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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↗

NASA NTRS1990

Pitch angle diffusion of newborn ions due to intrinsic turbulence in the solar wind

The objective of the present study is to understand the interaction of the solar wind with newborn ions in far upstream regions of a comet where the level of intrinsic turbulence is moderately low. Based on the assumption that quasi-linear theory is adequate and applicable, the pitch angle diffusion process and the time evolution of the newborn ion distribution function are investigated. Numerical solutions to the quasi-linear diffusion equation, including the effect of resonance broadening and that of continuous creation of newborn ions due to the ionization process, are obtained under several assumptions and approximations. It is found that theoretical results are consistent with the Giotto observations recently reported by Neugebauer et al. (1989).

Ziebell, L. F.↗

NASA NTRS1991

Modeling of chemical vapor infiltration for ceramic composites reinforced with layered, woven fabrics

A homogeneous model is developed for the chemical vapor infiltration by one-dimensional diffusion into a system of layered plies consisting of woven tows containing bundles of filaments. The model predictions of the amount of deposition and the porosity of the sample as a function of time are compared with the predictions of a recent nonhomogeneous model with aligned holes formed by the weave. The nonhomogeneous model allows for diffusion through the aligned holes, into the spaces between plies, and into the gaps around filaments; i.e., three diffusion equations apply. Relative to the nonhomogeneous results, the homogeneous model underestimates the amount of deposition, since the absence of holes and spaces allows earlier occlusion of gaps around filaments and restricts the vapor infiltration.

Chung, Gui-Yung↗

NASA NTRS1991

Flux-limited diffusion in a scattering medium

A diffusion equation (FDT) is presented with a coefficient that reduces to the appropriate limiting form in the streaming and near thermodynamic limits for a moving fluid in which the dominant source of opacity is Thomson scattering. The present results are compared to those obtained with the corresponding equations for an absorptive medium. It is found that FDT for a scattering medium is accurate to better than less than about 17 percent over the range of optical depths of tau in the range of about 0 to 3.

Melia, Fulvio↗

NASA NTRS1991

Layer tracking, asymptotics, and domain decomposition

A preliminary report is presented on the work on the tracking of internal layers in a singularly-perturbed convection-diffusion equation. It is shown why such tracking may be desirable, and it is also shown how to do it using domain decomposition based on asymptotic analysis.

Brown, D. L.↗