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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part I: Flux and Eigenvalue Solutions

Computing in the energy dimension is one of the greatest challenges confronting present-day deterministic neutron transport solvers. Accurately resolving the neutron flux as neutrons downscatter across resonances in the nuclear cross sections currently requires considerable computing power and suffers from approximation errors. Flux uncertainty resulting from the uncertainty of the resonance structure is the single-largest cause of reactivity uncertainty. Any additional reference solution for the critical neutron downscattering problem with resonance phenomena would be a boon to verification and validation of neutronics codes. This paper establishes a benchmark to verify the accuracy of neutron transport criticality solvers along the energy dimension. For the first time, the analytic solution of the flux amplitude is derived in the particular case of an infinite homogeneous medium with isotropic scattering in the center of mass and an arbitrary number of no-threshold, neutral particle reaction resonances (e.g., radiative capture, fission, and resonance scattering). Furthermore, original analytic expressions are established to quantify the discrepancy between the ψ k (E) and ψ α (E) flux amplitudes, respective solutions of the multiplication factor k, or the exponential time-evolution frequency α eigenproblems. The physical study of these relations led to analysis of their first-order relative difference near the criticality condition α=0. Finally, numerical solutions are provided to a benchmark problem constituted of the first resonance of 239 Pu, the 6.67-eV resonance of 238 U, and a scattering isotope with a flat cross section, allowing for the computational verification of the energy resolution of current neutron transport criticality codes. Through these novel results, this analytic benchmark can serve as a reference to verify the energy resolution and sensitivity analysis of neutron transport criticality calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

A Review of Lattice-Boltzmann Models Coupled with Geochemical Modeling Applied for Simulation of Advanced Waterflooding and Enhanced Oil Recovery Processes

To maintain economic profit and improve the oil production efficiency after the primary and secondary production phase, advanced waterflooding techniques such as low salinity waterflooding in carbonate reservoirs have been investigated in numerical simulations, laboratory experiments, and field pilot tests. Multiple underlying mechanisms have been proposed based on these studies, and they are still under debate. Various numerical modeling approaches are introduced, but there exists a lack of a pore-scale comprehensive modeling scheme to fully understand the processes. Lattice-Boltzmann method (LBM) is a type of numerical fluid flow modeling technique that shows capabilities and flexibilities in modeling pore-scale fluid flow to integrate physical–chemical processes within complex structures. The intrinsic feature of LBM makes it a promising framework for simulating advanced waterflooding due to its flexibility, accuracy, and parallel efficiency. LBM works either by itself for solving reactive transport problems or by coupling with a third-party reaction solver. This review mainly introduces the LBM fluid flow and reactive transport capabilities and the concept and modeling approaches to simulate advanced waterflooding techniques. Meanwhile, an evaluation of the coupled LBM models for enhanced oil recovery (EOR) simulations is discussed with future research challenges and directions concluded.

02 PETROLEUM↗
DOE OSTI2021

Solution Irregularity Remediation for Spatial Discretization Error Estimation for S N Transport Solutions

The discrete ordinates linear Boltzmann transport equation is typically solved in its spatially discretized form, incurring spatial discretization error. Quantification of this error for purposes such as adaptive mesh refinement or error analysis requires an a posteriori estimator, which utilizes the numerical solution to the spatially discretized equation to compute an estimate. Because the quality of the numerical solution informs the error estimate, irregularities, present in the true solution for any realistic problem configuration, tend to cause the largest deviation in the error estimate vis-a-vis the true error. In this paper, an analytical partial singular characteristic tracking (pSCT) procedure for reducing the estimator’s error is implemented within our novel residual source estimator for a zeroth-order discontinuous Galerkin scheme, at the additional cost of a single inner iteration. Here, a metric-based evaluation of the pSCT scheme versus the standard residual source estimator is performed over the parameter range of a Method of Manufactured Solutions test suite. The pSCT scheme generates near-ideal accuracy in the estimate in problems where the dominant source of the estimator’s error is the solution irregularity, namely, problems where the true solution is discontinuous and problems where the true solution’s first derivative is discontinuous and the scattering ratio is low. In problems where the scattering ratio is high and the true solution is discontinuous in the first derivative, the error in the scattering source, which is not converged by the pSCT scheme, is greater than the error incurred due to the irregularity. Ultimately, a pSCT scheme is judged to be useful for error estimation in problems where the computational cost of the scheme is justified. In the presence of many irregularities, such a scheme may be intractable for general use, but in benchmarks, as an analytical tool, or in problems that have nondissipative discontinuities, the scheme may prove invaluable.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1991

Transport of photons produced by lightning in clouds

The optical effects of the light produced by lightning are of interest to atmospheric scientists for a number of reasons. Two techniques are mentioned which are used to explain the nature of these effects: Monte Carlo simulation; and an equivalent medium approach. In the Monte Carlo approach, paths of individual photons are simulated; a photon is said to be scattered if it escapes the cloud, otherwise it is absorbed. In the equivalent medium approach, the cloud is replaced by a single obstacle whose properties are specified by bulk parameters obtained by methods due to Twersky. Herein, Boltzmann transport theory is used to obtain photon intensities. The photons are treated like a Lorentz gas. Only elastic scattering is considered and gravitational effects are neglected. Water droplets comprising a cuboidal cloud are assumed to be spherical and homogeneous. Furthermore, it is assumed that the distribution of droplets in the cloud is uniform and that scattering by air molecules is neglible. The time dependence and five dimensional nature of this problem make it particularly difficult; neither analytic nor numerical solutions are known.

Solakiewicz, Richard↗
NASA NTRS1995

Computing Interactions Of Free-Space Radiation With Matter

High Charge and Energy Transport (HZETRN) computer program computationally efficient, user-friendly package of software adressing problem of transport of, and shielding against, radiation in free space. Designed as "black box" for design engineers not concerned with physics of underlying atomic and nuclear radiation processes in free-space environment, but rather primarily interested in obtaining fast and accurate dosimetric information for design and construction of modules and devices for use in free space. Computational efficiency achieved by unique algorithm based on deterministic approach to solution of Boltzmann equation rather than computationally intensive statistical Monte Carlo method. Written in FORTRAN.

Wilson, J. W.↗
DOE OSTI2022

Performance enhancement of planar MOC calculation in hexagonal geometries by assembly-wise domain decomposition

The parallelization of planar Method of Characteristics (MOC) calculation with the higher order scattering in the hexagonal version of the nTRACER direct whole core calculation code is enhanced by adopting assembly-wise domain decomposition and other techniques. In order to augment the hexagonal domain decomposition, the three-color scheme, the angular decomposition, and the angular flux storage scheme are examined. The parallel performance assessed for the VVER benchmark problems demonstrates that the hexagonal assembly-wise domain decomposition significantly reduces the computing time in ray tracing by up to 64 %. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Formulation of the density eigenvalue problem in neutron transport for relevant engineering applications

A new formulation of the density eigenvalue problem for the neutron transport equation is presented. This new eigenvalue, named ζ eigenvalue can be introduced freely in the transport model, acting on a selected portion of the phase space. Despite its broader applications and its connection with the nature of the transport operator, the ζ eigenvalue has been presented here mainly as a design-oriented technique for the efficient evaluation of the critical concentration for a specific nuclide (or mixture of nuclides). This new eigenvalue is particularly adequate to study the definition of the material composition in the criticality design process of a multiplying system. The method is then applied for the study of classical problems such as the critical moderation ratio and the poison concentration to control the reactor. Some results are presented in one dimensional configuration using the multi- group spherical harmonics approach. This eigenvalue formulation proves to be a convenient and useful way to attain criticality, also for complex, realistic systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Bolt: A Fast Solver for Kinetic Theories Using a High-Resolution Constrained Transport Scheme [Slides]

Our understanding of collisionless and semi-collisional plasmas in the nonlinear regime is limited by the expense of computing solutions numerically. Bolt is a fast, GPU-accelerated code for rapidly computing such solutions with accurate transport and an approximate collision operator. Such calculations are relevant to both problems in astrophysics, such as heat conduction and magnetic reconnection in accretion disks around black holes, and also to programmatic interests at LANL. The bolt code paper, demonstrating accuracy via a suite of test problems calculated on kodiak, is currently in preparation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A Comparison of GPU-Accelerated Multiphase CFD Solvers on the Polaris Supercomputer: Part 1

This report is in support of the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program sponsored by the U.S. Department of Energy (USDOE). With INCITE-level resources, one project, titled BubblyFlow, was granted computational resources for the 2025 calendar year on the Polaris supercomputer at the Argonne Leadership Computing Facility (ALCF). The project aims to conduct simulations to understand the fundamental characteristics of turbulent bubbly flow phenomena in nature. Staff at the ALCF and Argonne’s Computational Science division, along with collaborators at the City College of New York and University of Illinois at Chicago, helped a summer student to assess the accuracy and performance of two high performance computing (HPC) codes. Both codes, ImExLBM and FluTAS, are fundamentally different in their mathematical and numerical modeling. However, both may be used to solve the same physical problem. The collaboration sought to better understand the differences between both codes in terms of accuracy and efficiency. This would ultimately help the BubblyFlow project better utilize resources and establish a knowledge-base of code capabilities in future simulation campaigns. We compare ImExLBM and FluTAS, two high-performance multiphase computational fluid dynamics (CFD) solvers, in terms of physical fidelity, time-to-solution, and parallel efficiency. We validate ImExLBM (Implicit-Explicit Lattice Boltzmann Method) against a canonical benchmark and assess it’s performance relative to FluTAS (Fluid Transport Accelerated Solver), a well-established open-source CFD code.

97 MATHEMATICS AND COMPUTING↗
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

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 OSTI2022

Analysis of cell-based diffusion acceleration for the slice balance approach

In this work, we perform analysis on the use of cell-based diffusion acceleration methodologies to accelerate the convergence of transport solutions discretized with the slice balance approach (SBA) on unstructured polygonal grids.We investigated both linear diffusion synthetic acceleration (DSA) and non linear diffusion acceleration (NDA), including its partial-current variant (pNDA). DSA and NDA were both shown to diverge for intermediate ranges of mesh optical thicknesses. However, pNDA and Krylov methods like GMRES and Broyden stabilized the acceleration schemes, including problems with degenerate cells formed by mesh refinement. (author)

42 ENGINEERING↗
DOE OSTI2023

Semiconductor Nanostructures by Scientific Design (Final Technical Report)

We developed and used quantum simulation techniques to predict structural, electronic, optical and thermal properties affecting the scientific design of semiconductor nanostructures. We focused on the study of surfaces and interfaces at the nanoscale, in particular embedding and solvation of semiconductor nanoparticles, and provided a microscopic description of nanostructured materials in realistic environments, directly comparable with experimental conditions. We addressed three major problems: (i) the design of realistic structural models of integrated nanostructures, e.g. quantum dots embedded in solid matrices and nanostructures immersed in fluids; (ii) the development of efficient and accurate calculations to describe the excited state properties of nanostructures, beyond standard Density Functional Theory, so as to understand and predict electronic properties involved in renewable energy applications, for example solar conversion devices. In particular we developed and used methods based on a many body perturbation theory. (iii) the development of calculations of heat transport properties of nanostructured materials, for thermoelectric applications, including predictive calculations of thermal and electrical conductivity and of Seebeck coefficients. Specifically, we developed and used methods based on the Boltzmann transport equation and molecular dynamics.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2026

A Proof of the Asymptotic Variance of Path Length Estimators for Single-Collision Monte Carlo Source Iteration in the Thick Diffusion Limit

Here, we prove a theorem relating the variance of path length estimators for single-collision Monte Carlo source iteration to a parameter that becomes infinitesimally small in an important physical regime arising in radiative transfer. In our usage, “single-collision Monte Carlo source iteration” refers to Monte Carlo Boltzmann transport methods in which each Monte Carlo particle history includes no more than a single collision, and the physics of multiple scattering is modeled by lagging the scattering source term and iterating until this term converges. Our theorem can be used to construct variance reduction techniques which improve the order of the estimator variance. This enables calculations that would otherwise require impractically large sample sizes to achieve practical estimator uncertainties. We believe this is the first postulation of a theorem relating estimator variance to a limiting case parameter for single-collision Monte Carlo source iteration, and the first proof of such a theorem. We illustrate the theorem’s value with an example in which the authors of a transport method used the theorem to design a variance reduction technique that improved the uncertainty of their solution by a factor of about 500 for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material.

Mathematics and Computing↗
DOE OSTI2022

Reduced-order modeling of neutron transport separated in energy by Minimax Proper Generalized Decomposition

In this article, we demonstrate a Petrov-Galerkin Proper Generalized Decomposition (PGD) known as Minimax PGD for modeling neutron transport separated in energy. To compare the Minimax with the classical Galerkin PGD, we assess both on a model problem of UO{sub 2} or Mixed Oxide (MOX) fuel pins in an infinite lattice with 3 industry-standard energy meshes. We find the Minimax PGD achieves a superior decomposition to Galerkin PGD, both with and without update of the energy modes. This suggests Minimax PGD may be more computationally efficient, provided this reduction in modes (to achieve a given accuracy) outweighs the cost of solving the necessary adjoint problems. In either case, we note that PGD offers an a priori Reduced-Order Model (ROM) which may be dramatically cheaper to solve than the full-order model, especially in problems with fine to ultrafine energy meshes. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS2004

The FLUKA code for space applications: recent developments

The FLUKA Monte Carlo transport code is widely used for fundamental research, radioprotection and dosimetry, hybrid nuclear energy system and cosmic ray calculations. The validity of its physical models has been benchmarked against a variety of experimental data over a wide range of energies, ranging from accelerator data to cosmic ray showers in the earth atmosphere. The code is presently undergoing several developments in order to better fit the needs of space applications. The generation of particle spectra according to up-to-date cosmic ray data as well as the effect of the solar and geomagnetic modulation have been implemented and already successfully applied to a variety of problems. The implementation of suitable models for heavy ion nuclear interactions has reached an operational stage. At medium/high energy FLUKA is using the DPMJET model. The major task of incorporating heavy ion interactions from a few GeV/n down to the threshold for inelastic collisions is also progressing and promising results have been obtained using a modified version of the RQMD-2.4 code. This interim solution is now fully operational, while waiting for the development of new models based on the FLUKA hadron-nucleus interaction code, a newly developed QMD code, and the implementation of the Boltzmann master equation theory for low energy ion interactions. c2004 COSPAR. Published by Elsevier Ltd. All rights reserved.

Non-NASA Center↗
DOE OSTI2026

Path integral molecular dynamics: A high-fidelity approach to quantum dynamics of electrons

We investigate electron transport in the uniform electron gas using ring-polymer molecular dynamics (RPMD). Working in the weakly coupled, non-degenerate regime, we use RPMD to probe how the onset of quantum diffraction effects at high temperature reshapes electron–electron collisions and leads to a classical-to-quantum crossover in macroscopic transport properties. Static thermodynamics obtained with RPMD are consistent with the weak-coupling equation of state, confirming correct quantum Boltzmann sampling. Real-time transport extracted from mean square displacements exhibits the expected ballistic-to-diffusive transition and a systematic reduction of the electronic self-diffusivity as quantum effects strengthen, due to quantum diffraction modifying electron–electron collisions. Direct ring-polymer scattering simulations reveal diffractive “softening” of binary deflections, providing a micro-to-macro link between collision physics and diffusion. The present study establishes RPMD as a quantitative, trajectory-based tool for electron transport across the classical–quantum crossover and furnishes benchmarks for improving Coulomb-log interpolation models. We outline extensions to multi-component plasmas and a path to incorporate Fermi–Dirac statistics within path-integral dynamics.

Electronic transport↗
DOE OSTI2022

Analytical benchmark solution for 1-D neutron transport coupled with thermal conduction and material expansion

In this work we present fully analytical solutions for a class of finite, homogeneous, 1-D slab benchmark problems with nonlinear temperature feedback effects. The proposed class of benchmarks include multiplicative 1-D neutron transport (limited to quasistatic S{sub 2} with μ = ±1) coupled with thermal conduction, convection, Doppler broadening, and expansion effects along the length of the slab. This class of benchmark models, along with the corresponding analytical solutions, are valuable for validating multiphysics analysis frameworks that support coupled neutronics/thermal/structural calculations. Analytical solutions for the benchmarks are obtained by introducing an ansatz that the equilibrium flux and temperature distributions in the slab have the same shape. Specific values for the total microscopic cross section, σ{sub t,0}, and conductive heat transfer coefficient, h, that satisfy the assumed ansatz are then determined. A discussion of the procedure for generating benchmark models and analytical solutions is provided, along with numerical results for an example set of model parameters and thoughts on practical applications of the benchmarks for multiphysics code validation. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗