results from another study, and the models and equations for capacitance, electrostatic forces, and electrical potential energy were derived from fundamental electrostatic equations. These methods and techniques were implemented within the STAR-CCM+ multiphysics software Version 2020.3 (15.06.008) environment. Results from this analysis revealed methodologies and techniques necessary to model the energy converters, which will enable future exploration and optimization of more specific designs and corresponding applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the “NIMROD benchmark” problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Numerical Method Improvements in Griffin for Pebble Bed Reactors with a Focus on the Computation of Burnup

Griffin, a MOOSE (Multiphysics Object-Oriented Simulation Environment) based application targeting transient multiphysics modeling of advanced reactors, has been used recently to model both high-temperature gas-cooled and fluoride-salt-cooled pebble bed reactors (PBRs). Griffin uses deterministic methods for solving neutron transport and an Eulerian approach to model pebble movement. An Eulerian approach is also used to directly compute burnup instead of using a pass approach like other tools such as VSOP or PANGU. This work discusses verification efforts and numerical method improvements related specifically to the Eulerian modeling approach implemented for directly computing pebble burnup.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A simple numerical method for evaluating heat dissipation from curved wires with periodic applied heating

In many situations, the dual-purpose heater/thermometer wires used in the three-omega method – one of the most precise and sensitive techniques for measuring the thermal conductivity of thin films and interfaces – must include bends and curves to avoid obstructions on the surface of a sample. Although the three-omega analysis assumes that the heating wire is infinitely long and straight, recent experimental work has demonstrated that in some cases curved-wire geometries can be used without introducing detectable systematic error. We describe a general numerical method that can be used to calculate the temperature of three-omega heating wires with arbitrary wire geometries. Furthermore, this method provides experimentalists with a simple quantitative procedure for calculating how large the systematic error caused by a particular wire asymmetry will be. We show calculations of two useful cases: a straight wire with a single bend of arbitrary angle and a wire that forms a circle. We find that the amplitude of the in-phase temperature oscillations near a wire that forms a circle differs from the prediction using the analytic straight-line source solution by <12%, provided that the thermal penetration depth is less than ten times the radius of curvature of the wire path. The in-phase temperature amplitude 1.5 wire widths away from a 90° bend in a wire is within 11% of the straight-line source prediction for all penetration depths greater than the wire width. Our calculations indicate that the straight-line source solution breaks down significantly when the wire bend angle is less than 45°.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

Numerical methods for nonlocal and fractional models

Partial differential equations (PDEs) are used with huge success to model phenomena across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDEs fail to adequately model observed phenomena, or are not the best available model for that purpose. On the other hand, in many situations, nonlocal models that account for interaction occurring at a distance have been shown to more faithfully and effectively model observed phenomena that involve possible singularities and other anomalies. Here, we consider a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis and of specific concrete examples. We then provide extensive discussions about numerical methods, including finite element, finite difference and spectral methods, for determining approximate solutions of the nonlocal models considered. In that discussion, we pay particular attention to a special class of nonlocal models that are the most widely studied in the literature, namely those involving fractional derivatives. The article ends with brief considerations of several modelling and algorithmic extensions, which serve to show the wide applicability of nonlocal modelling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Numerical methods for nonlocal and fractional models

Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDE models fail to adequately model observed phenomena or are not the best available model for that purpose. On the other hand, in many situations, nonlocal models that account for interaction occurring at a distance have been shown to more faithfully and effectively model observed phenomena that involve possible singularities and other anomalies. In this article, we consider a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis, and specific concrete examples. We then provide extensive discussions about numerical methods, including finite element, finite difference, and spectral methods, for determining approximate solutions of the nonlocal models considered. In that discussion, we pay particular attention to a special class of nonlocal models that are the most widely studied in the literature, namely those involving fractional derivatives. The article ends with brief considerations of several modeling and algorithmic extensions which serve to show the wide applicability of nonlocal modeling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Reactive Flows in Porous Media: Challenges in Theoretical and Numerical Methods

We review theoretical and computational research, primarily from the past 10 years, addressing the flow of reactive fluids in porous media. The focus is on systems where chemical reactions at the solid–fluid interface cause dissolution of the surrounding porous matrix, creating nonlinear feedback mechanisms that can often lead to greatly enhanced permeability. Here, we discuss insights into the evolution of geological forms that can be inferred from these feedback mechanisms, as well as some geotechnical applications such as enhanced oil recovery, hydraulic fracturing, and carbon sequestration. Until recently, most practical applications of reactive transport have been based on Darcy-scale modeling, where averaged equations for the flow and reactant transport are solved. We summarize the successes and limitations of volume averaging, which leads to Darcy-scale equations, as an introduction to pore-scale modeling. Pore-scale modeling is computationally intensive but offers new insights as well as tests of averaging theories and pore-network models. We include recent research devoted to validation of pore-scale simulations, particularly the use of visual observations from microfluidic experiments.

wormhole formation↗
DOE OSTI2020

Using numerical methods to screen magnetocaloric materials in an active magnetic regenerative cycle

A 2-dimensional numerical model of a room temperature operating Active Magnetic Regenerator (AMR) that comprises of a regenerator, hot and cold heat exchangers, heat transfer fluid is developed. The regenerator is made of a magnetocaloric material (MCM) which heats up upon applying a magnetic field, H, and cools down when the field is removed; thus, making it the most essential part of an AMR. The model takes experimentally measured ΔT ad (H,T) and the C p (H,T) data as input and provides quantitative performance metrics of the magnetic cooling system, such as ΔT span and the cooling load, as output. With this model, it is possible to assess a wide range of MCMs in an AMR. 4 different MCMs were investigated using this model in terms of their ΔT span and the cooling loads—LaFe 10.96 Co 0.97 Si 1.07 , MnFeP (1-x) As (x) and AlFe 2 B 2 and Gd. During the screening of MCMs, all the important operating conditions of the device were fixed such as the fluid flow rate, ambient temperature, cycle duration, magnetic field strength. Our results indicate that Gd exhibits the maximum ΔT span with respectable cooling load, while AlFe 2 B 2 generates the lowest ΔT span . Even though LaFeCoSi compound did not perform as well as Gd, it could be the MCM choice for the realization of magnetic refrigeration on a global scale due to its much lower cost.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Comparison of Numerical Methods for Modeling the Wave Field Effects Generated by Individual Wave Energy Converters and Multiple Converter Wave Farms

This numerical study compares the wave field generated by the spectral wave action balance code, SNL-SWAN, to the linear-wave boundary-element method (BEM) code, WAMIT. The objective of this study is to assess the performance of SNL-SWAN for modeling wave field effects produced by individual wave energy converters (WECs) and wave farms comprising multiple WECs by comparing results from SNL-SWAN with those produced by the BEM code WAMIT. BEM codes better model the physics of wave-body interactions and thus simulate a more accurate near-field wave field than spectral codes. In SNL-SWAN, the wave field’s energy extraction is modeled parametrically based on the WEC’s power curve. The comparison between SNL-SWAN and WAMIT is made over a range of incident wave conditions, including short-, medium-, and long-wavelength waves with various amounts of directional spreading, and for three WEC archetypes: a point absorber (PA), a pitching flap (PF) terminator, and a hinged raft (HR) attenuator. Individual WECs and wave farms of five WECs in various configuration were studied with qualitative comparisons made of wave height and spectra at specific locations, and quantitative comparisons of the wave fields over circular arcs around the WECs as a function of radial distance. Results from this numerical study demonstrate that in the near-field, the difference between SNL-SWAN and WAMIT is relatively large (between 20% and 50%), but in the far-field from the array the differences are minimal (between 1% and 5%). The resultant wave field generated by the two different numerical approaches is highly dependent on parameters such as: directional wave spreading, wave reflection or scattering, and the WEC’s power curve.

16 TIDAL AND WAVE POWER↗
DOE OSTI2024

Numerical methods for fractional Fokker–Planck equation with multiplicative Marcus Lévy noises

The Fokker–Planck equation (FPE) is an important deterministic tool for investigating stochastic dynamical systems. In this paper, we consider the space-time fractional FPE driven by multiplicative Marcus Lévy noises. Efficient numerical schemes are presented to solve the equations. Stability and convergence of the methods are also discussed. We give some numerical experiments to validate our schemes, and examine the effects of parameters on solutions. Additionally, we analyze the maximal likely trajectories and the critical time for the change of the most probability location.

Mathematics↗