Search NASA⌕ Search

SEARCH · Search NASA

Results for “Approximation methods”

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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Investigation of thermal protection systems effects on viscid and inviscid flow fields for manned entry systems

Procedures and methods for predicting aerothermodynamic heating to delta orbiter shuttle vehicles were reviewed. A number of approximate methods were found to be adequate for large scale parameter studies, but are considered inadequate for final design calculations. It is recommended that final design calculations be based on a computer code which accounts for nonequilibrium chemistry, streamline spreading, entropy swallowing, and turbulence. It is further recommended that this code be developed with the intent that it can be directly coupled with an exact inviscid flow field calculation when the latter becomes available. A nonsimilar, equilibrium chemistry computer code (BLIMP) was used to evaluate the effects of entropy swallowing, turbulence, and various three dimensional approximations. These solutions were compared with available wind tunnel data. It was found study that, for wind tunnel conditions, the effect of entropy swallowing and three dimensionality are small for laminar boundary layers but entropy swallowing causes a significant increase in turbulent heat transfer. However, it is noted that even small effects (say, 10-20%) may be important for the shuttle reusability concept.

Bartlett, E. P.↗
NASA NTRS2008

Accuracy of Gradient Reconstruction on Grids with High Aspect Ratio

Gradient approximation methods commonly used in unstructured-grid finite-volume schemes intended for solutions of high Reynolds number flow equations are studied comprehensively. The accuracy of gradients within cells and within faces is evaluated systematically for both node-centered and cell-centered formulations. Computational and analytical evaluations are made on a series of high-aspect-ratio grids with different primal elements, including quadrilateral, triangular, and mixed element grids, with and without random perturbations to the mesh. Both rectangular and cylindrical geometries are considered; the latter serves to study the effects of geometric curvature. The study shows that the accuracy of gradient reconstruction on high-aspect-ratio grids is determined by a combination of the grid and the solution. The contributors to the error are identified and approaches to reduce errors are given, including the addition of higher-order terms in the direction of larger mesh spacing. A parameter GAMMA characterizing accuracy on curved high-aspect-ratio grids is discussed and an approximate-mapped-least-square method using a commonly-available distance function is presented; the method provides accurate gradient reconstruction on general grids. The study is intended to be a reference guide accompanying the construction of accurate and efficient methods for high Reynolds number applications

Thomas, James↗
DOE OSTI2022

Photoionization of Atomic Systems Using the Random-Phase Approximation Including Relativistic Interactions

Approximation methods are unavoidable in solving a many-electron problem. One of the most successful approximations is the random-phase approximation (RPA). Miron Amusia showed that it can be used successfully to describe atomic photoionization processes of many-electron atomic systems. In this article, the historical reasons behind the term “random-phase approximation” are revisited. A brief introduction to the relativistic RPA (RRPA) developed by Walter Johnson and colleagues is provided and some of its illustrative applications are presented.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1980

Theoretical mean colors for RR Lyrae variables

A hydrodynamically pulsating 0.6 solar mass model of a typical RR Lyrae variable was studied with a radiation transport-hydrodynamic computer program to predict theoretical T sub 3 and colors at many phases and to find the proper methods for getting mean colors and the consequent mean effective temperatures. The variable Eddington radiation approximation method was used with gray and with multifrequency absorption coefficients to represent the radiation flow in the outer optically thin layers. Comparison between observed and computed B-V colors indicate that these low Z population 2 models are reasonably accurate using King 1A composition opacities. The well known Oke, Giver, and Searle relation between B-V and T sub e reproduced. Mean colors were found by four different averaging methods. The method that gives a mean color and the mean T sub e closest to the nonpulsating model was the separate intensity means of B and V.

Davis, C. G.↗
NASA NTRS1994

A rapid radiative transfer model for reflection of solar radiation

A rapid analytical radiative transfer model for reflection of solar radiation in plane-parallel atmospheres is developed based on the Sobolev approach and the delta function transformation technique. A distinct advantage of this model over alternative two-stream solutions is that in addition to yielding the irradiance components, which turn out to be mathematically equivalent to the delta-Eddington approximation, the radiance field can also be expanded in a mathematically consistent fashion. Tests with the model against a more precise multistream discrete ordinate model over a wide range of input parameters demonstrate that the new approximate method typically produces average radiance differences of less than 5%, with worst average differences of approximately 10%-15%. By the same token, the computational speed of the new model is some tens to thousands times faster than that of the more precise model when its stream resolution is set to generate precise calculations.

Xiang, X.↗
NASA NTRS1972

Adjoint variational methods in nonconservative stability problems.

A general nonself-adjoint eigenvalue problem is examined and it is shown that the commonly employed approximate methods, such as the Galerkin procedure, the method of weighted residuals and the least square technique lack variational descriptions. When used in their previously known forms they do not yield stationary eigenvalues and eigenfunctions. With the help of an adjoint system, however, several analogous variational descriptions may be developed and it is shown in the present study that by properly restating the method of least squares, stationary eigenvalues may be obtained. Several properties of the adjoint eigenvalue problem, known only for a restricted group, are shown to exist for the more general class selected for study.

Prasad, S. N.↗
DOE OSTI2020

Connected three-body terms in single-reference unitary many-body theories: Iterative and perturbative approximations

This work introduces various approaches to include connected three-body terms in unitary many-body theories, focusing on the driven similarity renormalization group (DSRG). Starting from the least approximate method—the linearized DSRG truncated to one-, two-, and three-body operators [LDSRG(3)]—we develop several approximate LDSRG(3) models with reduced computational cost. Through a perturbative analysis, we motivate a family of iterative LDSRG(3)-n and -n' (n = 1, 2, 3, 4) methods that contain a subset of the LDSRG(3) diagrams. Among these variants, the LDSRG(3)-2 scheme has the same computational complexity of coupled cluster theory with singles, doubles, and triples (CCSDT), but it outperforms CCSDT in the accuracy of the predicted correlation energies. We also propose and implement two perturbative triples corrections based on the linearized DSRG truncated to one- and two-body operators augmented with recursive semi-quadratic commutators [qDSRG(2)]. Overall, the resulting qDSRG(2)+(T) approach matches the accuracy of the “gold-standard” coupled cluster theory with singles, doubles, and perturbative triples model on the energetics of twenty-eight closed-shell atoms and small molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

A method for including external feed in depletion calculations with CRAM and implementation into ORIGEN

A method for including external feed with polynomial time dependence in depletion calculations with the Chebyshev Rational Approximation Method (CRAM) is presented and the implementation of CRAM to the ORIGEN module of the SCALE suite is described. In addition to being able to handle time-dependent feed rates, the new solver also adds the capability to perform adjoint calculations. Results obtained with the new CRAM solver and the original depletion solver of ORIGEN are compared to high precision reference calculations, which shows the new solver to be orders of magnitude more accurate. Lastly, in most cases, the new solver is up to several times faster due to not requiring similar substepping as the original one.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

The regulation mechanism of yitJ and metF riboswitches

Riboswitches which function at the transcriptional level are sensitive to cotranscriptional folding. Based on the recently proposed theory of cotranscriptional folding, we developed a transition node approximation method to effectively decrease the conformation space of long RNA chains. Our results indicate that this approximation is reliable for calculating the cotranscriptional folding kinetics of long mRNA chains. We theoretically studied the cotranscriptional folding behavior of the yitJ and metF riboswitches in the absence/presence of S-adenosylmethionine. Although the two S-box riboswitches have similar OFF-state structures and share common features of riboswitches operated at the transcriptional level, their regulation mechanisms are different. The yitJ riboswitch is regulated by a combination of thermodynamic and kinetic mechanisms, while the metF riboswitch is solely kinetically controlled. For the yitJ riboswitch, transcriptional pausing at the U-stretch directly following the terminator decreases the amount of ligand required to trigger the switch. The different regulation mechanisms and binding affinities of the two riboswitches result from the different lengths of the anti-terminator helix, which in yitJ is short and only disrupts helix P1 of the riboswitch aptamer, but in metF is long and breaks both the helices P1 and P4.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Majorant recursions to determine eigenstate bounds of a symmetric exponential quantum anharmonic oscillator

The determination of the energy states is highly studied issue in the quantum mechanics. Based on expectation values dynamics, energy states can be observed. But conditions and calculations vary depending on the created system. In this work, a symmetric exponential anharmonic oscillator is considered and development of a recursive approximation method is studied to find its ground energy state. The use of majorant values facilitates the approximate calculation of expectation values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Predicting the mineral composition of dust aerosols – Part 2: Model evaluation and identification of key processes with observations

A global compilation of nearly sixty measurement studies is used to evaluate two methods of simulating the mineral composition of dust aerosols in an Earth system model. Both methods are based upon a Mean Mineralogical Table (MMT) that relates the soil mineral fractions to a global atlas of arid soil type. The Soil Mineral Fraction (SMF) method assumes that the aerosol mineral fractions match the fractions of the soil. The MMT is based upon soil measurements after wet sieving, a process that destroys aggregates of soil particles that would have been emitted from the original, undisturbed soil. The second method approximately reconstructs the emitted aggregates. This model is referred to as the Aerosol Mineral Fraction (AMF) method because the mineral fractions of the aerosols differ from those of the wet-sieved parent soil, partly due to reaggregation. The AMF method remedies some of the deficiencies of the SMF method in comparison to observations. Only the AMF method exhibits phyllosilicate mass at silt sizes, where they are abundant according to observations. In addition, the AMF quartz fraction of silt particles is in better agreement with measured values, in contrast to the overestimated SMF fraction. Measurements at distinct clay and silt particle sizes are shown to be more useful for evaluation of the models, in contrast to the sum over all particles sizes that is susceptible to compensating errors, as illustrated by the SMF experiment. Model errors suggest that allocation of the emitted silt fraction of each mineral into the corresponding transported size categories is an important remaining source of uncertainty. Evaluation of both models and the MMT is hindered by the limited number of size-resolved measurements of mineral content that sparsely sample aerosols from the major dust sources. In conclusion, the importance of climate processes dependent upon aerosol mineral composition shows the need for global and routine mineral measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1987

Aerodynamic sensitivities from subsonic, sonic and supersonic unsteady, nonplanar lifting-surface theory

The technique of implicit differentiation has been used in combination with linearized lifting-surface theory to derive analytical expressions for aerodynamic sensitivities (i.e., rates of change of lifting pressures with respect to general changes in aircraft geometry, including planform variations) for steady or oscillating planar or nonplanar lifting surfaces in subsonic, sonic, or supersonic flow. The geometric perturbation is defined in terms of a single variable, and the user need only provide simple expressions or similar means for defining the continuous or discontinuous global or local perturbation of interest. Example expressions are given for perturbations of the sweep, taper, and aspect ratio of a wing with trapezoidal semispan planform. In addition to direct computational use, the analytical method presented here should provide benchmark criteria for assessing the accuracy of aerodynamic sensitivities obtained by approximate methods such as finite geometry perturbation and differencing. The present process appears to be readily adaptable to more general surface-panel methods.

Yates, E. Carson, Jr.↗
NASA NTRS1944

The conformal transformation of an airfoil into a straight line and its application to the inverse problem of airfoil theory

A method of conformal transformation is developed that maps an airfoil into a straight line, the line being chosen as the extended chord line of the airfoil. The mapping is accomplished by operating directly with the airfoil ordinates. The absence of any preliminary transformation is found to shorten the work substantially over that of previous methods. Use is made of the superposition of solutions to obtain a rigorous counterpart of the approximate methods of thin-airfoils theory. The method is applied to the solution of the direct and inverse problems for arbitrary airfoils and pressure distributions. Numerical examples are given. Applications to more general types of regions, in particular to biplanes and to cascades of airfoils, are indicated. (author)

Mutterperl, William↗
NASA NTRS1950

Application of radial-equilibrium condition to axial-flow compressor and turbine design

Basic general equations governing the three-dimensional compressible flow of gas through a compressor or turbine are given in terms of total enthalpy, entropy, and velocity components of the gas. Two methods of solution are obtained for the simplified, steady axially symmetric flow; one involves the use of a number of successive planes normal to the axis of the machine and short distances apart, and the other involves only three stations for a stage in which an appropriate radial-flow path is used. Methods of calculation for the limiting cases of zero and infinite blade aspect ratios and an approximate method of calculation for finite blade aspect ratio are also given. In these methods, the blade loading and the shape of the annular passage wall may be arbitrarily specified.

Wu, Chung-Hua↗
NASA NTRS2015

Predicting the Mineral Composition of Dust Aerosols: Model Evaluation and Identification of Key Processes with Observations - Part 2

A global compilation of nearly sixty measurement studies is used to evaluate two methods of simulating the mineral composition of dust aerosols in an Earth system model. Both methods are based upon a Mean Mineralogical Table (MMT) that relates the soil mineral fractions to a global atlas of arid soil type. The Soil Mineral Fraction (SMF) method assumes that the aerosol mineral fractions match the fractions of the soil. The MMT is based upon soil measurements after wet sieving, a process that destroys aggregates of soil particles that would have been emitted from the original, undisturbed soil. The second method approximately reconstructs the emitted aggregates. This model is referred to as the Aerosol Mineral Fraction (AMF) method because the mineral fractions of the aerosols differ from those of the wet-sieved parent soil, partly due to reaggregation. The AMF method remedies some of the deficiencies of the SMF method in comparison to observations. Only the AMF method exhibits phyllosilicate mass at silt sizes, where they are abundant according to observations. In addition, the AMF quartz fraction of silt particles is in better agreement with measured values, in contrast to the overestimated SMF fraction. Measurements at distinct clay and silt particle sizes are shown to be more useful for evaluation of the models, in contrast to the sum over all particles sizes that is susceptible to compensating errors, as illustrated by the SMF experiment. Model errors suggest that allocation of the emitted silt fraction of each mineral into the corresponding transported size categories is an important remaining source of uncertainty. Evaluation of both models and the MMT is hindered by the limited number of size-resolved measurements of mineral content that sparsely sample aerosols from the major dust sources. The importance of climate processes dependent upon aerosol mineral composition shows the need for global and routine mineral measurements.

aerosols↗
NASA NTRS1945

A method for the calculation of external lift, moment, and pressure drag of slender open-nose bodies of revolution at supersonic speeds

An approximate method is presented for the calculation of the external lift, moment, and pressure drag of slender open-nose bodies of revolution of supersonic speeds. The lift, moment, and pressure drag of a typical ram-jet body shape are calculated at Mach numbers 1.45, 1.60, 1.75, and 3.00; and the lift and moment results are compared with available experimental data. The agreement of the calculated lift and moment data with the experimental data is excellent. The pressure-drag comparison was not presented because of the uncertainty of the amount of skin-friction drag present in the experimental results.

Brown, Clinton E↗
NASA NTRS1977

Review of radiative transfer methods in scattering atmospheres

The radiative transfer in a scattering plane-parallel atmosphere is discussed, considering the exact analytical, the computational and the approximate methods. Some results of numerical comparisons are given. Finally, the difficulties of realistic atmospheric models are emphasized.

Lenoble, J.↗