Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “discrete ordinates”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

87 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Griffin Capability Improvements in Support of Ex-core Deep-Penetration Problems

Advanced reactor designs, especially portable reactors that are designed to be located closer to humans and operate autonomously, require the ability to accurately compute the ex-core neutron and gamma flux solutions in terms of shielding design optimization to reduce dose rates at the vessel boundary and detector signal prediction to drive the reactor control system. The Nuclear Energy Advanced Modeling and Simulation program has prioritized improvements to the Griffin discrete ordinates (SN) solver for deep-penetration problems in fiscal year 2025. Significant advancements have been made to the Griffin methodologies for solving ex-core deep-penetration problems for steady-state, fixed-source and transient calculations. This work presents the methodology improvements as well as a comprehensive demonstration with a Transient Test Reactor model and measurements.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

The Effect of the Flux Separability Approximation on Multigroup Neutron Transport

The angular dependence of flux-weighted multigroup cross sections is commonly neglected when generating multigroup libraries. The error of this flux separability approximation is typically not isolated from other error sources due to a lack of availability of library generation and corresponding solvers that cannot relax this approximation. These errors can now be isolated and quantified with the availability of a multigroup Monte Carlo transport and multigroup library-generation capability in the OpenMC Monte Carlo transport code. This work will discuss relevant details of the OpenMC implementation, provide an example case useful for detailing the type of errors one can expect from making the flux separability approximation, and end with more realistic problems which show the impact of the approximation and highlight how it can strongly arise from an energy-dependent resonance absorption effect. Since the angle-dependence is intrinsically linked to the energy group structure, these examples also show that relaxing the flux separability approximation with angle-dependent cross sections could be used to reduce either the fine-tuning required to set a multigroup energy structure for a specific reactor type or the number of energy groups required to obtain a desired level of accuracy for a given problem. This trade-off could increase the costs of generating multigroup cross sections, and has the potential to require more memory for storing the multigroup library during the transport calculations, but it can significantly reduce the computational time required since the runtime of a discrete ordinates or method of characteristics neutron transport solver scales roughly linearly with the number of groups.

42 ENGINEERING↗
DOE OSTI2025

Thermal Radiation Transport with Tensor Trains

We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated by the rank of the decomposition. When the solution is “low rank,” the memory footprint of the specific intensity solution vector may be significantly compressed. The algorithm, following a step-then-truncate approach of a traditional discrete ordinates method, operates directly on the compressed state vector, thereby enabling large speedups for low-rank solutions. To achieve these speedups, we rely on a recently developed rounding approach based on the Gram-SVD. We detail how familiar S N algorithms for (gray) thermal transport can be mapped to this TT framework and present several numerical examples testing both the optically thick and thin regimes. The TT framework finds low-rank structure and supplies up to ≃60× speedups and ≃1000× compressions for problems demanding large angle counts, thereby enabling previously intractable SN calculations and supplying a promising avenue to mitigate ray effects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Progress on the National Solar Radiation Data Base (NSRDB): A new DNI computation

This study introduces a new technique to compute direct normal irradiance (DNI) for improving the National Solar Radiation Data Base (NSRDB). A finite-surface integration algorithm is developed to compute solar radiation in differential solid angles and efficiently infer its contribution to a surface perpendicular to the solar direction. A lookup table of cloud bi-directional transmittance distribution function (BTDF) is developed by use of the discrete ordinates radiative transfer (DISORT) model for possible solar and observing directions and various cloud optical and microphysical properties. In each solar incident direction, DNI is given by the cloud BTDFs from approximately 200 differential solid angles. The simulated DNI is calibrated and evaluated using surface observations at the National Renewable Energy Laboratory's (NREL's) Solar Energy Research Laboratory (SRRL) and the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) facility.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Improvements to the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. This document summarizes the transport solver development efforts pursued during Fiscal Year 2022. We added the multiphysics transient capability for the coarse-mesh finite difference accelerated Richardson iteration for discontinuous finite element method discrete ordinates (DFEM-SN) scheme to support high-order heterogeneous transport simulations. HFEM (hybrid finite element method) - PN (spherical harmonics expansion) was completed and red-black iteration was added for solving the HFEM-PN system with both preconditioned Jacobian-free Newton Krylov and Richardson iteration solvers. The HFEM-PN scheme, as one of the low-order transport schemes, is expected for supporting routine design simulations. Pin power reconstruction capability was also designed and implemented with the Griffin ISOXML module to enhance all the low-order transport solvers for more accurate multiphysics simulations. Numerical results are presented for demonstrating the capabilities and verifying their performance, and future works are discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Development of a high fidelity model of the CROCUS experimental reactor

Measurements of scalar flux distributions with fine spatial and energy resolutions are needed to remedy one of the validation shortcomings of the novel neutronics full core solvers, such as MPACT and nTRACER. While a very detailed resolution of the flux can be calculated with such codes, only a limited experimental data set is available to check their accuracy. Such type of measurements are on-going at the zero power reactor CROCUS, operated at the Laboratory for Reactor Physics and System Behaviours of the EPFL, thanks to the development of advanced miniature neutron detection systems. This kind of experimental data would provide the community with a suitable benchmark for the validation of high fidelity neutronics solvers. In parallel, a multi-physics solver for steady-state and transient analysis of nuclear reactors, named GeN-Foam, has been developed. Based on the finite-volume OpenFOAM library, GeN-Foam provides us with enough flexibility to analyze non-conventional reactor geometries such as that of CROCUS. While CROCUS heterogeneities cannot be modeled by MPACT and nTRACER for the moment, GeN-Foam offers a unique opportunity to build a high fidelity model which mimics these codes' method to reach sub-pin simulation resolution. This document aims at describing the work achieved to get from the existing GeN-Foam model of the CROCUS reactor based on a structured mesh and using the neutron diffusion, the first high-fidelity model using discrete ordinates method as an approximation to neutron transport and an unstructured mesh for inter lattice water gap description and sub-pin heterogeneous modeling. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

High-fidelity Pebble Bed Reactor Depletion Based on Pebble Tracking Transport in Griffin

The pebble tracking transport (PTT) method is a high-fidelity, heterogeneous deterministic transport technique for pebble bed reactor analysis. It discretizes the broad-group neutron transport equation in space and angle with the discontinuous finite element and the discrete ordinates method, and utilizes various solving techniques, including mesh sweeping and diffusion acceleration, to provide pebble- wise reaction rates. This work presents the extension of the PTT method to enable fuel depletion capability in the Griffin code. We discuss the implementation details of the PTT-based high-fidelity depletion where isotope inventory of all individual pebbles is tracked through pre-determined pebble flow paths in the core. The implementation is verified with a generic pebble bed reactor model. Some preliminary equilibrium core results are included. Future works are also discussed.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fast All-sky Radiation Model for Solar applications (FARMS) 2023 [SWR-16-18]

The Fast All-sky Radiation Model for Solar applications (FARMS) is used to compute cloudy irradiance. Radiative transfer (RT) models simulating broadband solar radiation have been widely used by atmospheric scientists to model solar resources for various energy applications such as operational forecasting. Due to the complexity of solving the RT equation, the computation under cloudy conditions can be extremely time consuming though many approximations (e.g. two-stream approach and delta-M truncation scheme) have been utilized. Thus, a more efficient RT model is crucial for model developers as a new option for approximating solar radiation at the land surface with minimal loss of accuracy. We have developed a fast all-sky radiation model for solar applications (FARMS) using the simplified clear-sky RT model, REST2, and simulated cloud transmittances and reflectances from the Rapid Radiation Transfer Model (RRTM) with a sixteen-stream Discrete Ordinates Radiative Transfer (DISORT). Simulated lookup tables (LUTs) of cloud transmittances and reflectances were created by varying cloud optical thicknesses, cloud particle sizes, and solar zenith angles. Equations with optimized parameters were fitted to the cloud transmittances and reflectances to develop the model. Using this model the all-sky solar irradiance at the land surface can be computed rapidly by combining REST2 with the cloud transmittances and reflectances. This new RT model is more than 1000 times faster than those currently utilized in solar resource assessment and forecasting since it does not explicitly solve the RT equation for each individual cloud condition. Our results indicate the accuracy of the fast radiative transfer model is comparable to or better than two-stream approximation in term of computing cloud transmittance and solar radiation.

Xie, Yu↗
DOE OSTI2020

Diffusion Synthetic Acceleration for Heterogeneous Domains, Compatible with Voids

A standard approach to solving the S N transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues with DSA preconditioning, particularly on highly heterogeneous domains. For large-scale parallel simulation, it is critical that both (a) preconditioned source iteration converges rapidly and (b) the action of the DSA preconditioner can be applied using fast, scalable solvers, such as algebraic multigrid (AMG). For heterogeneous domains, these two interests can be at odds. In particular, there exist DSA diffusion discretizations that can be solved rapidly using AMG, but they do not always yield robust/fast convergence of the larger source iteration. Conversely, there exist robust DSA discretizations where source iteration converges rapidly on difficult heterogeneous problems, but fast parallel solvers like AMG tend to struggle applying the action of such operators. Moreover, very few current methods for the solution of deterministic transport are compatible with voids. This paper develops a new heterogeneous DSA preconditioner based on only preconditioning the optically thick subdomains. The resulting method proves robust on a variety of heterogeneous transport problems, including a linearized hohlraum mesh related to inertial confinement fusion. Moreover, the action of the preconditioner is easily computed using O(1) AMG iterations, convergence of the transport iteration typically requires 2 to 5× fewer iterations than current state-of-the-art “full” DSA, and the proposed method is trivially compatible with voids. On the hohlraum problem, rapid convergence is obtained by preconditioning less than 3% of the mesh elements with five to ten AMG iterations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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 OSTI2022

Historical review and proof-of-concept future method demonstration of adaptive mesh refinement in nuclear engineering for increased fidelity and computational efficiency

As the nuclear industry's use of computational tool increases, the need for increased fidelity and computational efficiency is well known. While most approaches to increased fidelity rely on applying a fine mesh over the problem domain, a more efficient method is to apply an adaptive mesh refinement (AMR) algorithm to the mesh definition. In the field of nuclear engineering, AMR has previously been used in conjunction with deterministic methods, including: S{sub N} transport methods, Lattice Boltzmann Methods, and COMSOL. The future of AMR in nuclear engineering is to couple it to a Monte Carlo code with the goal of reducing calculation time. A proof-of-concept example yielded positive results for using the gradient of the flux as a refinement criteria. The refinement criteria was varied from 0.01 to 0.10, which yielded a recommended range of 0.01 to 0.04, and the number of refinement iterations was varied from 0 to 7, with diminishing returns seen after 5 iterations. After the success of the proof-of-concept exercise, work began on creating a full program coupling MCNP6.2 and the AMR algorithm in the deal.II library. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

High-order diamond differencing schemes for the Boltzmann Fokker-Planck equation in 3D Cartesian geometries

The Boltzmann Fokker-Planck, an approximate form of the linear Boltzmann equation is commonly used to treat efficiently the transport of charged particles in matter. This paper introduces the application of high-order diamond differencing schemes (HODD), specifically the DD1 and DD2 schemes which are 4- and 6-order accurate respectively, to handle the spatial discretization of that equation in 3D Cartesian geometries. The energy deposition solutions for the coupled transport of electrons and photons presented in this work shows that HODD, compared to classical DD scheme, provides correction to the oscillations and a reduced propensity to yield negative fluxes. They are useful tools to minimize local error, notably in regions with abrupt variations of the flux solution. They also can be used to reduced execution time by decreasing the needed number of voxels to obtain a fixed accuracy. On the tested benchmarks, the DD1 scheme is 87%- 92%-91% more accurate than the classical DD scheme for total, mean per-voxels and maximum deviation of energy deposition values respectively. For comparison, a calculation with 8 times more voxels, requiring roughly 2.5 times more time to execute, is 92%-90%-77% more accurate. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

The MP{sub N} method: a new angular discretization method based on piecewise polynomial interfaces fluxes

In transport calculations, it is well known how S{sub N} method is extremely inefficient in problems where the particle physics is dominated by streaming. The ray-effect eventually produced by the insufficient angular discretization, appears to be extremely persistent with respect to the refinement of the angular quadrature. The MP{sub N} method, that relies on continuous angular representation, offers a robust remedy to such an issue. MP{sub N} is based on the decomposition of the unit sphere into solid angles and on a piecewise continuous definition of interface fluxes, which are expanded in polynomials in each solid angle. This allows propagating more than one angular degree of freedom simultaneously while maintaining unaltered the block-diagonal pattern of the displacement plus removal operator. The method is therefore well suited for the flux resolution by means of a conventional sweep algorithm. Furthermore, unlike the S{sub N} method, MP{sub N} does not rely on discrete directions and, thus, on an angular quadrature formula, but rather constructs a set of linear equations solving for the angular moments of the flux for all discrete solid angles within the sweep. MP{sub N} shows an error convergence rate higher than S{sub N} at the expense of an increased size of the coefficient matrices, so of the computational cost. Although MP{sub N} is not free from ray-effect, the latter is effectively mitigated and less persistent with respect to the increase of the angular refinement order. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Distributed Optimization Approaches with Discrete Variables in the Power Distribution Systems

Traditionally, centralized approaches have predominantly been used for the power system operation and control. With increasing penetration of small-scale distributed energy resources (DERs) in the distribution network, especially independently owned renewable resources, distributed algorithms can serve as a potential alternative for improving scalability, resiliency and addressing privacy concerns. However, the complexity of distributed algorithms significantly increases with the integration of the legacy devices, the operation of which depend on discrete control variables. This paper aims to provide a review of the distributed optimization algorithms incorporating discrete control variables for the power distribution system. While the research in this domain is still at its nascence, an extensive comparison of the approaches in the literature for applying quadratic penalty, branch and bound,ordinal optimization and proximal operator to handle discrete variables in the framework of ADMM and dual decomposition have been addressed. Future research direction in this field have been also provided.

Adan, Jannatul↗
DOE OSTI2023

Verification Problems for Smooth Step Amplitude Load Curves in DYNA3D/Paradyn

This report documents the addition of three new verification tests in the LOADCURVE directory of the DYNA3D/Paradyn Software Quality Assurance test suite. Each test consists of a single element, where the velocities of each node are specified by either the newly added smooth step tabular load curve or another load curve option. The first test assesses the initialization and interpolation of the newly inputted load curve option through tabulated abscissa-ordinate pairs of data. The second test uses the same set of abscissa-ordinate data points and applies offset and scaling parameters available within the load curve definition. The third test defines the smooth step load curve in an original input deck, and assesses its correct redefinition using a restart file. The simulation velocities are compared to their true values at discrete points in time, and each test is verified up to numerical precision. These results confirm that the smooth step load curve option is functioning correctly and as intended.

97 MATHEMATICS AND COMPUTING↗