Solution of rarefied gas transport problems.
Monte Carlo method solution of heat transfer in rarefied gas between infinite flat plates
MONTE CARLO METHOD↗
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Feautrier solution of the electron transport equation
An efficient, accurate, and stable solution to the electron transport problem is presented. The two-stream approximation is discussed in detail, but the solution is developed for the general multistream case. Applied to the photoelectron problem, it is shown that accurate escape fluxes are obtained using only 10 altitudes distributed over the region 100 - 1000 km. The local equilibrium, two-stream, and multistream solutions to the photoelectron problem are compared. In addition, a recursion relation for the moments of the elastic angular scattering phase function is presented.
Link, R.↗
A Systematic Solution Approach for Neutron Transport Problems in Diffuse Regimes
A systematic solution approach for the neutron transport equation, based on a least-squares finite-element discretization, is presented. This approach includes the theory for the existence and uniqueness of the analytical as well as of the discrete solution, bounds for the discretization error, and guidance for the development of an efficient multigrid solver for the resulting discrete problem. To guarantee the accuracy of the discrete solution for diffusive regimes, a scaling transformation is applied to the transport operator prior to the discretization. The key result is the proof of the V-ellipticity and continuity of the scaled least-squares bilinear form with constants that are independent of the total cross section and the absorption cross section. For a variety of least-squares finite-element discretizations this leads to error bounds that remain valid in diffusive regimes. Moreover, for problems in slab geometry a full multigrid solver is presented with V(1, 1)-cycle convergence rates approximately equal to 0.1, independent of the size of the total cross section and the absorption cross section.
Manteuffel, T. A.↗
Effects of particle drift on cosmic ray transport. II - Analytical solution to the modulation problem with no latitudinal diffusion
An analytical solution to a model of the modulation of galactic cosmic rays in the presence of particle drifts is presented and discussed. The solution assumes an energy-independent radial diffusion coefficient proportional to distance and no latitudinal diffusion, and includes energy-independent particle drift velocities similar to those expected in a Parker spiral magnetic field with an equatorial current sheet. The solutions clearly demonstrate the large effects of drifts on the modulated cosmic-ray intensity. For values of the radial diffusion coefficient and particle drift velocity which are plausible for 1-GV-rigidity protons, the logarithmic radial gradient in the inner solar system is reduced by more than a factor of 5 over the value calculated in the absence of drifts. It is found that even for much smaller values of particle drift velocity and radial diffusion coefficient, such as might be expected for protons with energies of the order of 10 MeV, the effects of the drifts can be substantial.
Isenberg, P. A.↗
Application of the method of discrete ordinates to the solution of the transport equation in the case of an inhomogeneous planetary atmosphere
A version of the method of discrete ordinate (MDO) which can be used for an optically thick inhomogeneous atmosphere was developed. The MDO may be implemented as an algorithm simpler than those proposed earlier. The algorithm is the same for each azimuth dependent component of intensity. The MDO can determine the scattered radiation field over its entire length along the vertical. It is shown the MDO, when used for homogeneous atmospheres is in agreement with the results obtained by other methods.
Zasova, L. V.↗
P1 Nonconforming Finite Element Method for the Solution of Radiation Transport Problems
The simulation of radiation transport in the optically thick flux-limited diffusion regime has been identified as one of the most time-consuming tasks within large simulation codes. Due to multimaterial complex geometry, the radiation transport system must often be solved on unstructured grids. In this paper, we investigate the behavior and the benefits of the unstructured P(sub 1) nonconforming finite element method, which has proven to be flexible and effective on related transport problems, in solving unsteady implicit nonlinear radiation diffusion problems using Newton and Picard linearization methods. Key words. nonconforrning finite elements, radiation transport, inexact Newton linearization, multigrid preconditioning
Kang, Kab S.↗
Melanin Inspired Solutions for Transformative Transportation
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Melanin↗
The exact solution of the monoenergetic transport equation for critical cylinders
An analytic solution for the critical, monoenergetic, bare, infinite cylinder is presented. The solution is obtained by modifying a previous development based on a neutron density transform and Case's singular eigenfunction method. Numerical results for critical radii and the neutron density as a function of position are included and compared with the results of other methods.
Westfall, R. M.↗
Efficient yet accurate solution of the linear transport equation in the presence of internal sources - The exponential-linear-in-depth approximation
The present solutions to the linear transport equation pertain to monoenergetic particles' interaction with a multiple scattering/absorbing layered medium with a general anisotropic internal source term. Attention is given to a novel exponential-linear approximation to the internal source, as a function of scattering depth, which furnishes an at-once efficient and accurate solution to the linear transport equation through its reduction of the spatial mesh size. The great superiority of the proposed method is demonstrated by the numerical results obtained in the illustrative cases of (1) an embedded thermal source and (2) a rapidly varying beam pseudosource.
Kylling, Arve↗
Effects of isotope selection on solution convergence in HZE transport
A fragmenting iron ion produces hundreds of isotopes during nuclear reactions. These isotopes are represented in the solution of the transport problem. A reduced set of isotopes is selected to minimize the computational burden but introduces error in the final result. A minimum list of 122 isotopes is required for adequate representation of the mass and charge distributions of the secondary radiation fields. A reduced set of 80 isotopes is sufficient to represent the charge distribution alone and represents reasonably well the linear energy transfer properties of the iron beam. Because iron fragmentation produces nearly every isotope lighter than iron, the resulting 122-isotope list should be adequate for ion beams with charges equal to or less than 26.
Kim, Myung-Hee Y.↗
Membrane rejection of nitrogen compounds
Rejection characteristics of nitrogen compounds were examined for reverse osmosis, nanofiltration, and low-pressure reverse osmosis membranes. The rejection of nitrogen compounds is explained by integrating experimental results with calculations using the extended Nernst-Planck model coupled with a steric hindrance model. The molecular weight and chemical structure of nitrogen compounds appear to be less important in determining rejection than electrostatic properties. The rejection is greatest when the Donnan potential exceeds 0.05 V or when the ratio of the solute radius to the pore radius is greater than 0.8. The transport of solute in the pore is dominated by diffusion, although convective transport is significant for organic nitrogen compounds. Electromigration contributes negligibly to the overall solute transport in the membrane. Urea, a small organic compound, has lower rejection than ionic compounds such as ammonium, nitrate, and nitrite, indicating the critical role of electrostatic interaction in rejection. This suggests that better treatment efficiency for organic nitrogen compounds can be obtained after ammonification of urea.
NASA Discipline Life Support Systems↗
Kinetic theory of dense gases. iv - transport virial coefficients.
Generalized Enskog equation solution containing transport virial coefficients with density corrections for three-body collision effects
TRANSPORT COEFFICIENT↗
Benchmark solutions for the galactic ion transport equations: Energy and spatially dependent problems
Nontrivial benchmark solutions are developed for the galactic ion transport (GIT) equations in the straight-ahead approximation. These equations are used to predict potential radiation hazards in the upper atmosphere and in space. Two levels of difficulty are considered: (1) energy independent, and (2) spatially independent. The analysis emphasizes analytical methods never before applied to the GIT equations. Most of the representations derived have been numerically implemented and compared to more approximate calculations. Accurate ion fluxes are obtained (3 to 5 digits) for nontrivial sources. For monoenergetic beams, both accurate doses and fluxes are found. The benchmarks presented are useful in assessing the accuracy of transport algorithms designed to accommodate more complex radiation protection problems. In addition, these solutions can provide fast and accurate assessments of relatively simple shield configurations.
Ganapol, Barry D.↗
Solutions to bi-Maxwellian transport equations for SAR-arc conditions
The first subsonic solutions of the bi-Maxwellian-based 16-moment set of transport equations for stable auroral red (SAR) arc conditions are presented. These are compared with the solutions obtained from the Maxwellian-based 13-moment transport equations for the same boundary conditions. Close agreement between the 16-moment and 13-moment solutions was obtained for the drift velocity, total electron temperature, total proton heat flow, and total electron heat flow profiles. On the other hand, significant discrepancies were found. Thus, the 16-moment density profile falls off more rapidly with increasing altitude than that computed with the 13-moment equations; the total proton temperature is less in the 16-moment case than in the 13-moment case by several thousand degrees at most altitudes; and differences exist in the ratios of the proton and electron temperature anisotropies with the altitude. A simplified set of transport equations was obtained by dropping terms which remain relatively small at all altitudes.
Demars, H. G.↗
On the transport and propagation of cosmic rays in galaxies. I - Solution of the steady-state transport equation for cosmic ray nucleons, momentum spectra and heating of the interstellar medium
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Lerche, I.↗
Benchmark solutions for the galactic ion transport equations with spatial and energy coupling
In order to anticipate future space shielding requirements, NASA has initiated an effort to formulate computational methods to simulate radiation effects in space. As part of the program, numerical transport algorithms have been developed for the deterministic Boltzman equation describing galactic cosmic ray (GCR) interactions with matter. It thus becomes necessary to assess the accuracy of proposed deterministic algorithms. For this reason, analytical benchmark solutions to mathematically tractable galactic cosmic ray equations have recently been obtained. Even though these problems involve simplifying assumptions of the associated physics, they still contain the essential features of the basic transport processes. The solutions obtained are features of the basic transport processes. The solutions obtained are compared to results from numerical algorithms in order to ensure proper coding and to provide a measure of the accuracy of the numerical methods used in the algorithm. For the first time, mathematical methods have been applied to the galactic ion transport (GIT) equations in the straight ahead approximation with constant nuclear properties. The approach utilizes a Laplace transforms inversion yielding a closed form benchmark solution which is also computationally efficient.
Ganapol, Barry D.↗
Solutions to bi-Maxwellian transport equations for the polar wind
In this study, polar wind solutions are obtained for a broad range of O(+) density, H(+) drift velocity, electron temperature and H(+) temperature boundary conditions. The bi-Maxwellian-based 16-moment set of transport equations is used, since this set is expected to be superior to Maxwellian-based equations in describing large temperature anisotropies and heat flows. The present solutions corroborate earlier results when similar boundary conditions are used. Also, for previously unexplored combinations of boundary conditions, the present solutions are often qualitatively different from any obtained before.
Demars, H. G.↗
Monoenergetic-source solutions of the steady-state cosmic-ray equation of transport
Analytic, steady state, solutions of the cosmic-ray equation of transport for the solar cavity are given for monoenergetic particles released continuously at a specified heliocentric radius. The solutions are used to illustrate energy change processes. A new feature is an apparent buildup of particles at very low energies.
Webb, G. M.↗