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NASA NTRS1999

Solving Upwind-Biased Discretizations: Multigrid Solver Using Semicoarsening - 2

This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid).

Diskin, Boris↗

NASA NTRS1999

Institutional Memory Preservation at NASA Glenn Research Center

In this era of downsizing and deficit reduction, the preservation of institutional memory is a widespread concern for U.S. companies and governmental agencies. The National Aeronautical and Space Administration faces the pending retirement of many of the agency's long-term, senior engineers. NASA has a marvelous long-term history of success, but the agency faces a recurring problem caused by the loss of these engineers' unique knowledge and perspectives on NASA's role in aeronautics and space exploration. The current work describes a knowledge elicitation effort aimed at demonstrating the feasibility of preserving the more personal, heuristic knowledge accumulated over the years by NASA engineers, as contrasted with the "textbook" knowledge of launch vehicles. Work on this project was performed at NASA Glenn Research Center and elsewhere, and focused on launch vehicle systems integration. The initial effort was directed toward an historic view of the Centaur upper stage which is powered by two RL-10 engines. Various experts were consulted, employing a variety of knowledge elicitation techniques, regarding the Centaur and RL-10. Their knowledge is represented in searchable Web-based multimedia presentations. This paper discusses the various approaches to knowledge elicitation and knowledge representation employed, and assesses successes and challenges in trying to perform large-scale knowledge preservation of institutional memory. It is anticipated that strategies for knowledge elicitation and representation that have been developed in this grant will be utilized to elicit knowledge in a variety of domains including the complex heuristics that underly use of simulation software packages such as that being explored in the Expert System Architecture for Rocket Engine Numerical Simulators.

Coffey, J.↗

NASA NTRS1999

Advanced Multigrid Solvers for Fluid Dynamics

The main objective of this project has been to support the development of multigrid techniques in computational fluid dynamics that can achieve "textbook multigrid efficiency" (TME), which is several orders of magnitude faster than current industrial CFD solvers. Toward that goal we have assembled a detailed table which lists every foreseen kind of computational difficulty for achieving it, together with the possible ways for resolving the difficulty, their current state of development, and references. We have developed several codes to test and demonstrate, in the framework of simple model problems, several approaches for overcoming the most important of the listed difficulties that had not been resolved before. In particular, TME has been demonstrated for incompressible flows on one hand, and for near-sonic flows on the other hand. General approaches were advanced for the relaxation of stagnation points and boundary conditions under various situations. Also, new algebraic multigrid techniques were formed for treating unstructured grid formulations. More details on all these are given below.

Brandt, Achi↗

NASA NTRS2000

Mars Oxidant: Proof of Concept and Quantitative Analysis

Textbooks make us believe that in every silicate mineral, on Earth, Mars and elsewhere, the oxygen anions exist in just one oxidation state, namely 2(-) as in 0(-2). Yet, a surprisingly large fraction of the oxygen anions in rock-forming minerals may exist in a more oxidized form, namely the 1- state, as 0(-) in peroxy. This has far-reaching consequences for understanding the Mars soil oxidant and its biocompatibility.

Freund, Friedemann↗

NASA NTRS2001

Factorizable Upwind Schemes: the Triangular Unstructured Grid Formulation

The upwind factorizable schemes for the equations of fluid was introduced recently. They facilitate achieving the Textbook Multigrid Efficiency (TME) and are expected also to result in the solvers of unparalleled robustness. The approach itself is very general. Therefore, it may well become a general framework for the large-scale Computational Fluid Dynamics. In this paper we outline the triangular grid formulation of the factorizable schemes. The derivation is based on the fact that the factorizable schemes can be expressed entirely using vector notation, without explicitly mentioning a particular coordinate frame. We describe the resulting discrete scheme in detail and present some computational results verifying the basic properties of the scheme/solver.

Nielsen, Eric J.↗

NASA NTRS2001

Factorizable Upwind Schemes: The Triangular Unstructured Grid Formulation

The upwind factorizable schemes for the equations of fluid were introduced recently. They facilitate achieving the Textbook Multigrid Efficiency (TME) and are expected also to result in the solvers of unparalleled robustness. The approach itself is very general. Therefore, it may well become a general framework for the large-scale, Computational Fluid Dynamics. In this paper we outline the triangular grid formulation of the factorizable schemes. The derivation is based on the fact that the factorizable schemes can be expressed entirely using vector notation. without explicitly mentioning a particular coordinate frame. We, describe the resulting discrete scheme in detail and present some computational results verifying the basic properties of the scheme/solver.

Sidilkover, David↗

NASA NTRS2001

Distributed Relaxation for Conservative Discretizations

A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.

Diskin, Boris↗

NASA NTRS2001

NASA's Lessons Learned and Technical Standards: A Logical Marriage

Lessons Learned have been the basis for our accomplishments throughout the ages. They have been passed down from father to son, mother to daughter, teacher to pupil, and older to younger worker. Lessons Learned have also been the basis for NASA's accomplishments for more than forty years. Both government and industry have long recognized the need to systematically document and utilize the knowledge gained from past experiences in order to avoid the repetition of failures and mishaps. Lessons Learned have formed the foundation for discoveries, inventions, improvements, textbooks, and Technical Standards.

Gill, Paul↗

NASA NTRS2001

Lessons Learned and Technical Standards: A Logical Marriage

A comprehensive database of lessons learned that corresponds with relevant technical standards would be a boon to technical personnel and standards developers. The authors discuss the emergence of one such database within NASA, and show how and why the incorporation of lessons learned into technical standards databases can be an indispensable tool for government and industry. Passed down from parent to child, teacher to pupil, and from senior to junior employees, lessons learned have been the basis for our accomplishments throughout the ages. Government and industry, too, have long recognized the need to systematically document And utilize the knowledge gained from past experiences in order to avoid the repetition of failures and mishaps. The use of lessons learned is a principle component of any organizational culture committed to continuous improvement. They have formed the foundation for discoveries, inventions, improvements, textbooks, and technical standards. Technical standards are a very logical way to communicate these lessons. Using the time-honored tradition of passing on lessons learned while utilizing the newest in information technology, the National Aeronautics and Space Administration (NASA) has launched an intensive effort to link lessons learned with specific technical standards through various Internet databases. This article will discuss the importance of lessons learned to engineers, the difficulty in finding relevant lessons learned while engaged in an engineering project, and the new NASA project that can help alleviate this difficulty. The article will conclude with recommendations for more expanded cross-sectoral uses of lessons learned with reference to technical standards.

Gill, Paul↗

NASA NTRS1995

The FOSTER Project: Teacher Enrichment Through Participation in NASA's Airborne Astronomy Program

NASA's airborne astronomy program offers a unique opportunity for K-12 science teacher enrichment and for NASA to reach out and serve the educational community. Learning from a combination of summer workshops, curriculum supplement materials, training in Internet skills and ultimately flying on NASA's C-141 airborne observatory, the teachers are able to share the excitement of scientific discovery with their students and convey that excitement from first hand experience rather than just from reading about science in a textbook. This year the program has expanded to include teachers from the eleven western states served by NASA Ames Research Center's Educational Programs Office as well as teachers from communities from around the country where the scientist who fly on the observatory reside. Through teacher workshops and inservice presentations, the FOSTER (Flight Opportunities for Science Teacher EnRichment) teachers are sharing the resources and experiences with many hundreds of other teachers. Ultimately, the students are learning first hand about the excitement of science, the scientific method in practice, the team work involved, the relevance of science to their daily lives and the importance of a firm foundation in math and science in today's technologically oriented world.

Koch, David↗

NASA NTRS1999

Jupiter, Tether, and Lenz's Law

Jupiter has a large, complex, and intense magnetic field that is thought to arise from electrical currents in the rapidly spinning metallic hydrogen interior. The strong magnetic field can induce currents when the conductive tether is directed toward or away from Jupiter. The currents can be stored and used for both propulsion and power generation. Therefore, our spacecraft might be able to visit several Jovian moons or maintain in the orbit around Jupiter. In our future space traveling, we also can use this technical skill to travel to other planets without any fuel. First-year physics textbooks describe Lenz's Law in which current is induced in a conductor moving through a stationary magnetic field. A demonstration of induced current in a stationary conductor and moving magnetic field is described, which may have space-tether application.

Lee, Russell↗

NASA NTRS1999

ANSYS Modeling of Hydrostatic Stress Effects

Classical metal plasticity theory assumes that hydrostatic pressure has no effect on the yield and postyield behavior of metals. Plasticity textbooks, from the earliest to the most modem, infer that there is no hydrostatic effect on the yielding of metals, and even modem finite element programs direct the user to assume the same. The object of this study is to use the von Mises and Drucker-Prager failure theory constitutive models in the finite element program ANSYS to see how well they model conditions of varying hydrostatic pressure. Data is presented for notched round bar (NRB) and "L" shaped tensile specimens. Similar results from finite element models in ABAQUS are shown for comparison. It is shown that when dealing with geometries having a high hydrostatic stress influence, constitutive models that have a functional dependence on hydrostatic stress are more accurate in predicting material behavior than those that are independent of hydrostatic stress.

Allen, Phillip A.↗

NASA NTRS1991

NASA's Software Bank (CLIPS)

C Language Integrated Production System (CLIPS) is a NASA Johnson Space Center developed software shell for developing expert systems, is used by researchers at Ohio State University to determine solid waste disposal sites to assist in historic preservation. The program has various other applications and has even been included in a widely-used textbook.

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NASA NTRS1990

Space Science Curricula

Johnson High School, Huntsville, Alabama started an international magnet program in 1987. One of the courses in the curriculum was in space science. They appealed to Marshall Space Flight Center (MSFC) when they couldn't find a suitable textbook, nor locate other classes in space science to provide a guideline. MSFC agreed to help and placed the school under an official 'Adopt-A-School' program. MSFC's chief scientist and others at the space center helped prepare a very comprehensive space science program. Examples of the subjects covered include problems of space travel, materials processing in space, technology utilization, robotics, space colonization, etc. MSFC followed up by working with Johnson High to determine if the curriculum is generally usable and workable. If it is, MSFC may make it available to other schools. MSFC not only developed the space science curriculum; they continue to support the program by sponsoring hands- on activities and tours of space research facilities.

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NASA NTRS1981

Breaking the Language Barrier

Preparation for the Apollo Soyuz mission entailed large-scale informational exchange that was accomplished by a computerized translation system. Based on this technology of commercial machine translation, a system known as SYSTRAN II was developed by LATSEC, Inc. and the World Translation Company of Canada. This system increases the output of a human translator by five to eight times, affording cost savings by allowing a large increase in document production without hiring additional people. Extra savings accrue from automatic production of camera-ready copy. Applications include translation of service manuals, proposals and tenders, planning studies, catalogs, list of parts and prices, textbooks, technical reports and education/training materials. System is operational for six language pairs. Systran users include Xerox Corporation, General Motors of Canada, Bell Northern Research of Canada, the U.S. Air Force and the European Commission. The company responsible for the production of SYSTRAN II has changed its name to SYSTRAN.

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NASA NTRS2003

What is Your Cosmic Connection to the Elements?

This booklet provides information and classroom activities covering topics in astronomy, physics, and chemistry. Chemistry teachers will find information about the cosmic origin of the chemical elements. The astronomy topics include the big bang, life cycles of small and large stars, supernovae, and cosmic rays. Physics teachers will find information on fusion processes, and physical principles important in stellar evolution. While not meant to replace a textbook, the information provided here is meant to give the necessary background for the theme of :our cosmic connection to the elements." The activities can be used to re-enforce the material across a number of disciplines, using a variety of techniques, and to engage and excite students about the topic. Additional activities, and on-line versions of the activities published here, are available at http://imagine.gsfc.nasa.gov/docs/teachers/elements/.

Lochner, J.↗

NASA NTRS2003

Oh, Develop

In a mature view of the subject, career development is not simply four years of college or a week at training, culminating in a diploma or a certificate to hang on an office wall. That's why we wanted to take a broad look at career development in this issue of ASK. Take for example, Dr. Gerald Mulenburg s contribution, Fly on the Wall. When Mulenburg and other members of a knowledge-sharing group at Ames were invited to observe an upcoming project review, Mulenburg thought it would be interesting to learn how another project does its reviews. Note that Mulenburg is no fresh out who's never attended a NASA project review. Not only has he been through a fair share of them as the reviewed, he has also been on the other side of the table as a reviewer. This experienced project manager recognizes that at any stage of a career there is room to grow and develop one's repertoire. Too often people associate career development with textbooks and role classroom training, far removed from project life. But classroom training need not be like this, as you'll find in our Special Feature, The Enterprise Project by Wendy Dolci, which sprung out of an APPL Advanced Project Management class in July 2003 at Ames Research Center. In addition to Dolci, some of her classmates contribute to the story. Mike Sander of the Jet Propulsion Laboratory, project manager for the Mars Science Laboratory mission, who provided the assignment on which the story is based, also has a cameo in the story. We think Dolci's story is an inspiring example of what classroom training can be if it's approached imaginatively and made to serve a practical purpose. Another story from Ames, by Frank Larsen, takes a different twist on career development. At the annual Experimental Aircraft Association Fly-in in Oshkosh, Wisconsin, Larsen represented Ames at a NASA booth. While there, Larsen met a colleague from Glenn Research Center. Months later on a project with a quick turnaround, he remembered his colleague from Glenn who had equipment that might help Larsen save time and money on his project. Although they had never worked together and they had to unravel a lot of red tape before they could collaborate, they managed a way to get the job done. There are other stories in this issue that deal directly with this theme of career development. Then there are others in which it is less explicit. But if you take the view that career development happens all the time, and is as necessary to your survival as breathing, then you can read almost any story in ASK with your career development in mind. In that case, all the best, and so then-start developing.

Post, Todd↗

NASA NTRS2003

Fundamentals of Polarized Light

The analytical and numerical basis for describing scattering properties of media composed of small discrete particles is formed by the classical electromagnetic theory. Although there are several excellent textbooks outlining the fundamentals of this theory, it is convenient for our purposes to begin with a summary of those concepts and equations that are central to the subject of this book and will be used extensively in the following chapters. We start by formulating Maxwell's equations and constitutive relations for time- harmonic macroscopic electromagnetic fields and derive the simplest plane-wave solution that underlies the basic optical idea of a monochromatic parallel beam of light. This solution naturally leads to the introduction of such fundamental quantities as the refractive index and the Stokes parameters. Finally, we define the concept of a quasi-monochromatic beam of light and discuss its implications.

Mishchenko, Michael↗