SEARCH · Search NASA

Results for “diffusion equation”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 577 records · Page 32

All sources NASA NTRS DOE OSTI

NASA NTRS1986

Fluctuation and rotation in diffusion-influenced monomolecular reactions

Models of partially absorbing boundaries for calculating diffusion-influenced chemical reactions are examined analytically. The limitations of diffusion-equation and random-walk models are indicated; the presence of an ambiguous length parameter in a standard radiation-boundary-condition (RBC) model is demonstrated; the RBC model for a boundary with oscillation (at a rate much faster than the rate of thermal collisions) between absorbing and nonabsorbing states is considered; an alternative stochastically switching absorber (SSA) model is introduced and shown to be physically consistent; the equivalence of one-dimensional RBC and SSA models under some conditions is shown; one time passage is calculated for an axially symmetric three-dimensional SSA model with anisotropic absorption; and the analogy between rotation and stochastic switching is explored.

Bashford, Donald↗

NASA NTRS1987

Numerical simulation of cometary nuclei. III - Internal temperatures of cometary nuclei

The thermal diffusion equation for the internal temperature of cometary nuclei is exactly solved by means of a one-dimensional numerical model in order to shed light on the complex behavior of these temperatures with varying orbital and thermal parameters and in order to consider possible cometary nucleus thermal evolution targets for comet rendezvous and/or sample-return missions. The concept of 'new' and 'old' comets, classified in terms of how many passages around the sun have been made, may take on new meaning in view of the present demonstration that differences in eccentricity between two comets having the same period and number of apparitions may yield significantly different internal temperature profiles.

Herman, Gary↗

NASA NTRS1987

Monte Carlo modeling of ionospheric oxygen acceleration by cyclotron resonance with broad-band electromagnetic turbulence

It is demonstrated that cyclotron resonance with observed electric field fluctuations is responsible for production of the oxygen-ion conics that are observed by the Dynamics Explorer 1 satellite in the central plasma-sheet region of the earth's magnetosphere. The ion-velocity distribution is described by a quasi-linear diffusion equation which is solved by the Monte Carlo technique. The acceleration produced by the observed wave spectrum agrees well with the ion observations, in both form and magnitude. This is believed to represent the first successful comparison of an observed conic with any theoretical model.

Retterer, John M.↗

NASA NTRS1987

A ray tracing model for leaf bidirectional scattering studies

A leaf is modeled as a deterministic two-dimensional structure consisting of a network of circular arcs designed to represent the internal morphology of major species. The path of an individual ray through the leaf is computed using geometric optics. At each intersection of the ray with an arc, the specular reflected and transmitted rays are calculated according to the Snell and Fresnel equations. Diffuse scattering is treated according to Lambert's law. Absorption is also permitted but requires a detailed knowledge of the spectral attenuation coefficients. An ensemble of initial rays are chosen for each incident direction with the initial intersection points on the leaf surface selected randomly. The final equilibrium state after all interactions then yields the leaf bidirectional reflectance and transmittance distributions. The model also yields the internal two dimensional light gradient profile of the leaf.

Brakke, T. W.↗

NASA NTRS1987

A new method of boundary parameter estimation for a two-dimensional diffusion system under noisy observations

The purpose of this paper is to establish a method for identifying unknown parameters involved in the boundary state of a class of diffusion systems under noisy observations. A mathematical model of the system dynamics is given by a two-dimensional diffusion equation. Noisy observations are made by sensors allocated on the system boundary. Starting with the mathematical model mentioned above, an online parameter estimation algorithm is proposed within the framework of the maximum likelihood estimation. Existence of the optimal solution and related necessary conditions are discussed. By solving a local variation of the cost functional with respect to the perturbation of parameters, the estimation mechanism is proposed in a form of recursive computations. Finally, the feasibility of the estimator proposed here is demonstrated through results of digital simulation experiments.

Sunahara, Y.↗

NASA NTRS1988

Applications of an exponential finite difference technique

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

Handschuh, Robert F.↗

NASA NTRS1988

An improvement in the numerical integration procedure used in the NASA Marshall engineering thermosphere model

A proposed replacement scheme for the integration of the barometric and diffusion equations in the NASA Marshall Engineering Thermosphere (MET) model is presented. This proposed integration scheme is based on Gaussian Quadrature. Extensive numerical testing reveals it to be faster, more accurate and more reliable than the present integration scheme (a modified form of Simpson's Rule) used in the MET model. Numerous graphical examples are provided, along with a listing of a modified form of the MET model in which subroutine INTEGRATE (using Simpson's Rule) is replaced by subroutine GAUSS (which uses Gaussian Quadrature). It is recommended that the Gaussian Quadrature integration scheme, as used here, be used in the MET model.

Hickey, Michael Philip↗

NASA NTRS1987

Heat transfer to and from vegetated surfaces - An analytical method for the bulk exchange coefficients

The semianalytical model outlined in a previous study (Massman, 1987) to describe momentum exchange between the atmosphere and vegetated surfaces is extended to include the exchange of heat. The methods employed are based on one-dimensional turbulent diffusivities, and use analytical solutions to the steady-state diffusion equation. The model is used to assess the influence that the canopy foliage structure and density, the wind profile structure within the canopy, and the shelter factor can have upon the inverse surface Stanton number (kB exp -1), as well as to explore the consequences of introducing a scalar displacement height which can be different from the momentum displacement height. In general, the triangular foliage area density function gives results which agree more closely with observations than that for constant foliage area density. The intended application of this work is for parameterizing the bulk aerodynamic resistances for heat and momentum exchange for use within large-scale models of plant-atmosphere exchanges.

Massman, William J.↗

NASA NTRS1988

Existence, uniqueness and regularity of a time-periodic probability density distribution arising in a sedimentation-diffusion problem

The sedimentation and diffusion of a nonneutrally buoyant Brownian particle in vertical fluid-filled cylinder of finite length which is instantaneously inverted at regular intervals are investigated analytically. A one-dimensional convective-diffusive equation is derived to describe the temporal and spatial evolution of the probability density; a periodicity condition is formulated; the applicability of Fredholm theory is established; and the parameter-space regions are determined within which the existence and uniqueness of solutions are guaranteed. Numerical results for sample problems are presented graphically and briefly characterized.

Nitsche, Ludwig C.↗

NASA NTRS1987

Implementation of an ADI method on parallel computers

In this paper the implementation of an ADI method for solving the diffusion equation on three parallel/vector computers is discussed. The computers were chosen so as to encompass a variety of architectures. They are the MPP, an SIMD machine with 16-Kbit serial processors; Flex/32, an MIMD machine with 20 processors; and Cray/2, an MIMD machine with four vector processors. The Gaussian elimination algorithm is used to solve a set of tridiagonal systems on the Flex/32 and Cray/2 while the cyclic elimination algorithm is used to solve these systems on the MPP. The implementation of the method is discussed in relation to these architectures and measures of the performance on each machine are given. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Finally conclusions are presented.

Fatoohi, Raad A.↗

NASA NTRS1988

Monte Carlo modeling of large-scale ion-conic generation

Cyclotron resonance with observed electric field fluctuations is demonstrated to be responsible for production of the oxygen ion conics that are observed by the Dynamics Explorer 1 satellite in the central plasma sheet region of the earth's auroral zone. The ion velocity distribution is described by a quasi-linear diffusion equation which is solved using the Monte Carlo technique. The acceleration produced by the observed wave spectrum agrees well with the ion observations, in both form and magnitude.

Retterer, J. M.↗

NASA NTRS1988

A method of boundary parameter estimation for a two-dimensional diffusion system under noisy observations

Sunahara, Y.↗

NASA NTRS1988

Element-by-element and implicit-explicit finite element formulations for computational fluid dynamics

Preconditioner algorithms to reduce the computational effort in FEM analyses of large-scale fluid-dynamics problems are presented. A general model problem is constructed on the basis of the convection-diffusion equation and the two-dimensional vorticity/stream-function formulation of the Navier-Stokes equations; this problem is then analyzed using element-by-element, implicit-explicit, and adaptive implicit-explicit approximation schemes. Numerical results for the two-dimensional advection and rigid-body rotation of a cosine hill, flow past a circular cylinder, and driven cavity flow are presented in extensive graphs and shown to be in good agreement with those obtained using implicit methods.

Tezduyar, T. E.↗

NASA NTRS1989

Distribution function of continuously created newborn and pickup ions in outer cometary exospheres

The time evolution of the distribution function of newborn ions in the solar wind is investigated using a quasi-linear-type diffusion equation. The initial distribution is taken to be a ring beam, which is approximated by delta function in pitch angle and velocity, and it is assumed that the ions are created at a constant rate with a similar distribution. A long-time asymptotic form of ion distribution is obtained, which is a mixture of newborn ions and ions generated throughout the entire process. It is shown that the time asymptotic distribution function exists even in the presence of a continuous ionization process. The stability of the long-time asymptotic distribution was examined for the case of parallel propagation, and the results show that the distribution function can be unstable to low-frequency hydromagnetic waves. The results of the analysis were found to agree with recent satellite observations.

Gaffey, J. D., Jr.↗

NASA NTRS1990

Computation of the unsteady facilitated transport of oxygen in hemoglobin

The transport of a reacting permeant diffusing through a thin membrane is extended to more realistic dissociation models. A new nonlinear analysis of the reaction-diffusion equations, using implicit finite-difference methods and direct block solvers, is used to study the limits of linearized and equilibrium theories. Computed curves of molecular oxygen permeating through hemoglobin solution are used to illustrate higher-order reaction models, the effect of concentration boundary layers at the membrane interfaces, and the transient buildup of oxygen flux.

Davis, Sanford↗

NASA NTRS1990

Fourier analysis of finite element preconditioned collocation schemes

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

Deville, Michel O.↗

NASA NTRS1990

Electric currents in E-like planetary ionospheres

In this paper an MHD approach is used to consider the conduction of electric current in a lightly ionized gas, taking into account the gradients of pressure in the ion and electron gases, in addition to the electric field. The coefficients of electrical conductivity are found for each driver of current. New expressions for the components of heat dissipation associated with each driver of current are developed, which are fully consistent with kinetic theory. The relationship of the results to those obtained by kinetic theory is discussed. New components of currents associated with planetary equatorial electrojets are found. A new diffusion equation for magnetic induction is found, applicable in E-like regions of planetary ionospheres, and stellar photospheres.

Cole, K. D.↗

NASA NTRS1990

Electron heating in quasi-perpendicular shocks - A Monte Carlo simulation

To study the problem of electron heating in quasi-perpendicular shocks, under the combined effects of 'reversible' motion, in the shock electric potential and magnetic field, and wave-particle interactions a diffusion equation was derived, in the drift (adiabatic) approximation and it was solved by using a Monte Carlo method. The results show that most of the observations can be explained within this framework. The simulation has also definitively shown that the electron parallel temperature is determined by the dc electromagnetic field and not by any wave particle induced heating. Wave-particle interactions are effective in smoothing out the large gradients in phase space produced by the 'reversible' motion of the electrons, thus producing a 'cooling' of the electrons. Some constraints on the wave-particle interaction process may be obtained from a detailed comparison between the simulation and observations. In particular, it appears that the adiabatic approximation must be violated in order to explain the observed evolution of the perpendicular temperature.

Veltri, Pierluigi↗