Certain nonlinear problems of the theory of radiative transfer
Nonlinear problems of theory of radiative transfer, and determination of diffuse reflection for forbidden and other transitions
FORBIDDEN TRANSITION↗
SEARCH · Search NASA
Results for “Diffusion problems”
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.
Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations
The current status of streamline-upwind/Petrov-Galerkin (SUPG) methods for the analysis of flow problems is surveyed in an analytical review. Problem areas addressed include classical Galerkin, upwind, artificial-diffusion, SUPG, discontinuous Galerkin, space-time FEM, and discontinuity-capturing approaches to the scalar advection-diffusion equation; incompressible flows; advective-diffusive systems; and the compressible Euler and Navier-Stokes equations. Graphs and diagrams are provided, and the good stability properties of state-of-the-art SUPG methods are pointed out.
Hughes, Thomas J. R.↗
The abundance of interstellar CO
Data from recent observations of interstellar CO column densities are compiled in tables and graphs and compared with the predictions of theoretical models. The energy-level structure of CO and the excitation of interstellar CO are discussed; UV-absorption and IR line observations are characterized; and techniques used to estimate the CO column density from mm-wavelength observations (based on calibration of the CO line intensity with the column density of H2) are described in detail. Consideration is then given to CO chemistry under interstellar-cloud conditions (isotope fractionation and photodissociation) and models for diffuse, translucent, and dense clouds. A number of unsolved problems requiring additional observations or laboratory investigations are identified.
Van Dishoeck, Ewine F.↗
Radiative transfer solutions for cylindrical coordinates with emitting, absorbing, and anisotropic scattering medium
The radiative transfer equation is solved by the S-N discrete ordinates method in one-dimensional radial and two-dimensional r-z coordinates systems. The walls of the enclosures are diffuse, and the participating medium absorbs, emits and anisotropically scatters the radiative energy. Diffuse wall incidence, isothermal medium emission and collimated incidence problems are considered. Effects of the scattering phase functions on average incident radiation and net radiative heat fluxes are studied. In addition, the effects of scattering albedo, optical thickness and the wall emissivity are briefly discussed.
Jendoubi, Slah↗
An Investigation of Wave Propagations in Discontinuous Galerkin Method
Analysis of the discontinuous Galerkin method has been carried out for one- and two-dimensional system of hyperbolic equations. Analytical, as well as numerical, properties of wave propagation in a DGM scheme are derived and verified with direct numerical simulations. In addition to a systematic examination of the dissipation and dispersion errors, behaviours of a DG scheme at an interface of two different grid topologies are also studied. Under the same framework, a quantitative discrete analysis of various artificial boundary conditions is also conducted. Progress has been made in numerical boundary condition treatment that is closely related to the application of DGM in aeroacoustics problems. Finally, Fourier analysis of DGM for the Convective diffusion equation has also be studied in connection with the application of DG schemes for the Navier-Stokes equations. This research has resulted in five(5) publications, plus one additional manuscript in preparation, four(4) conference presentations, and three(3) departmental seminars, as summarized in part II. Abstracts of papers are given in part 111 of this report.
Hu, Fang Q.↗
A new method of optimal design for a two-dimensional diffuser by using dynamic programming
A new method for predicting the optimal velocity distribution on the wall of a two dimensional diffuser is presented. The method uses dynamic programming to solve the optimal control problem with inequality constraints of state variables. The physical model of optimization is designed to prevent the separation of the boundary layer while approaching the maximum pressure ratio in a diffuser of a specified length. The computational results are in fair agreement with the experimental ones. Optimal velocity distribution on a diffuser wall is said to occur when the flow decelerates quickly at first and then smoothly, while the flow is near separation, but always protected from it. The optimal velocity distribution can be used to design the contour of the diffuser.
Gu, Chuangang↗
The use of modern turbulence theory for calculating eddy diffusivities
Modern turbulence theory and applications to obtain analytical solutions to turbulent transport problems
Hill, J. C.↗
Numerical methods of solving a system of multi-dimensional nonlinear equations of the diffusion type
The principles of conservation and stability of difference schemes achieved using the iteration control method were examined. For the schemes obtained of the predictor-corrector type, the conversion was proved for the control sequences of approximate solutions to the precise solutions in the Sobolev metrics. Algorithms were developed for reducing the differential problem to integral relationships, whose solution methods are known, were designed. The algorithms for the problem solution are classified depending on the non-linearity of the diffusion coefficients, and practical recommendations for their effective use are given.
Agapov, A. V.↗
A Fourier-Chebyshev pseudospectral method for solving steady 3-D Navier-Stokes and heat equations in cylindrical cavities
A Fourier-Chebyshev pseudospectral method for solving steady 3D Navier-Stokes equations in cylindrical cavities is presented and discussed. The general method is pseudo-unsteady and uses a semi-implicit finite difference scheme for the time discretization. The generalized ADI (Alternating Direction Implicit) procedure is then applied to reduce the problem to a successive solution of one-dimensional problems. The spatial approximation uses a Fourier-Galerkin approximation in the periodic direction and a Chebyshev-collocation approximation in the other directions. Difficulties related to the pressure are surmounted by using the artifical compressibility method. A suitable variable change was chosen to avoid the problem of singularity at the axis generated by cylindrical coordinates. The method is first tested on an advection-diffusion equation and then on the Navier-Stokes equations. Finally, the method is illustrated by a convection problem of a differentially heated fluid.
Pulicani, J. P.↗
A spectral collocation method for the Navier-Stokes equations
A Fourier-Chebyshev spectral method for the incompressible Navier-Stokes equations is described. It is applicable to a variety of problems including some with fluid properties which vary strongly both in the normal direction and in time. In this fully spectral algorithm, a preconditioned iterative technique is used for solving the implicit equations arising from semi-implicit treatment of pressure, mean advection and vertical diffusion terms. The algorithm is tested by applying it to hydrodynamic stability problems in channel flow and in external boundary layers with both constant and variable viscosity.
Malik, M. R.↗
A spectral collocation method for the Navier-Stokes equations
A Fourier-Chebyshev spectral method for the incompressible Navier-Stokes equations is described. It is applicable to a variety of problems including some with fluid properties which vary strongly both in the normal direction and in time. In this fully spectral algorithm, a preconditioned iterative technique is used for solving the implicit equations arising from semi-implicit treatment of pressure, mean advection and vertical diffusion terms. The algorithm is tested by applying it to hydrodynamic stability problems in channel flow and in external boundary layers with both constant and variable viscosity.
Malik, M. R.↗
Rocket exhaust plume impingement on the Voyager spacecraft
In connection with the conduction of the long-duration Voyager missions to the outer planets and the sophisticated propulsion systems required, it was necessary to carry out an investigation to avoid exhaust plume impingement problems. The rarefied gas dynamics literature indicates that, for most engineering surfaces, the assumption of diffuse reemission and complete thermal accommodation is warranted in the free molecular flow regime. This assumption was applied to an analysis of a spacecraft plume impingement problem in the near-free molecular flow regime and yielded results to within a few percent of flight data. The importance of a correct treatment of the surface temperature was also demonstrated. Specular reflection, on the other hand, was shown to yield results which may be unconservative by a factor of 2 or 3. It is pointed out that one of the most difficult portions of an exhaust plume impingement analysis is the simulation of the impinged hardware. The geometry involved must be described as accurately and completely as possible.
Baerwald, R. K.↗
The Interstellar Medium
The Interstellar Medium (ISM) forms an integral part of the lifecycle of stars and the galaxy. Stars are formed by gravitational contraction of interstellar clouds. Over their life, stars return much of their mass to the ISM through winds and supernova explosions, resulting in a slow enrichment in heavy elements. Understanding the origin and evolution of the ISM is a key problem within astrophysics. The KAO has made many important contributions to studies of the interstellar medium both on the macro and on the micro scale. In this overview, I will concentrate on two breakthroughs in the last decade in which KAO observations have played a major role: (1) the importance of large Polycyclic Aromatic Hydrocarbon (PAH) molecules for the ISM (section 3) and (2) the study of Photodissociation Regions (PDRs) as an analog for the diffuse ISM at large (section 4). Appropriately, the micro and macro problem are intricately interwoven in these problems. Finally, section 5 reviews the origin of the (CII) emission observed by COBE.
Tielens, Alexander G. G. M.↗
Analytical continuation for calculating multigroup-multizone eigenvalue problems using Lie series.
Critical volume of cylindrical reactors calculated using n-group diffusion theory
REACTOR CORE↗
Time-dependent approximation schemes for some problems of parameter estimation in distributed systems
A parameter estimation method that can be used to estimate functional parameters in delay differential equations and moving boundary problems is discussed. In either problem, the original model equation (which is infinite-dimensional) is approximated by a system of ordinary differential equations that can be solved numerically in an efficient way. The approximation scheme is based on time-dependent spline elements. For the delay equation with time-varying delay, convergence results are presented that indicate the estimates obtained using the approximating system. Numerical test examples converge in some sense to a best-fit parameter for the original system are included by means of which time-varying and state-dependent delays and a time-varying diffusion coefficient in a one-phase, one-dimensional Stefan problem are estimated.
Murphy, K. A.↗
Intensified silicon photodiode array detector linearity Application to coherent anti-Stokes Raman spectroscopy
The linearity of an intensified silicon photodiode array multichannel detector is studied with coherent anti-Stokes Raman and other similar signals. Studies with diffuse and focused (spherically and cylindrically) signals resolved apparent saturation problems which limit the dynamic range of the detector. In addition, it has been shown that there is no short-range wavelength (473-532-nm) dependence on this saturation. Theoretical explanations for these phenomena are also included.
Antcliff, R. R.↗
CONDIF - A modified central-difference scheme for convective flows
The paper presents a method, called CONDIF, which modifies the CDS (central-difference scheme) by introducing a controlled amount of numerical diffusion based on the local gradients. The numerical diffusion can be adjusted to be negligibly low for most problems. CONDIF results are significantly more accurate than those obtained from the hybrid scheme when the Peclet number is very high and the flow is at large angles to the grid.
Runchal, Akshai K.↗
The gabbro-eclogite phase transition and the elevation of mountain belts on Venus
The hypothesis is explored that the crust-mantle boundary of Venus is not in phase equilibrium but rather is rate-limited by the temperature-dependent volume diffusion of the slowest ionic species. The 1D thermal evolution problem is solved assuming that the mountains formed by uniform horizontal shortening of the crust and the lithospheric mantle at a constant rate. The time-dependent density structure and surface elevation are calculated by assuming a temperature-dependent reaction rate and local Airy isostatic compensation. For a horizontal strain rate of 10 exp -15/s or greater, the temperature increase at the base of the crust during mountain formation is modest to negligible, the deepening lower crust is metastable, and the surface elevation increases as the crust thickens. For strain rates less than 10 exp -16/s, crustal temperature increases with time because of internal heat production and the lower crust is more readily transformed to the dense eclogite assemblage. For such models, a maximum elevation is reached during crustal shortening.
Namiki, Noriyuki↗