Some path-following techniques for solution of nonlinear equations and comparison with parametric differentiation

Some path-following techniques are described and compared with other methods. Use of multipurpose techniques that can be used at more than one stage of the path-following computation results in a system that is relatively simple to understand, program, and use. Comparison of path-following methods with the method of parametric differentiation reveals definite advantages for the path-following methods. The fact that parametric differentiation has found a broader range of applications indicates that path-following methods have been underutilized

Convection and heat transfer in layered sloping warm-water\ud aquifers

What convective flow is induced if a geologically-tratified groundwater aquifer is subject to a vertical temperature gradient? How strong is the flow? What is the nett heat transfer? Is the flow stable? How does the convection affect the subsequent species distribution if a pollutant finds its way into the aquifer? This paper begins to address such questions. Quantitative models for buoyancy-driven fluid flow in long, sloping warm-water aquifers with both smoothly- and discretely-layered structures are formulated. The steady-state profiles are calculated for the temperature and for the fluid specific volume flux (Darcy velocity) parallel to the boundaries in a sloping system subjected to a perpendicular temperature gradient, at low Rayleigh numbers. The conducted and advected heat fluxes are compared and it is shown that the system acts somewhat like a heat pipe. The maximum possible ratio of naturally advected-to-conducted heat transfer is determined, together with the corresponding permeability and thermal conductivity profiles

Study of high-speed angular-contact ball bearings under dynamic load

Research program studies behavior of specific high-speed, angular-contact ball bearings. Program is aimed at detailed investigation of ball-separator behavior and lubrication surface-finish effects in a specific gyro wheel

Workshop on Heteroepitaxial InP Solar Cells

In a generic sense, the justification for any sort of InP solar cell research applies, i.e. to take advantage of the inherently high radiation resistance and efficiency of InP solar cells. To be more specific, the approach is justified by its potential for significant cost reduction and the availability of greatly increased cell area afforded by substrates such as Si and Ge. The use of substrates, such as the latter two, would result in increased ruggedness, ease of handling, and improved manufacturability. The use of more rugged substrates would lead to a greatly increased capability for cell thinning leading to the desirable feature of reduced array weight

A Non-Intrusive Polynomial Chaos Method for Uncertainty Propagation in CFD Simulations

An inexpensive non-intrusive polynomial chaos (NIPC) method for the propagation of input uncertainty in CFD simulations is presented. The method is straightforward to implement for any stochastic fluid dynamics problem and computationally less expensive than sampling or quadrature based non-intrusive methods. To validate the present NIPC approach, the method has been applied to: (1) an inviscid oblique shock wave problem with geometric uncertainty, (2) an inviscid expansion wave problem with geometric uncertainty, and (3) a subsonic, two-dimensional, laminar boundary layer flow over a flat plate with an uncertain free-stream dynamic viscosity. For all test cases, the statistics (mean and the standard deviation) obtained with the NIPC method were in good agreement with the results of the Monte Carlo simulations. A fourth order polynomial chaos expansion was sufficient to approximate the statistics and the shape of the output uncertainty distributions with the desired accuracy. Only in the shock region of the first test case a sixth order polynomial expansion was required to estimate the statistics of pressure within the 95% confidence intervals of the Monte Carlo results, since the shape of the distributions obtained with 3rd order spatially accurate Euler solutions were highly non-Gaussian in this region

Use of Orbital Radars for Geoscience Investigations

Studies sponsored by NASA at the University of Kansas in cooperation with several other universities and government research agencies are substantiating the applicability of remote sensing by radar to many fields within the earth sciences, agriculture, and oceanography. 1 The purpose of this paper is to show how the properties of the radar return are used to provide geoscience information

Chains of infinite order, chains with memory of variable length, and maps of the interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we caracterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval

Exploring Agricultural Production Systems and Their Fundamental Components with System Dynamics Modelling

Agricultural production in the United States is undergoing marked changes due to rapid shifts in consumer demands, input costs, and concerns for food safety and environmental impact. Agricultural production systems are comprised of multidimensional components and drivers that interact in complex ways to influence production sustainability. In a mixed-methods approach, we combine qualitative and quantitative data to develop and simulate a system dynamics model that explores the systemic interaction of these drivers on the economic, environmental and social sustainability of agricultural production. We then use this model to evaluate the role of each driver in determining the differences in sustainability between three distinct production systems: crops only, livestock only, and an integrated crops and livestock system. The result from these modelling efforts found that the greatest potential for sustainability existed with the crops only production system. While this study presents a stand-alone contribution to sector knowledge and practice, it encourages future research in this sector that employs similar systems-based methods to enable more sustainable practices and policies within agricultural production

Towards a generalized computational fluid dynamics technique for all Mach numbers

Currently there exists no single unified approach for efficiently and accurately solving computational fluid dynamics (CFD) problems across the Mach number regime, from truly low speed incompressible flows to hypersonic speeds. There are several CFD codes that have evolved into sophisticated prediction tools with a wide variety of features including multiblock capabilities, generalized chemistry and thermodynamics models among other features. However, as these codes evolve, the demand placed on the end user also increases simply because of the myriad of features that are incorporated into these codes. In order for a user to be able to solve a wide range of problems, several codes may be needed requiring the user to be familiar with the intricacies of each code and their rather complicated input files. Moreover, the cost of training users and maintaining several codes becomes prohibitive. The objective of the current work is to extend the compressible, characteristic-based, thermochemical nonequilibrium Navier-Stokes code GASP to very low speed flows and simultaneously improve convergence at all speeds. Before this work began, the practical speed range of GASP was Mach numbers on the order of 0.1 and higher. In addition, a number of new techniques have been developed for more accurate physical and numerical modeling. The primary focus has been on the development of optimal preconditioning techniques for the Euler and the Navier-Stokes equations with general finite-rate chemistry models and both equilibrium and nonequilibrium thermodynamics models. We began with the work of Van Leer, Lee, and Roe for inviscid, one-dimensional perfect gases and extended their approach to include three-dimensional reacting flows. The basic steps required to accomplish this task were a transformation to stream-aligned coordinates, the formulation of the preconditioning matrix, incorporation into both explicit and implicit temporal integration schemes, and modification of the numerical flux formulae. In addition, we improved the convergence rate of the implicit time integration schemes in GASP through the use of inner iteration strategies and the use of the GMRES (General Minimized Resisual) which belongs to the class of algorithms referred to as Krylov subspace iteration. Finally, we significantly improved the practical utility of GASP through the addition of mesh sequencing, a technique in which computations begin on a coarse grid and get interpolated onto successively finer grids. The fluid dynamic problems of interest to the propulsion community involve complex flow physics spanning different velocity regimes and possibly involving chemical reactions. This class of problems results in widely disparate time scales causing numerical stiffness. Even in the absence of chemical reactions, eigenvalue stiffness manifests itself at transonic and very low speed flows which can be quantified by the large condition number of the system and evidenced by slow convergence rates. This results in the need for thorough numerical analysis and subsequent implementation of sophisticated numerical techniques for these difficult yet practical problems. As a result of this work, we have been able to extend the range of applicability of compressible codes to very low speed inviscid flows (M = .001) and reacting flows