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Results for “Boltzmann transport equation”

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 OSTI2024

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann transport equation

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. Importantly, the ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Phoebe: a high-performance framework for solving phonon and electron Boltzmann transport equations

Understanding the electrical and thermal transport properties of materials is critical to the design of electronics, sensors, and energy conversion devices. Computational modeling can accurately predict material properties but, in order to be reliable, requires accurate descriptions of electron and phonon states and their interactions. While first-principles methods are capable of describing the energy spectrum of each carrier, using them to compute transport properties is still a formidable task, both computationally demanding and memory intensive, requiring integration of fine microscopic scattering details for estimation of macroscopic transport properties. To address this challenge, we present Phoebe—a newly developed software package that includes the effects of electron–phonon, phonon–phonon, boundary, and isotope scattering in computations of electrical and thermal transport properties of materials with a variety of available methods and approximations. This open source C++ code combines MPI-OpenMP hybrid parallelization with GPU acceleration and distributed memory structures to manage computational cost, allowing Phoebe to effectively take advantage of contemporary computing infrastructures. We demonstrate that Phoebe accurately and efficiently predicts a wide range of transport properties, opening avenues for accelerated computational analysis of complex crystals.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

Here a new group of structure and asymptotic preserving reduced-order models (ROMs) for multidimensional nonlinear thermal radiative transfer (TRT) problems is presented. They are formulated by means of the nonlinear projective approach and data compression techniques. The nonlinear projection is applied to the Boltzmann transport equation (BTE) to derive a hierarchy of low-order moment equations. Approximation of the Eddington tensor that provides exact closure for the system of moment equations is found with projection-based data-driven methodologies. These include the (i) proper orthogonal decomposition (POD), (ii) dynamic mode decomposition (DMD) and (iii) a variant of the DMD. A parameterization is derived for this ROM for the temperature of radiation incoming to the problem domain (the radiation drive temperature). This parameterization is informed from results of a dimensionless study of the TRT problem. Analysis of the ROMs is performed on the classical Fleck-Cummings TRT multigroup test problem in 2D geometry with a radiation-driven Marshak wave. Numerical results are presented to demonstrate the performance of these ROMs for the simulation of evolving radiation and heat waves. Results show these models to be sufficiently accurate for practical computations with rather low-rank representations of the Eddington tensor. As the rank of the approximation is increased, the errors of solutions generated by the ROMs gradually decreases.

42 ENGINEERING↗
DOE OSTI2024

Impact of classical statistics on thermal conductivity predictions of BAs and diamond using machine learning molecular dynamics

Machine learning interatomic potentials (MLIPs) have greatly enhanced molecular dynamics (MD) simulations, achieving near-first-principles accuracy in thermal conductivity studies. In this work, we reveal that this accuracy, observed in BAs and diamond at sub-Debye temperatures, stems from an accidental error cancelation: classical statistics overestimates specific heat while underestimating phonon lifetimes, balancing out in thermal conductivity predictions. However, this balance is disrupted when isotopes are introduced, leading MLIP-based MD to significantly underpredict thermal conductivity compared to experiments and quantum statistics-based Boltzmann transport equation. This discrepancy arises not from classical statistics affecting phonon–isotope scattering rates but from its impact on the interplay between phonon–isotope and phonon–phonon scattering in the normal scattering-dominated BAs and diamond. In conclusion, this work underscores the limitations of MLIP-based MD for thermal conductivity studies at sub-Debye temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A combined theoretical-experimental investigation of thermal transport in low-dose irradiated thorium dioxide

During reactor operation, nuclear fuels are subject to extreme temperature and irradiation conditions which can significantly degrade the fuel's thermal transport properties. The reduction in thermal conductivity of the fuel as a result of irradiation-induced lattice defects is arguably the most important fuel performance metric in regard to reactor efficiency and safety. Because thorium dioxide (ThO2) is suitable as a model system for more complex materials such as UO2 and its mixed oxides, we present a theoretical investigation of thermal conductivity reduction seen in defect-bearing thorium dioxide and compare directly to experimental measurements. Phonon-mediated thermal transport of the fuel is modeled by a solution to the Boltzmann transport equation (BTE) for phonons. A cluster dynamics (CD) model for lattice defect evolution during irradiation predicts defect densities which are used as input to the BTE for modeling phonon-defect scatterings. Phonon scatterings by lattice defects include those from point defects and vacancy clusters and interstitial clusters of various sizes. The CD model is benchmarked against structural defect characterization of irradiated thorium dioxide using electron microscopy. Thermal conductivity predicted by the BTE model is compared to measured values for irradiated thorium dioxide specimens below room temperature to isolate effects of phonon-defect scattering from intrinsic 3-phonon processes, which dominate at higher temperatures. The computed conductivity values are in partial agreement at temperatures close to room temperature while slight deviations are observed at the lowest measured temperatures, suggesting that implemented phonon-defect scattering cross-section expressions may not be adequate for low temperatures. The presented work provides a necessary investigation of the influence of irradiation induced defects on fuel performance and represents a first step toward a full characterization of phonon mediated thermal transport in irradiated materials with complex defect microstructure.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A finite element method for angular discretization of the radiation transport equation on spherical geodesic grids

Discrete ordinate (S N ) and filtered spherical harmonics (FP N ) based schemes have been proven to be robust and accurate in solving the Boltzmann transport equation but they have their own strengths and weaknesses in different physical scenarios. We present a new method based on a finite element approach in angle that combines the strengths of both methods and mitigates their disadvantages. The angular variables are specified on a spherical geodesic grid with functions on the sphere being represented using a finite element basis. A positivity-preserving limiting strategy is employed to prevent non-physical values from appearing in the solutions. Here, the resulting method is then compared with both S N and FP N schemes using four test problems and is found to perform well when one of the other methods fail.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Dynamic mode decomposition of nonequilibrium electron-phonon dynamics: accelerating the first-principles real-time Boltzmann equation

Abstract Nonequilibrium dynamics governed by electron–phonon ( e -ph) interactions plays a key role in electronic devices and spectroscopies and is central to understanding electronic excitations in materials. The real-time Boltzmann transport equation (rt-BTE) with collision processes computed from first principles can describe the coupled dynamics of electrons and atomic vibrations (phonons). Yet, a bottleneck of these simulations is the calculation of e –ph scattering integrals on dense momentum grids at each time step. Here we show a data-driven approach based on dynamic mode decomposition (DMD) that can accelerate the time propagation of the rt-BTE and identify dominant electronic processes. We apply this approach to two case studies, high-field charge transport and ultrafast excited electron relaxation. In both cases, simulating only a short time window of ~10% of the dynamics suffices to predict the dynamics from initial excitation to steady state using DMD extrapolation. Analysis of the momentum-space modes extracted from DMD sheds light on the microscopic mechanisms governing electron relaxation to a steady state or equilibrium. The combination of accuracy and efficiency makes our DMD-based method a valuable tool for investigating ultrafast dynamics in a wide range of materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Quarkonium Polarization Kinetic Equation from Open Quantum Systems and Effective Field Theories

Recent measurements of polarization phenomena in relativistic heavy ion collisions have aroused a great interest in understanding dynamical spin evolution of the QCD matter. In particular, the spin alignment signature of J/ψ has been recently observed in Pb-Pb collisions at LHC, which may infer nontrivial spin transport of quarkonia in quark gluon plasmas. Motivated by this, we study the spin-dependent in-medium dynamics of quarkonia by using the potential nonrelativistic QCD (pNRQCD) and the open quantum system framework. By applying the Markovian approximation and Wigner transformation, we systematically derive the Boltzmann transport equation for vector quarkonia with polarization dependence in the quantum optical limit. As opposed to the previous study for the spin-independent case where the collision terms depend on chromoelectric correlators, the new kinetic equation incorporates gauge invariant correlators of chromomagnetic fields that determine the recombination and dissociation terms with polarization dependence at the order we are working in the multipole expansion. In the quantum Brownian motion limit, the Lindblad equation with new transport coefficients defined in terms of the chromomagnetic field correlators have also been derived. Our formalism is generic and valid for both weakly-coupled and strongly-coupled quark gluon plasmas. It may be further applied to study spin alignment of vector quarkonia in heavy ion collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

A Characteristics Approach to the Finite Element Method

Herein, we present a new method for solving the linear Boltzmann transport equation. Two commonly used and well-understood methods for solving partial differential equations are the method of characteristics (MOC) and the finite element method (FEM). We propose a new method that combines the fundamental concept of the FEM with the analytic solution from the MOC to obtain coefficients for the FEM basis function expansion. Traditionally, coefficients for the FEM basis function expansion are obtained via matrix inversion. Instead, we solve for the coefficients with the MOC and represent the underlying fields with the basis function expansion using these coefficients. We provide a convergence study for our method with results from two sets of FEM basis functions: Gauss-Legendre and Gauss-Lobatto sets. We also compare two different variations of our method categorized as short characteristics and intermediate characteristics.

42 ENGINEERING↗
DOE OSTI2023

A First Principles Approach to Spectral Phonon Transport in Heterostructures

Understanding thermal transport across interfaces which give rise to a thermal resistance (also known as Kapitza resistance) is a critical issue affecting the development of nanotechnologies. Much modern and emergent nanotechnology consist of adjacent materials, and phonon mediated heat transfer governs thermal behavior across internal interfaces in these devices. The physics of thermal transport in solids are governed both by phenomena occurring at the atomic scale and interactions with the material's microstructure. The forecasting of fundamental quantities such as temperature, heat flux and thermal conductivity typically employs the semi-classical Boltzmann transport equation to predict the macroscopic behavior of materials in terms of the microscopic dynamics of its heat carriers. Kapitza resistance was first discovered in liquid helium experiments and has led to a fundamental research thrust in micro and nano-scale heat transport, the behavior of thermal carriers across internal interfaces. Thermal interfacial resistance (TIR) is a widely studied phenomenon, first engaged by Swartz and Pohl through their development of the acoustic and diffuse mismatch methods, then continued through myriad efforts with varying methods and approaches in an attempt to resolve carrier behavior at thermal interfaces. Many of the fundamental approaches to TIR have been at the nanoscale, and research is conducted with molecular dynamics (MD) and density functional theory (DFT) methods. The limitations of these methods is system size; atomistic methods tend to be limited to system sizes of 100,000 atoms or less. Larger length-scale methods have also been pursued, based on the principles of acoustic or diffuse mismatch, but not all include simulation of TIR using a full phonon band spectrum, or temperature dependent methods. Our approach to enabling phonon transport in layered materials draws upon our previous work of demonstrating spectrally coupled phonon transport in homogeneous and heterogeneous materials. We use a semi-analytical approach in which the Bose-Einstein (B-E) statistics set the strength of the phonon radiance in a frequency group, but the B-E statistics are informed with information from the transport system. The B-E statistics in a single frequency group feels the influence of all the groups through the spatial temperature. We also include a new field term which is an indicator of the amount of non-equilibrium behavior of the phonon spectrum---this is added to the phonon source term in all groups to ensure closure and conservation of energy, as the phonon groups in the transport system and the analytical systems are coupled. This work builds upon our previous approach by adding a phonon coupling term at an internal interface, using the principles of the DMM through transmission and reflection coefficients. In this work, the coefficients are determined through computing a common temperature at the interface, influenced by the phonon band structure of both materials, in effect, providing mixing between the two material systems and using the common temperature to set the strength of the phonon radiance at the boundaries on either side of the interface. Our approach uses material properties computed along various crystallographic orientations, and while some isotropy is built into the interface condition, the material properties weight the phonon distributions in the proper crystalline direction. Greater resolution of phonon behavior in proximity to an interface, and more accurate predictions of TIR are obtained. While it is true the assumption of diffuse mismatch can yield inconsistent results compared to experiment especially at low temperatures, this work focuses on room temperature and beyond effects, for future applications in nuclear fuel, or thermoelectric devices; a modified mismatch approach may be feasible if applied properly. Additionally, our methods focus on bridging mesoscale to engineering scale

36 MATERIALS SCIENCE↗
DOE OSTI2022

Panoramic Mapping of Phonon Transport from Ultrafast Electron Diffraction and Scientific Machine Learning

Abstract One central challenge in understanding phonon thermal transport is a lack of experimental tools to investigate frequency‐resolved phonon transport. Although recent advances in computation lead to frequency‐resolved information, it is hindered by unknown defects in bulk regions and at interfaces. Here, a framework that can uncover microscopic phonon transport information in heterostructures is presented, integrating state‐of‐the‐art ultrafast electron diffraction (UED) with advanced scientific machine learning (SciML). Taking advantage of the dual temporal and reciprocal‐space resolution in UED, and the ability of SciML to solve inverse problems involving coupled Boltzmann transport equations, the frequency‐dependent interfacial transmittance and frequency‐dependent relaxation times of the heterostructure from the diffraction patterns are reliably recovered. The framework is applied to experimental Au/Si UED data, and a transport pattern beyond the diffuse mismatch model is revealed, which further enables a direct reconstruction of real‐space, real‐time, frequency‐resolved phonon dynamics across the interface. The work provides a new pathway to probe interfacial phonon transport mechanisms with unprecedented details.

36 MATERIALS SCIENCE↗
DOE OSTI2025

OpenSn: A massively parallel, open-source simulation environment for discrete ordinates radiation transport

OpenSn is an open-source, massively parallel deterministic radiation transport code for solving the discrete-ordinates ( S N ) form of the Boltzmann transport equation on unstructured, arbitrary polyhedral meshes. It supports high-fidelity simulations involving steady-state, eigenvalue, and adjoint problems for neutral particles (e.g., neutrons, photons, multi-particles), using the multigroup approximation in energy. OpenSn combines angular discretization via discrete ordinates with a discontinuous Galerkin finite element method (DGFEM) in space, enabling accurate resolution of transport physics on arbitrary polyhedral cells, included locally refined spatial grids. It includes multiple angular quadrature types, including locally refined angular quadratures. Written in modern C++ with a Python API, OpenSn runs efficiently on platforms ranging from laptops to supercomputers. The transport sweep algorithm is implemented using a task-based, directed-acyclic-graph (DAG) approach for each angle and supports asynchronous parallelism across thousands of MPI ranks. Group-set aggregation improves compute intensity, and synthetic acceleration techniques (e.g., diffusion synthetic acceleration, second-moment method) enhance solver convergence. OpenSn has been verified on reactor physics problems and demonstrated excellent weak and strong scaling performance on more than 32,768 processes, making it a versatile and robust platform for large-scale transport simulations in complex geometries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

A hybrid Monte Carlo-deterministic second moment method with efficient variance reduction

In this work, we present a hybrid method that combines Monte Carlo with deterministic finite element methods to solve a linear Boltzmann transport equation. Our hybrid method runs orders of magnitude faster than Monte Carlo, without sacrificing accuracy, for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material. We believe that this is the first demonstration of a hybrid Second Moment Method in more than one spatial dimension, the first to consider more than one material, and the first to use variance reduction. Our variance reduction approach arises from an asymptotic analysis in which we show that the magnitude of the scattering source grows without bound. We transform the problem to compute the deviation of the radiation intensity from isotropy. The magnitude of the source in the transformed problem is bounded, and the quality of the hybrid method solution is dramatically improved by a substantial reduction in the variance.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Phonon modal analysis of thermal transport in ThO 2 with point defects using equilibrium molecular dynamics

Defects can significantly degrade the thermal conductivity of ThO 2 , an advanced nuclear fuel material as well as a surrogate for other fluorite-structured materials. Here, we investigate how point defects in ThO 2 impact phonon mode-resolved thermal transport. By incorporating phonon modes from lattice dynamics, we decompose the trajectory and heat flux to phonon normal mode space and extract key phonon properties, including phonon relaxation times and their contributions to thermal conductivity. We implement two methods. The first method is based on the Green Kubo formalism to resolve the contribution of each phonon mode to thermal conductivity. The second resolves the lifetime of individual phonon modes and the thermal conductivity is calculated using the Boltzmann transport equation within relaxation time approximation. Notably, a lower contribution of acoustic modes is revealed compared to perturbative approaches considering only three-phonon scattering processes. The effects of four types of point defects are evaluated. The strongest impact on a reduction in thermal conductivity is from Th interstitials, followed by Th vacancies. O interstitials/vacancies have a similar impact, albeit smaller than defects on the thorium sublattice. These observations are consistent with previous studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Experimental confirmation of first-principles thermal conductivity in Zirconium-doped ThO 2

The degradation of thermal conductivity in advanced nuclear fuels due to the accumulation of fission products and irradiation-induced defects is inevitable, and must be considered as part of safety and efficiency analyses of nuclear reactors. Here, this study examines the thermal conductivity of a zirconium-doped ThO 2 crystal, synthesized via the hydrothermal method using a spatial domain thermoreflectance technique. Zirconium is one of the soluble fission products in oxide fuels that can effectively scatter heat-carrying phonons in the crystalline lattice of fuel. Thus, thermal property measurements of zirconium-doped ThO 2 single crystals provide insights into the effects of substitutional zirconium doping, isolated from extrinsic factors such as grain boundary scattering. The experimental results are compared with first-principles calculations of the lattice thermal conductivity of ThO 2 , employing an iterative solution of the Peierls-Boltzmann transport equation. Additionally, the non-perturbative Green's function methodology is utilized to compute phonon-point defect scattering rates, accounting for local distortions around point defects, including mass difference changes, interatomic force constants, and structural relaxation. The congruence between the predicted results from first-principles calculations and the measured temperature-dependent thermal conductivity validates the computational methodology. Furthermore, the methodologies employed in this study enable systematic investigations of thermal conductivity reduction by fission products, potentially leading to the development of more accurate fuel performance codes.

36 - MATERIALS SCIENCE↗
DOE OSTI2025

Screening of Coulombic Interactions To Achieve a Higher Power Factor in Conjugated Polymers

Thermoelectric properties of conducting polymers typically suffer from molecular chain disordering, as charge transport is predominantly controlled by morphology. This is especially more problematic when counterions are introduced to tune the carrier concentration for optimal thermoelectric performance, which disturbs the morphology further. Here, in this work, we introduce a new avenue for enhancing thermoelectric properties without needing to regulate the morphology, namely, by controlling the coulombic interaction between polarons and counterions. We perform in situ de-doping thermoelectric experiments over 3 orders of magnitude change in electrical conductivity of three distinct thermoelectric polymers, namely, poly(3-hexylthiophene-2,5-diyl) (P3HT), poly[2,5-bis(3-dodecylthiophen-2-yl)thieno[3,2-b]thiophene] (PBTTT-C 12 ), and poly[2,5-(2-octyldodecyl)-3,6-diketopyrrolopyrrole-alt-5,5-(2,5-di(thien-2-yl)thieno[3,2-b]thiophene)] (OD-PDPP2T-TT) conjugated polymers, followed by grazing-incidence wide-angle X-ray scattering (GIWAXS) to study their respective morphologies. We demonstrate a 9-fold enhancement in the thermoelectric power factor in OD-PDPP2T-TT compared to PBTTT-C 12 and link it to the coulombic screening of charge carriers, including in the optimally doped regime. We support this hypothesis using Boltzmann transport equations and show that, in both P3HT and PBTTT-C 12 , as the polymer is doped, impurity scattering remains the dominant scattering mechanism, while in OD-PDPP2T-TT, the scattering mechanism changes from impurity to acoustic phonon limited, resulting in more effective screening of ionized counterions. Our results provide an additional knob to enhance the fundamental understanding of thermoelectric physics of conducting polymers and provide a pathway to achieve higher performance in the field of organic thermoelectrics.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Wide-range continuous tuning of the thermal conductivity of La0.5Sr0.5CoO3-δ films via room-temperature ion-gel gating

Abstract Solid-state control of the thermal conductivity of materials is of exceptional interest for novel devices such as thermal diodes and switches. Here, we demonstrate the ability to continuously tune the thermal conductivity of nanoscale films of La 0.5 Sr 0.5 CoO 3- δ (LSCO) by a factor of over 5, via a room-temperature electrolyte-gate-induced non-volatile topotactic phase transformation from perovskite (with δ ≈ 0.1) to an oxygen-vacancy-ordered brownmillerite phase (with δ = 0.5), accompanied by a metal-insulator transition. Combining time-domain thermoreflectance and electronic transport measurements, model analyses based on molecular dynamics and Boltzmann transport equation, and structural characterization by X-ray diffraction, we uncover and deconvolve the effects of these transitions on heat carriers, including electrons and lattice vibrations. The wide-range continuous tunability of LSCO thermal conductivity enabled by low-voltage (below 4 V) room-temperature electrolyte gating opens the door to non-volatile dynamic control of thermal transport in perovskite-based functional materials, for thermal regulation and management in device applications.

42 ENGINEERING↗