Supersonic leading edge problem according to the ellipsoidal model
Supersonic leading edge problem solved by ellipsoidal model using discrete ordinate method compared with BGK model solution
Huang, A. B.↗
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A new method of recursive estimation in discrete linear systems
Gain of optimal filter and predictor, using recursive estimation in discrete linear systems
Kashyap, R. L.↗
Global convergence of Newton-Gauss-Seidel methods
Global convergence of iterative schemes by Newton-Gauss-Seidel method, considering discrete approximations of elliptic partial differential equations
More, J. J.↗
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.↗
Penetration of solar irradiances through the atmosphere and plant canopies.
The equation of radiative transfer is applied to an analysis of solar irradiances penetrating into a plant canopy covered by a turbid atmosphere. The method of discrete coordinates is applied to vertically inhomogeneous atmospheres and plant canopies. It is shown that four-point quadrature yields results with an accuracy that is consistent with irradiance measurements. It is believed that the presented computational scheme may have considerable agricultural applications.
Weinman, J. A.↗
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.↗
Calculations of neutron flux spectra induced in the earth's atmosphere by galactic cosmic rays
Calculations have been carried out to determine the neutron flux induced in the earth's atmosphere by galactic protons and alpha particles at solar minimum for a geomagnetic latitude of 42 N. Neutron flux spectra were calculated using Monte Carlo and discrete ordinates methods, and various comparisons with experimental data are presented. The magnitude and shape of the calculated neutron-leakage spectrum at the particular latitude considered support the theory that the cosmic-ray-albedo-neutron-decay mechanism is the source of the protons and electrons trapped in the Van Allen belts.
Armstrong, T. W.↗
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.↗
Calculations of neutron flux spectra induced in the earth's atmosphere by galactic cosmic rays.
Calculations have been carried out to determine the neutron flux induced in the earth's atmosphere by galactic protons and alpha particles at solar minimum for a geomagnetic latitude of 42 N. Neutron flux spectra in the energy range from about 10 to the minus 8th to about 100,000 MeV at various depths in the atmosphere were calculated by using Monte Carlo and discrete ordinates methods, and various comparisons with experimental data are presented. The magnitude and shape of the calculated neutron leakage spectrum at the particular latitude considered support the theory that the cosmic ray albedo neutron decay (Crand) mechanism is the source of the protons trapped in the inner radiation belt.
Armstrong, T. W.↗
High-speed leading edge problem.
The sharp leading edge problem 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 discrete ordinate method with a closed-boundary value approach as a tool. Plate length relative to the freestream mean free path is taken to be 52. The gas-surface interaction law is assumed to be diffuse reflection. The local distribution functions of molecular velocities and internal energies (for the diatomic gas) for the entire flowfield have been calculated for a freestream Mach number of 6.1. Comparisons are made between the calculated results and experimental data.
Huang, A. B.↗
Shock-wave structure in a fully ionized gas.
The structure of a steady plane shock in a fully ionized gas has been investigated using the Boltzmann equation with the Gross-Krook type model as the governing equation and the discrete-ordinate method as a tool. The present results agree well with the results obtained by the continuum approach for weak shocks. For strong shocks the present approach gives results that are considerably different from those yielded by the continuum approach, particularly in the high pressure region. Also, the present method gives smooth and continuous shock profiles for high Mach numbers. On the other hand, the results from the continuum approach contain discontinuities in slope. The ion and electron distribution functions across the shock are found to be singly peaked for all cases considered and the effects of the induced electric field is small.
Lu, C. S.↗
Shock-wave structure in a partially ionized gas
The structure of a steady plane shock in a partially ionized gas has been investigated using the Boltzmann equation with a kinetic model as the governing equation and the discrete ordinate method as a tool. The effects of the electric field induced by the charge separation on the shock structure have also been studied. Although the three species of an ionized gas travel with approximately the same macroscopic velocity, the individual distribution functions are found to be very different. In a strong shock the atom distribution function may have double peaks, while the ion distribution function has only one peak. Electrons are heated up much earlier than ions and atoms in a partially ionized gas. Because the interactions of electrons with atoms and with ions are different, the ion temperature can be different from the atom temperature.
Lu, C. S.↗
Theoretical study of lift-generated vortex wakes designed to avoid rollup
Two hypothetical vortex wakes are introduced and studied theoretically to explore whether the rollup of lift-generated vortex sheets can be suppressed. The circulation distribution across each wake is specified such that one rotates and the other translates as a unit due to their self-induced velocities. Several span loadings are constructed from these solutions and the resulting inviscid wake structure is computed for several span lengths behind the generating wing by use of the discrete vortex method wherein the vortex wake is represented by an array of vortices. The final distribution of vortices is then used to estimate the rolling moment on an encountering wing. It is found that, even though the initial specified motions are not sustained, substantial reductions in rolling moment are predicted for certain ranges of the ratio of the span of the generating wing to the following wing.
Rossow, V. J.↗
Fully unsteady subsonic and supersonic potential aerodynamics for complex aircraft configurations for flutter applications
A general theory for study, oscillatory or fully unsteady potential compressible aerodynamics around complex configurations is presented. Using the finite-element method to discretize the space problem, one obtains a set of differential-delay equations in time relating the potential to its normal derivative which is expressed in terms of the generalized coordinates of the structure. For oscillatory flow, the motion consists of sinusoidal oscillations around a steady, subsonic or supersonic flow. For fully unsteady flow, the motion is assumed to consist of constant subsonic or supersonic speed for time t or = 0 and of small perturbations around the steady state for time t 0.
Tseng, K.↗
Turbulent plane Couette flow using probability distribution functions
A numerical scheme employing a combination of the discrete ordinate method and finite differences is developed for solving the one-dimensional form of Lundgren's (1967) model equation for turbulent plane Couette flow. The approach used requires no a priori assumption about the form of the turbulent distribution function, and the numerical solution is obtained directly from the governing differential equations. Two different types of boundary conditions (zero-gradient and Chapman-Enskog) for the distribution function are evaluated by comparing the numerical results with experimental data. It is found that: (1) the present approach gives convergent and stable results over a wide range of Reynolds numbers; (2) Lundgren's equation yields results that compare well with experimental data for mean velocity and skin friction in the case of simple Couette flow; (3) the zero-gradient boundary condition leads to a logarithmic flow profile; and (4) the Chapman-Enskog boundary condition provides very good agreement with experimental data when applied within the near-wall region.
Srinivasan, R.↗
Kinetic theory analysis of rarefied gas flow through finite length slots
A kinetic-theory analysis is made of the flow of a rarefied monatomic gas through a two-dimensional slot connecting two reservoirs. Numerical solutions are obtained by the moment and discrete-ordinate methods. The former method portrays the transition-regime characteristics well but has limitations in the free-molecule regime. The latter method gives accurate results in the free-molecule and slip regimes and bolsters confidence in the accuracy of the transition-regime results. The numerical solution for the mass flux through the slot agrees well with an approximate analytical solution of the moment equations for length-to-width ratios from 6 to 0.5, pressure ratios from 0.8 to 0.1, and Knudsen numbers from 5 to 0.5.
Raghuraman, P.↗
Microwave absorption characteristics of the clouds of Venus from Mariner 10 radio occultation
Measurements of received signal strength at S-band (13 cm) and X-band (4.8 cm) wavelengths during the radio occultation of Mariner 10 by Venus on February 5, 1974, are examined in order to study the structure and composition of the absorbing medium. The frequency excursions of the signals are determined and used to obtain the structure of the refractive index in the lower atmosphere. Profiles of excess signal attenuation due to atmospheric scattering and absorption are presented which indicate that the X-band signal experienced much more absorption and was extinguished at about 50 km, while the S-band signal penetrated to about 42 km. The optical-depth data are inverted by means of a discrete inversion method to obtain the absorption coefficient for each band as a function of height, and the resulting absorption-coefficient profiles are compared with the attenuation at vertical incidence modeled from planetary radar and passive microwave observations of Venus. The absorption coefficients at the two wavelengths are employed to estimate the liquid content and composition of the microwave-absorbing cloud particles.
Kliore, A. J.↗
Discrete analog of an iterative method for inverse eigenvalue problems for Jacobi matrices
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Barcilon, V.↗