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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 OSTI2010

A Fully Second Order Implicit/Explicit Time Integration Technique for Hydrodynamics Plus Nonlinear Heat Conduction Problems

We present a second order non-linearly consistent implicit/explicit time integration tech¬nique for solving hydrodynamics coupled with nonlinear heat conduction problems. The idea is to hybridize an implicit and an explicit discretization in a nonlinearly consistent way in order to achieve second order time convergent calculations. In this scope, the hydrody¬namics equations are discretized explicitly making use of the capability of well-understood explicit schemes. On the other hand , the nonlinear heat conduction is solved implicitly. Such methods are often referred to as IMEX methods [2,1,3]. The Jacobian-Free Newton Krylov (JFNK) method (e.g, [10,9]) is applied to the problem in such a way as to render a nonlinearly iterated IMEX method. We solve three test problems in order to validate the nu-merical order of the scheme. For each test, we established second order time convergence. We support these numerical results with a Modi?ed Equation Analysis (MEA) [23,22]. The set of equations studied here constitute a base model for radiation hydrodynamics.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Latent Space Dynamics Identification

LaSDI is a data-driven physical simulation software that forms a latent space for a given high-fidelity model and discovers a set of ordinary differential equations for the latent space dynamics. It allows a fast and accurate solution process, which is useful for multi-query decision making applications, such as design optimization and uncertainty quantification. The performance of the LaSDI framework is demonstrated on four different problems, i.e., 1D and 2D Burgers equations, nonlinear heat conduction, and radial advection problems. Both linear and nonlinear compression techniques, such as neural network and proper orthogonal decomposition, are used to form a latent space. A concept of local dynamics identification procedure is introduced to enable a parametric model, which enhances the accuracy level over a given parameter space.

Fries, William↗
DOE OSTI2022

LaSDI: Parametric Latent Space Dynamics Identification

Enabling fast and accurate physical simulations with data has become an important area of computational physics to aid in inverse problems, design-optimization, uncertainty quantification, and other various decision-making applications. This paper presents a data-driven framework for parametric latent space dynamics identification procedure that enables fast and accurate simulations. The parametric model is achieved by building a set of local latent space model and designing an interaction among them. An individual local latent space dynamics model achieves accurate solution in a trust region. By letting the set of trust region to cover the whole parameter space, our model shows an increase in accuracy with an increase in training data. Herein we introduce two different types of interaction mechanisms, i.e., point-wise and region-based approach. Both linear and nonlinear data compression techniques are used. We illustrate the framework of Latent Space Dynamics Identification (LaSDI) enable a fast and accurate solution process on various partial differential equations, i.e., Burgers’ equations, radial advection problem, and nonlinear heat conduction problem, achieving 0 (100)x speed-up and 0 (1)% relative error with respect to the corresponding full order models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

gLaSDI: Parametric physics-informed greedy latent space dynamics identification

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. Here, an interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a -nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658× speed-up with 1 to 5% relative errors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Solution of second order quasi-linear boundary value problems by a wavelet method

A wavelet Galerkin method based on expansions of Coiflet-like scaling function bases is applied to solve second order quasi-linear boundary value problems which represent a class of typical nonlinear differential equations. Two types of typical engineering problems are selected as test examples: one is about nonlinear heat conduction and the other is on bending of elastic beams. Numerical results are obtained by the proposed wavelet method. Through comparing to relevant analytical solutions as well as solutions obtained by other methods, we find that the method shows better efficiency and accuracy than several others, and the rate of convergence can even reach orders of 5.8.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

COYOTE

COYOTE is designed for the analysis of steady and transient, multi-dimensional, nonlinear heat conduction problems. The spatial discretization technique is based on the Galerkin finite element method. The code contains a library of linear and quadratic elements and incudes bars and shells. COYOTE Implicit and explicit time integration methods, with adaptive time step control, are available for transient problems and fixed-point methods are used for Conjugate gradient iterative methods are used for the matrix solution. Coupled enclosure radiation with efficient view factor computation is included. Simulation capabilities include material motion, dynamic radiation enclosures, contact boundary conditions, multipoint constraints, material (element) addition, and deletion, bulk nodes, chemically reactive materials, and coupling with other mechanics codes. The code is designed for single or multi-processor computing

Gartling, DavidK.↗
DOE OSTI2012

BISON Framework for the Analysis of Performance of Metallic Fuels

This report documents the completion of the LANL milestone, M3FT-13LA0203123-Complete Final Assessment of Metal Fuel Sensitivity & Validation Data Set. We had made progress toward understanding how to develop a kernel for the zirconium diffusion in the first documentation this summer. The progress was limited but the work had identified several issues with the implementation of the diffusion kernel and the phase diagrams. In this report we have developed potential solutions to those issues. We have worked toward developing a more robust diffusion kernel including better smoothing, meshing, and artificial diffusion flux algorithms. This report summarizes the progress we have made on the development of robust diffusion kernel for BISON. In the current work we used appropriate simple constitutive models and the BISON framework being developed at Idaho National Laboratory (INL) in order to create an initial capability to simulate the behavior of metallic fuel under irradiation. Within the MOOSE/BISON framework a new Zirconium diffusion kernel was implemented that substantially improved the reliability and stability for solving Zirconium migration problems in metallic nuclear fuels. Several benchmark problems were created, including a simple 1-D rod and several 2-D segments of a fuel rod that covered several temperature regimes. The simulations were then compared to results from the code Pedernal, which is a “high-performance solver for coupled, nonlinear heat conduction and multi-component species diffusion". Comparison between the BISON based solver and Pedernal showed exceptional agreement for all benchmark cases. Very small differences appeared at longer time frames (2,000 days) for the hotter fuel simulations; however this is believed to be due, primarily, to the different time-stepping algorithms used in the two codes. Overall the domain of the benchmark covered all components of the U-Pu-Zr phase diagram (alpha, delta, beta and gamma phases) and showed excellent agreement when compared to Pedernal based results.

Nuclear Fuel Cycle & Fuel Materials(11)↗
DOE OSTI2015

Fully-Implicit Orthogonal Reconstructed Discontinuous Petrov-Galerkin Method for Multiphysics Problems

This document is focussed on the development of reconstructed discontinuous Galerkin (RDG P n P m ) method, based on orthogonal basis functions. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time discretization. The method is designed for generic partial differential equations, including transient hyperbolic, parabolic and/or elliptic operators, which are attributed to many multiphysics problems. Our driving application of interest is additive manufacturing, which requires simulations of fluid-solid-gas systems, with compressibility effects and phase change (melting/ solidification). Thus, we demonstrate the method capabilities for solving nonlinear heat conduction equation coupled with multi-material Navier-Stokes based compressible fluid (in low Mach number limit) systems. We focus our attention to the method accuracy (in both time and space), as well as solvability of linear algebra involved in linear steps of the Newton-based solver. We demonstrate the accuracy and efficacy of the method, emphasizing the advantages from the orthogonality of basis functions, which makes better conditioning of underlying (approximate) Jacobian matrices, and rapid convergence of Krylov methods. iii

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Effect of quantum correction on nonlinear thermal wave of electrons driven by laser heating

In thermal interaction of laser pulse with a deuterium-tritium (DT) plane, the thermal waves of electrons are generated instantly. Since the thermal conductivity of electron is a nonlinear function of temperature, a nonlinear heat conduction equation is used to investigate the propagation of waves in solid DT. This paper presents a self-similar analytic solution for the nonlinear heat conduction equation in a planar geometry. The thickness of the target material is finite in numerical computation, and it is assumed that the laser energy is deposited at a finite initial thickness at the initial time which results in a finite temperature for electrons at initial time. Since the required temperature range for solid DT ignition is higher than the critical temperature which equals 35.9 eV, the effects of quantum correction in thermal conductivity should be considered. This letter investigates the effects of quantum correction on characteristic features of nonlinear thermal wave, including temperature, penetration depth, velocity, heat flux, and heating and cooling domains. Although this effect increases electron temperature and thermal flux, penetration depth and propagation velocity are smaller. This effect is also applied to re-evaluate the side-on laser ignition of uncompressed DT.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2010

The first measurements of soft x-ray flux from ignition scale Hohlraums at the National Ignition Facility using DANTE (invited)

The first 96 and 192 beam vacuum Hohlraum target experiments have been fielded at the National Ignition Facility demonstrating radiation temperatures up to 340 eV and fluxes of 20 TW/sr as viewed by DANTE representing an {approx}20 times flux increase over NOVA/Omega scale Hohlraums. The vacuum Hohlraums were irradiated with 2 ns square laser pulses with energies between 150 and 635 kJ. They produced nearly Planckian spectra with about 30{+-}10% more flux than predicted by the preshot radiation hydrodynamic simulations. To validate these results, careful verification of all component calibrations, cable deconvolution, and software analysis routines has been conducted. In addition, a half Hohlraum experiment was conducted using a single 2 ns long axial quad with an irradiance of {approx}2x10{sup 15} W/cm{sup 2} for comparison with NIF Early Light experiments completed in 2004. We have also completed a conversion efficiency test using a 128-beam nearly uniformly illuminated gold sphere with intensities kept low (at 1x10{sup 14} W/cm{sup 2} over 5 ns) to avoid sensitivity to modeling uncertainties for nonlocal heat conduction and nonlinear absorption mechanisms, to compare with similar intensity, 3 ns OMEGA sphere results. The 2004 and 2009 NIF half-Hohlraums agreed to 10% in flux, but more importantly, the 2006 OMEGA Au Sphere, the 2009 NIF Au sphere, and the calculated Au conversion efficiency agree to {+-}5% in flux, which is estimated to be the absolute calibration accuracy of the DANTEs. Hence we conclude that the 30{+-}10% higher than expected radiation fluxes from the 96 and 192 beam vacuum Hohlraums are attributable to differences in physics of the larger Hohlraums.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Causal explicit algorithm for heat conduction in a plasma

Hyperbolic heat conduction extends standard Spitzer-Harm heat conduction by including a term proportional to the time derivative of the heat flux. The new term arises from a kinetic derivation of the heat flux that includes higher order corrections. Here we present a causal explicit numerical algorithm for solving the nonlinear hyperbolic heat conduction equation in an unmagnetized plasma. The maximum stable timestep for the causal explicit algorithm scales linearly with the cell size, owing to the hyperbolic nature of the problem. This is in contrast to the quadratic scaling of the maximum stable timestep with the cell size for the parabolic forward time centered space algorithm. The favorable scaling of the timestep with the cell size enables a practical explicit implementation of heat conduction in high-performance massively parallel plasma codes. In particular, we have implemented the causal explicit algorithm in the laser plasma interaction code pF3D. We verify the CE algorithm and analyze its convergence rate by simulating a harmonic mode, which has an analytic solution within the context of the HHC model. We also compare simulations using the CE algorithm to those using the forward time centered space algorithm on a pair of test problems: evolution in time of a Gaussian temperature perturbation in a uniform plasma and heat transport in the presence of inverse bremsstrahlung heating by a Gaussian laser speckle.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

MAPS: the MFEM Anisotropic Plasma Solver

Simulating magnetically confined fusion plasmas presents a uniquely challenging problem due to the nonlinear anisotropic heat conduction. We introduce the MAPS (MFEM Anisotropic Plasma Solver) tool, which uses a high-order finite element method to compute transport solutions on unstructured meshes. We show results for a set of three 2-D verification tests, two of which demonstrate the expected convergence properties for various mesh resolutions and polynomial degrees. We then discuss the convergence rate for the third test.

Barnett, Rhea [ORNL] (ORCID:0000000317527979)↗
DOE OSTI2016

V{sub 3}O{sub 5}: Insulator-metal transition and electric-field-induced resistive-switching

V{sub 3}O{sub 5} is one of the two vanadium oxides that exhibit insulator to metal transitions above room temperature. We report on the DC I–V characteristics of polycrystalline samples and single-crystals of V{sub 3}O{sub 5} over a wide range of currents. For all samples self-heating induced hysteretic nonlinear conductivity followed at higher currents by onset of negative differential resistivity regime, and finally, at highest currents, by switching to the metallic state. Slow switching towards a partially transformed state with a prolonged memory is typical of polycrystalline samples. High currents applied in the metallic state of one of the single crystals affected the oxygen content of the material and even caused appearance and disappearance of a VO{sub 2} inclusion. Simple and reproducible I–V plots were obtained for a single crystal with the currents that barely induced the metallic state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Global gyrokinetic simulations of electrostatic microturbulent transport in LHD stellarator with boron impurity

Abstract Global gyrokinetic simulations of electrostatic microturbulent transport for discharge # 166256 of the Large Helical Device stellarator in the presence of boron impurity show the co-existence of the ion temperature gradient (ITG) turbulence and trapped electron mode (TEM) turbulence before and during boron powder injection. ITG turbulence dominates in the core, whereas TEM dominates near the edge, consistent with the experimental observations. Linear TEM frequency increases from ∼ 80 kHz to ∼ 100 kHz during boron injection, and ITG frequency decreases from ∼ 20 kHz to ∼ 13 kHz, consistent with the experiments. The poloidal wave number spectrum is broad for both ITG (0–0.5 mm −1 ) and TEM (0–0.25 mm −1 ). The nonlinear simulations with boron impurity show a reduction in the heat conductivity compared to the case without boron. The comparison of the nonlinear transport before and during boron injection shows that the ion heat transport is substantially reduced in the region where the TEM is dominant. However, the average electron heat transport throughout the radial domain and the average ion heat transport in the region where the ITG is dominant are similar. The simulations with boron show the effective heat conductivity values qualitatively agree with the estimate obtained from the experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Unification of nonequilibrium molecular dynamics and the mode-resolved phonon Boltzmann equation for thermal transport simulations

Nano-size confinement induces many intriguing non-Fourier heat conduction phenomena, such as nonlinear temperature gradients, temperature jumps near the contacts, and size-dependent thermal conductivity. Over the past decades, these effects have been studied and interpreted by nonequilibrium molecular dynamics (NEMD) and phonon Boltzmann transport equation (BTE) simulations separately, but no theory that unifies these two methods has ever been established. In this work, we unify these methods using a quantitative mode-level comparison and demonstrate that they are equivalent for various thermostats. We show that different thermostats result in different non-Fourier thermal transport characteristics due to the different mode-level phonon excitations inside the thermostats, which explains the different size-dependent thermal conductivities calculated using different reservoirs, even though they give the same bulk thermal conductivity. Specifically, the Langevin thermostat behaves like a thermalizing boundary in phonon BTE and provides mode-level thermal-equilibrium phonon outlets, while the Nose-Hoover chain thermostat and velocity rescaling method behave like biased reservoirs, which provide a spatially uniform heat generation and mode-level nonequilibrium phonon outlets. These findings explain why different experimental measurement methods can yield different size-dependent thermal conductivity. They also indicate that the thermal conductivity of materials can be tuned for various applications by specifically designing thermostats. Finally, the unification of NEMD and phonon BTE will largely facilitate the study of thermal transport in complex systems in the future by, e.g., replacing computationally unaffordable first-principles NEMD simulations with computationally less expensive spectral BTE simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2011

Soliton mechanism of the uranium nitride microdynamics and heat conductivity at high temperatures

The microdynamics of soliton waves and localized modes of nonlinear acoustic and optical oscillations in uranium nitride has been investigated. It is shown that, upon heating, the energies of solitons in the gap between the optical and acoustic phonon bands increase, while the energies of local modes decrease. The experimentally observed quasi-resonance features, which are shifted in the gap with a change in temperature, can be manifestations of the revealed soliton waves and local modes. The microdynamics of uranium nitride heat conductivity with the stochastic generation of the observed solitons and local modes at remote energy absorption have been investigated. The temperature dependence of the heat conductivity coefficient has been determined from the temperature gradient and energy flux within the standard approach (which is to be generalized).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Electroconvection of a poorly conducting fluid under unipolar charge injection in a steady electric field

We study the stability of equilibrium and nonlinear regimes of a nonuniformly heated poorly conducting fluid in a horizontal capacitor in the gravity field and in a dc electric field under a unipolar charge injection. A model in which the density of charges injected from the cathode is proportional to the electric field strength in the capacitor is considered. The dependences of critical parameters on the degree of heating and charge injection are determined. The effect of the Prandtl number on the equilibrium instability boundary and on the frequency of neutral vibrations is analyzed. Nonlinear regimes of electroconvection are studied for heating from below.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗