Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “DISCRETE ORDINATE METHOD”

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.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS2024

Sensitivity studies of nighttime top-of-atmosphere radiances from artificial light sources using a 3-D radiative transfer model for nighttime aerosol retrievals

By accounting for surface-based light source emissions and top-of-atmosphere (TOA) downward lunar fluxes, we adapted the spherical harmonics discrete ordinate method (SHDOM) 3-dimensional (3-D) radiative transfer model (RTM) to simulate nighttime 3-D TOA radiances as observed from the Visible Infrared Imaging Radiometer Suite (VIIRS) Day/Night Band (DNB) on board the Suomi-NPP satellite platform. Used previously for daytime 3-D applications, these new SHDOM enhancements allow for the study of the impacts of various observing conditions and aerosol properties on simulated VIIRS-DNB TOA radiances. Observations over Dakar, Senegal, selected for its bright city lights and a large range of aerosol optical depth (AOD), were investigated for potential applications and opportunities for using observed radiances containing VIIRS-DNB “bright pixels” from artificial light sources to conduct aerosol retrievals. We found that using the standard deviation (SD) of such bright pixels provided a more stable quantity for nighttime AOD retrievals than direct retrievals from TOA radiances. Further, both the mean TOA radiance and SD of TOA radiances over artificial sources are significantly impacted by satellite viewing angles. Light domes, the enhanced radiances adjacent to artificial light sources, are strong functions of aerosol properties and especially aerosol vertical distribution, which may be further utilized for retrieving aerosol layer height in future studies. Through inter-comparison with both day- and nighttime Aerosol Robotic Network (AERONET) data, the feasibility of retrieving nighttime AODs using 3-D RTM SHDOM over artificial light sources was demonstrated. Our study shows strong potential for using artificial light sources for nighttime AOD retrievals, while also highlighting larger uncertainties in quantifying surface light source emissions. This study underscores the need for surface light emission source characterizations as a key boundary condition, which is a complex task that requires enhanced input data and further research. We demonstrate how quality-controlled nighttime light data from NASA’s Black Marble product suite could serve as a primary input into estimations of surface light source emissions for nighttime aerosol retrievals.

Jianglong Zhang↗
NASA NTRS1985

Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing

The principal features of the discrete-ordinates finite-element method are reviewed, and the applicability of general-purpose discrete-ordinates codes to atmospheric radiative transfer and remote sensing problems is demonstrated. In particular, numerical results for typical problems arising in meteorology, climatology, and remote sensing are shown to be in good agreement with results from other methods and measurements. A sample two-dimensional calculation demonstrates that specific capabilities available in the discrete-ordinates code TWOTRAN can produce new results that are valuable in the characterization of atmospheric effects on remote sensing (e.g., the adjacency effect). The intrinsic limitations of the method are also considered, and it is concluded that the strengths of the discrete-ordinates finite-element method outweigh its weaknesses.

Gerstl, S. A. W.↗
DOE OSTI2022

First-collision source treatment for ray effect mitigation in discrete-ordinate radiation transport solutions

Deterministic transport codes play a fundamental role in the modelling and simulation of neutron transport. One of the most common deterministic methods is the method of discrete ordinates, also known as the S method. While offering significant advantages over other deterministic methods or stochastic methods like Monte Carlo, the method of discrete ordinates suffers from non-physical artifacts in its local solution due to its discretization of angle. These artifacts, referred to as ray effects because of their ray-like appearance, tend to be worse in problems with small sources in areas with little scattering. Significant effort has gone into developing methods to mitigate ray effects, such as the first-collision source treatment, which separates the angular flux into the uncollided and collided fluxes and solving them using non-traditional techniques such as ray tracing. One such code capable of doing this is Lawrence Livermore National Laboratory's deterministic transport code ARDRA. Current ray tracing methods typically trace to a set of points inside a zone to compute an overall flux. However, this approach has significant drawbacks, such as a low order of convergence and not being conservative. Therefore, a new method has been developed that traces instead to a set of points on each of a zone's surfaces and computing the currents, before using these to obtain the flux. A comparison between these two ray tracing methods showed significant advantages to the new surface method, including inherent conservation, a higher convergence rate, and an increase in calculable information like leakage. This work performed under the auspices of the U.S. Department of Energy by Lawrence Liver- more National Laboratory under Contract DE-AC52-07NA27344. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1974

Radiative transfer of visible radiation in turbid atmosphere

Methods are presented for solving radiative transfer problems; they include the doubling method and the closely related matrix method, iterative method, Chandrasekhar's method of discrete ordinates, and Monte Carlo method. To consider radiation transport through turbid atmosphere, an atmospheric model was developed characterizing aerosols by parameters. Intensity and polarization of radiation in turbid atmospheres is discussed, as well as lower atmospheric heating due to solar radiation absorption by aerosols.

Yamamoto, G.↗
DOE OSTI2021

Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering

Here we present an error analysis for the discontinuous Galerkin (DG) method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation with isotropic scattering. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter which characterizes the strength of scattering in the system. However, the rate is not optimal and can be polluted by the presence of boundary layers. In one-dimensional slab geometries, we demonstrate optimal convergence when boundary layers are not present and analyze a simple strategy for balance interior and boundary layer errors. Some numerical tests are also provided in this reduced setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Accelerated Deterministic Phonon Transport With Consistent Material Temperature and Intensities

Abstract We present a method for deterministically solving the frequency and temperature dependent phonon radiative transport (PRT) equation in the single-mode relaxation time (SMRT) approximation in the self-adjoint angular flux (SAAF) form. To handle the nonlinear coupling between the phonon intensities and the material temperature, we apply a linearization approach that is similar to one in thermal radiative transport. This procedure leads to the PRT equation with pseudo-scattering. The method presented includes acceleration of both the inner pseudo-scattering source iterations and outer temperature iteration with a gray diffusion synthetic acceleration (DSA) and Anderson acceleration, respectively. We use the finite-element method to discretize the PRT equation in space and the method of discrete ordinates (SN) for angular discretization. The proposed method is verified by a gray method of manufactured solutions problem and demonstrated on a problem using temperature and direction dependent multigroup data from lithium aluminate (LiAlO2). The iterative performance of the acceleration method in each test is then compared to the unaccelerated method.

Engineering↗
DOE OSTI2021

Data-driven acceleration of thermal radiation transfer calculations with the dynamic mode decomposition and a sequential singular value decomposition

In this work, we present a method for accelerating discrete ordinates radiative transfer calculations for radiative transfer. Our method works with nonlinear positivity fixes, in contrast to most acceleration schemes. The method is based on the dynamic mode decomposition (DMD) and using a sequence of rank-one updates to compute the singular value decomposition needed for DMD. Using a sequential method allows us to automatically determine the number of solution vectors to include in the DMD acceleration. We present results for slab geometry discrete ordinates calculations with the standard temperature linearization. Compared with positive source iteration, our results demonstrate that our acceleration method reduces the number of transport sweeps required to solve the problem by a factor of about 3 on a standard diffusive Marshak wave problem, a factor of several thousand on a cooling problem where the effective scattering ratio approaches unity, and a factor of 20 improvement in a realistic, multimaterial radiating shock problem.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2016

Fast and Accurate Hybrid Stream PCRTMSOLAR Radiative Transfer Model for Reflected Solar Spectrum Simulation in the Cloudy Atmosphere

A hybrid stream PCRTM-SOLAR model has been proposed for fast and accurate radiative transfer simulation. It calculates the reflected solar (RS) radiances with a fast coarse way and then, with the help of a pre-saved matrix, transforms the results to obtain the desired high accurate RS spectrum. The methodology has been demonstrated with the hybrid stream discrete ordinate (HSDO) radiative transfer (RT) model. The HSDO method calculates the monochromatic radiances using a 4-stream discrete ordinate method, where only a small number of monochromatic radiances are simulated with both 4-stream and a larger N-stream (N ≥ 16) discrete ordinate RT algorithm. The accuracy of the obtained channel radiance is comparable to the result from N-stream moderate resolution atmospheric transmission version 5 (MODTRAN5). The root-mean-square errors are usually less than 5x10(exp -4) mW/sq cm/sr/cm. The computational speed is three to four-orders of magnitude faster than the medium speed correlated-k option MODTRAN5. This method is very efficient to simulate thousands of RS spectra under multi-layer clouds/aerosols and solar radiation conditions for climate change study and numerical weather prediction applications.

Yang, Qiguang↗
NASA NTRS1992

Numerical solution of a three-dimensional cubic cavity flow by using the Boltzmann equation

A three-dimensional cubic cavity flow has been analyzed for diatomic gases by using the Boltzmann equation with the Bhatnagar-Gross-Krook (B-G-K) model. The method of discrete ordinate was applied, and the diffuse reflection boundary condition was assumed. The results, which show a consistent trend toward the Navier-Stokes solution as the Knudson number is reduced, give us confidence to apply the method to a three-dimensional geometry for practical predictions of rarefied-flow characteristics. The CPU time and the main memory required for a three-dimensional geometry using this method seem reasonable.

Hwang, Danny P.↗
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 OSTI2024

Neutron transport methods for multiphysics heterogeneous reactor core simulation in Griffin

Griffin is a reactor physics application based on the Multiphysics Object-Oriented Simulation Environment (MOOSE). This work discloses the methods, algorithms, and implementation for simulating heterogeneous reactor dynamics models. Griffin utilizes a discontinuous finite-element method with discrete ordinates (DFEM-S ) to discretize the field variable of the multigroup neutron transport equation. Multiphysics feedback is handled using two-step tabulated cross-section methodology. Feedback quantities are evaluated using the MOOSE-MultiApp system to couple various engineering phenomena, such as heat conduction and thermal fluids. The multiphysics DFEM-S system is solved using fixed-point iteration with a fully asynchronous parallel sweeper, unstructured coarse-mesh finite difference acceleration, and a multi-timescale improved quasi-static method scheme. The implementation is applied to a multiphysics microreactor model, with two transients: one initiated by a single heat-pipe failure and another by control drum rotation. Importantly, these examples demonstrate the ability of Griffin to tractably solve the neutron transport equation considering seven independent variables and feedback.

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

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 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↗
NASA NTRS1972

The design of asymmetric 4 pi shields for space reactors

A one dimensional shield optimization program based on the method of discrete ordinates has been developed and is used to determine material thicknesses used in asymmetric 4 pion shields for space power reactors. The two dimensional discrete ordinates program DOT is used to check the design, and the information generated in the DOT calculation is used as a guide in shaping the shield which may be considered a first step in two dimensional shield optimization.

Engle, W. W., Jr.↗
NASA NTRS1972

Analytic approach to photoelectron transport.

The equation governing the transport of photoelectrons in the ionosphere is shown to be equivalent to the equation of radiative transfer. In the single-energy approximation this equation is solved in closed form by the method of discrete ordinates for isotropic scattering and for a single-constituent atmosphere. The results include prediction of the angular distribution of photoelectrons at all altitudes and, in particular, the angular distribution of the escape flux. The implications of these solutions in real atmosphere calculations are discussed.

Stolarski, R. S.↗
NASA NTRS1973

Test of statistical models for gases with and without internal energy states.

The problem of nonlinear rarefied Couette flow with heat transfer has been studied for both monatomic and diatomic gases using the Boltzmann equation with the Bhatnagar-Gross-Krook type models as the governing equation and the method of discrete ordinates as a tool. The calculated results have been compared with the existing experimental data in order to test the accuracy and the applicability of the statistical models for this one-dimensional problem. The calculated density results are found to be in good agreement with available experimental data; the calculated heat flux solution for the linear case is found to always be lower than the experimental data of Teagan and Springer. The comparisons made here indicate that the statistical models are indeed reasonably accurate so that their use is justified in the type of problems investigated.

Huang, A. B.↗