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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
NASA NTRS2002

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.↗
NASA NTRS1993

A multilevel cost-space approach to solving the balanced long transportation problem

We develop a multilevel scheme for solving the balanced long transportation problem, that is, given a set (c(sub kj)) of shipping costs from a set of M supply nodes S(sub k) to a set of N demand nodes D(sub j), we seek to find a set of flows, (x(sub kj)), that minimizes the total cost Sigma(sub k=1)(exp M) Sigma(sub j=1)(exp N) x(sub kj)c(sub kj). We require that the problem be balanced, that is, the total demand must equal the total supply. Solution techniques for this problem are well known from optimization and linear programming. We examine this problem, however, in order to develop principles that can then be applied to more intractible problems of optimization. We develop a multigrid scheme for solving the problem, defining the grids, relaxation, and intergrid operators. Numerical experimentation shows that this line of research may prove fruitful. Further research directions are suggested.

Cavanaugh, Kevin J.↗
NASA NTRS2002

Isotopic Effects in Nuclear Fragmentation and GCR Transport Problems

Improving the accuracy of the galactic cosmic ray (GCR) environment and transport models is an important goal in preparing for studies of the projected risks and the efficiency of potential mitigations methods for space exploration. In this paper we consider the effects of the isotopic composition of the primary cosmic rays and the isotopic dependence of nuclear fragmentation cross sections on GCR transport models. Measurements are used to describe the isotopic composition of the GCR including their modulation throughout the solar cycle. The quantum multiple-scattering approach to nuclear fragmentation (QMSFRG) is used as the data base generator in order to accurately describe the odd-even effect in fragment production. Using the Badhwar and O'Neill GCR model, the QMSFRG model and the HZETRN transport code, the effects of the isotopic dependence of the primary GCR composition and on fragment production for transport problems is described for a complete GCR isotopic-grid. The principle finding of this study is that large errors ( 100%) will occur in the mass-flux spectra when comparing the complete isotopic-grid (141 ions) to a reduced isotopic-grid (59 ions), however less significant errors 30%) occur in the elemental-flux spectra. Because the full isotopic-grid is readily handled on small computer work-stations, it is recommended that they be used for future GCR studies.

Cucinotta, Francis A.↗
NASA NTRS1996

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.↗
NASA NTRS1980

Application of a Galerkin finite element method to atmospheric transport problems

Numerical simulation of the movement of a contaminant within the atmosphere presents difficulties due to the multidimensionality of the problem and the fact that the horizontal transport is usually convection dominated, that the boundary conditions are mixed, and that both slow and fast atmospheric chemical reactions can be important. In this study, numerical experiments using a Crank-Nicolson Galerkin finite element method to solve the time-dependent partial differential equations demonstrate the applicability and accuracy of this method for the variety of conditions encountered in atmospheric pollutant modeling. The Crank-Nicolson Galerkin method using piecewise linear, piecewise cubic Hermite polynomials, and upwind finite elements is shown to accurately model the pure convection of initial wave forms. Numerical results studying the interactions of convection, diffusion, chemical reaction, pollutant removal, and the effects of contaminant emission source strength, source location and multiple sources are also presented.

Carmichael, G. R.↗
DOE OSTI2023

A dynamic variational multiscale method on unstructured meshes for stationary transport problems

Here, this paper presents a variational multiscale (VMS) based finite element method where the stabilization parameter is computed dynamically. The current dynamic procedure takes in a general structure/form of the stabilization parameter with unknown coefficients and computes them dynamically in a local fashion resulting in a dynamic VMS-based finite element method. Thus, a static stabilization parameter with pre-defined coefficients is not needed. A variational Germano identity (VGI) based local procedure suitable for unstructured meshes is developed to perform the dynamic computation in a local fashion. The local VGI based procedure is applied for each interior vertex in the mesh and unknown coefficients are first determined locally at each vertex, and subsequently, for each element a maximum value is taken over the vertices of the element. To make the current procedure practical, a coarser secondary solution is constructed from the primary coarse-scale solution, which is done locally over a patch of elements around each interior vertex. Further, averaging steps are employed to make the local dynamic procedure robust. Currently, the new dynamic VMS formulation is applied to steady problems governed by the advection-diffusion and incompressible Navier-Stokes equations in both 1D and 2D to demonstrate its efficacy and effectiveness.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

The Physics Imposed on a Streaming Operator by Spherical Transport Problems

The streaming operator, which generates a displacement of a particle on a straight line at a constant speed in transport theory, is derived algebraically from a spherical coordinate formulation of Newton’s second law. This derivation leads to an operator that has more partial derivatives than a Cartesian coordinate formulation of the operator. The additional partial derivatives, which are with respect to the normalized velocity variables of a particle, take into account the intrinsic curvature of a ball. Moreover, these partial derivatives mitigate ray effects, which arise when a finite number of normalized velocities (also called directions or discrete ordinates) are used to simulate a continuous S 2 sphere of directions, by rotating the polar axis of the S 2 sphere into the radial direction of the coordinate system. As a consequence of this rotation, the number of actual discrete ordinates is greatly amplified to an enormous number of effective discrete ordinates by a multiplier that is equal to the number of patches that partitions a spherical surface. In addition to the derivation of the streaming operator, we provide in closed form a solution to the system of characteristic equations that is equivalent to the streaming operator. Furthermore, the solution to the system of characteristic equations enables the construction of an integral operator that is the inverse to the streaming operator. Examples in which ray effects are immensely mitigated by spherical coordinates are presented.

integral operator↗
NASA NTRS1964

Monte Carlo techniques for solving transport problems

The Monte Carlo procedure is a model sampling technique. A model is established, and the behavior of sample units in this model is followed. A sufficient number of sample units are followed to obtain a statistical average or macroscopic quantities, which are the quantities of interest. This technique was used in crude form by Fermi in connection with the building of the first atomic pile. Later, Von Neumann and Ulam developed and used the Monte Carlo procedure extensively in developing the atomic bomb. Since then this technique has gained considerable use in nuclear reactor problems (refs. 1 and 2), and we at the Lewis Research Center have been extending it to thermal radiation (refs. 3 and 4), rarefied gas flows, and plasma flow problems (ref. 5). This technique, which requires a large number of sample histories to obtain solutions with small variances, is receiving greater use because of the development of the high-speed electronic computers.

SAMPLED DATA SYSTEM↗
NASA NTRS1986

Exact solution of three-dimensional transport problems using one-dimensional models

Several parameters of certain three-dimensional semiconductor devices including diodes, transistors, and solar cells can be determined without solving the actual boundary-value problem. The recombination current, transit time, and open-circuit voltage of planar diodes are emphasized here. The resulting analytical expressions enable determination of the surface recombination velocity of shallow planar diodes. The method involves introducing corresponding one-dimensional models having the same values of these parameters.

Misiakos, K.↗