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NASA NTRS2004

A Meteorological Model's Dependence on Radiation Update Frequency

Numerical weather models are used to simulate circulations in the atmosphere including clouds and precipitation by applying a set of mathematical equations over a three-dimensional grid. The grid is composed of discrete points at which the meteorological variables are defined. As computing power continues to rise these models are being used at finer grid spacing, but they must still cover a wide range of scales. Some of the physics that must be accounted for in the model cannot be explicitly resolved, and their effects, therefore, must be estimated or "parameterized". Some of these parameterizations are computationally expensive. To alleviate the problem, they are not always updated at the time resolution of the model with the assumption being that the impact will be small. In this study, a coupled land-atmosphere model is used to assess the impact of less frequent updates of the computationally expensive radiation physics for a case on June 6, 2002, that occurred during a field experiment over the central plains known as International H20 Project (IHOP). The model was tested using both the original conditions, which were dry, and with modified conditions wherein moisture was added to the lower part of the atmosphere to produce clouds and precipitation (i.e., a wet case). For each of the conditions (i.e., dry and wet), four set of experiments were conducted wherein the model was run for a period of 24 hours and the radiation fields (including both incoming solar and outgoing longwave) were updated every 1, 3, 10, and 100 time steps. Statistical tests indicated that average quantities of surface variables for both the dry and wet cases were the same for the various update frequencies. However, spatially the results could be quite different especially in the wet case after it began to rain. The near-surface wind field was found to be different most of the time even for the dry case. In the wet case, rain intensities and average vertical profiles of heating associated with cloudy areas were found to differ for the various radiation update frequencies. The latter implies that the mean state of the model could be different as a result of not updating the radiation fields every time step and has important implications for longer term climate studies

Eastman, Joseph L.↗

NASA NTRS1986

The application of a sparse, distributed memory to the detection, identification and manipulation of physical objects

To determine the relation of the sparse, distributed memory to other architectures, a broad review of the literature was made. The memory is called a pattern memory because they work with large patterns of features (high-dimensional vectors). A pattern is stored in a pattern memory by distributing it over a large number of storage elements and by superimposing it over other stored patterns. A pattern is retrieved by mathematical or statistical reconstruction from the distributed elements. Three pattern memories are discussed.

Kanerva, P.↗

NASA NTRS1984

Research in applied mathematics, numerical analysis, and computer science

Research conducted at the Institute for Computer Applications in Science and Engineering (ICASE) in applied mathematics, numerical analysis, and computer science is summarized and abstracts of published reports are presented. The major categories of the ICASE research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers.

Source record↗

NASA NTRS1989

Solution of steady-state one-dimensional conservation laws by mathematical programming

Solution techniques for a class of steady-state scalar conservation laws are developed analytically. Discretization by finite-volume formulas is employed to obtain an overdetermined system of algebraic equations, which are then perturbed nonsingularly (with perturbation coefficient = epsilon) and solved using the l(1) mathematical-programming algorithm of Seneta and Steiger (1984); this approach limits the matrix bandwidth to two, so that an explicit solution can be found efficiently. It is shown that, for small values of epsilon, the l(1) solutions exhibit sharp correctly located shocks and are nonoscillatory O(epsilon) approximations of the physically relevant solutions.

Lavery, J. E.↗

NASA NTRS2010

General Pressurization Model in Simscape

System integration is an essential part of the engineering design process. The Ares I Upper Stage (US) is a complex system which is made up of thousands of components assembled into subsystems including a J2-X engine, liquid hydrogen (LH2) and liquid oxygen (LO2) tanks, avionics, thrust vector control, motors, etc. System integration is the task of connecting together all of the subsystems into one large system. To ensure that all the components will "fit together" as well as safety and, quality, integration analysis is required. Integration analysis verifies that, as an integrated system, the system will behave as designed. Models that represent the actual subsystems are built for more comprehensive analysis. Matlab has been an instrument widely use by engineers to construct mathematical models of systems. Simulink, one of the tools offered by Matlab, provides multi-domain graphical environment to simulate and design time-varying systems. Simulink is a powerful tool to analyze the dynamic behavior of systems over time. Furthermore, Simscape, a tool provided by Simulink, allows users to model physical (such as mechanical, thermal and hydraulic) systems using physical networks. Using Simscape, a model representing an inflow of gas to a pressurized tank was created where the temperature and pressure of the tank are measured over time to show the behavior of the gas. By further incorporation of Simscape into model building, the full potential of this software can be discovered and it hopefully can become a more utilized tool.

Servin, Mario↗

NASA NTRS2016

Numerical Simulation of Bolide Entry with Ground Footprint Prediction

As they decelerate through the atmosphere, meteors deposit mass, momentum and energy into the surrounding air at tremendous rates. Trauma from the entry of such bolides produces strong blast waves that can propagate hundreds of kilometers and cause substantial terrestrial damage even when no ground impact occurs. We present a new simulation technique for airburst blast prediction using a fully-conservative, Cartesian mesh, finite-volume solver and investigate the ability of this method to model far- field propagation over hundreds of kilometers. The work develops mathematical models for the deposition of mass, momentum and energy into the atmosphere and presents verification and validation through canonical problems and the comparison of surface overpressures, and blast arrival times with actual results in the literature for known bolides. The discussion also examines the effects of various approximations to the physics of bolide entry that can substantially decrease the computational expense of these simulations. We present parametric studies to quantify the influence of entry-angle, burst-height and other parameters on the ground footprint of the airburst, and these values are related to predictions from analytic and handbook-methods.

Simulation↗

NASA NTRS1996

Fluid Creep Effects on Near-Wall Solute Transport for Non-Isothermal Ampoules

There is a growing practical and theoretical interest in developing accurate macroscopic modelling for flows arising in chemical or physical vapor transport (VT) crystal growth experiments, including those conducted in reduced gravity environments. Rosner was the first person to point out that previously neglected rarefield gas dynamics phenomena (Stefan and bouyancy-driven flows) become rather important sources of convection. In particular, the combination of rarefaction and strong gradients of temperature (and/or concentration) tangential to the side-walls of the ampoule induces convective flows known as thermal (and concentration) 'creep' respectively. His order-of-magnitude estimates revealed that thermal creep effects can be non-negligible even at normal gravitational levels. On the macroscopic level, the bulk fluid mechanics can be adequately described by the familiar macroscopic equations as long as the boundary conditions are modified to account for the integrated effect of kinetic boundary layers adjacent to solid boundaries. Motivated by the growing importance of these phenomena, we have embarked on a series of computational studies to elucidate these fundamental creep-induced effects for a rarefied gas in simple, two-dimensional confined geometries. However, unlike previous related studies, we resort to a microscopic description of the gas, mathematically expressed by the Boltzmann integro-differential equation. We employ the direct simulation Monte Carlo (DSMC) method of Bird, the theoretical foundations and several practical applications. In the case of thermally induced flows, the no-time counter method of Bird is used, as implemented for a hard-sphere gas. The scheme has been also extended to account for realistic molecular interaction models, an extension necessary if the diffusion physics underlying concentration creep are to be captured.

Papadopoulos, Dimitrios↗

NASA NTRS1995

Visualization: A pathway to enhanced scientific productivity in the expanding missions of Space and Earth Sciences

The movement toward the solution of problems involving large-scale system science, the ever-increasing capabilities of three-dimensional, time-dependent numerical models, and the enhanced capabilities of 'in situ' and remote sensing instruments bring a new era of scientific endeavor that requires an important change in our approach to mission planning and the task of data reduction and analysis. Visualization is at the heart of the requirements for a much-needed enhancement in scientific productivity as we face these new challenges. This article draws a perspective on the problem as it crosses discipline boundaries from solar physics to atmospheric and ocean sciences. It also attempts to introduce visualization as a new approach to scientific discovery and a tool which expedites and improves our insight into physically complex problems. A set of simple illustrations demonstrates a number of visualization techniques and the discussion emphasizes the trial-and-error and search-and-discover modes that are necessary for the techniques to reach their full potential. Further discussions also point to the importance of integrating data access, management, mathematical operations, and visualization into a single system. Some of the more recent developments in this area are reviewed.

Szuszczewicz, E. P.↗

NASA NTRS1977

Theory of motion of Jupiter's Galilean satellites

Final results are presented for a theory enabling one to calculate the positions of the Galilean satellites and their partial derivatives. Extensive use of algebraic manipulation software on a digital computer is made to generate the final expressions. The theory is, in effect, a revitalization of Sampson's (1921) theory. Algebraic and mathematical errors existing in Sampson's work are removed, some neglected effects due to solar interactions and the 3-7 commensurability are introduced, allowance is made for nonzero amplitude and phase of the free libration, and the final results are expressed as analytic functions of variations in 49 arbitrary constants of integration and physical parameters. The theory is constructed in a manner which readily allows for future revision, and analytic expressions are provided for the partial derivatives with respect to the 49 parameters.

Lieske, J. H.↗

NASA NTRS1987

The effect of decay of the amplitude of oscillation on random process models for QPO X-ray stars

Random process models provide a useful mathematical framework for analysis of the quasi-periodic oscillations (QPO) recently discovered in the X-ray emission from certain luminous Galactic X-ray stars. In this paper, consideration is given to the effects of the power spectrum of the decay of the amplitude of oscillation that is expected in some physical models for the QPO phenomena. The resulting changes in the power spectrum depend on the ratio of the decay time of the amplitude of oscillation to the lifetime of the shot envelope. For values of this ratio less than about 10, it is found that incoherent QPO peaks in the power spectrum are significantly reduced in height and total power and are broadened in width, making them more difficult to detect. Coherent terms in the power spectrum, if present, are reduced in height and total power, but their width is unaffected. The red noise component remains unchanged. The present results are applied to the beat-frequency modulated accretion model in order to set constraints on the physical properties of the boundary layer between the inner edge of the accretion disk and the neutron star magnetosphere.

Shibazaki, N.↗

NASA NTRS1992

Inertial Oscillation of a Vertical Rotating Draft with Application to a Supercell Storm: Video Supplement to NASA-TP-3230

In this video (8 min., color, sound, VHS), animation depicts the inertial oscillation of a new mathematical model ('vertical rotating draft') for spinning up a single supercell storm. The oscillation consists of a long quiescent phase when the draft is large in diameter and rotates anticyclonically and a short intense phase when the draft is small and cyclonic. During the intense phase, the rotating draft resembles a supercell. The physical basis for the oscillation is depicted by tracking air parcels in the draft as they move along inertial circles (projected on a horizontal plane), where the horizontal pressure gradient is zero and the Coriolis force balances the centrifugal force. A side view of the oscillation shows that contraction and expansion are linked, respectively, to buoyantly driven compressible downdraft and updraft. An aerial view tracks the draft as it moves above the surface of the Earth and turns to the right during the intense phase. Radar echoes from a supercell storm are superimposed for comparison. The data appear to support only the intense phase. A critical experiment would measure the predominantly downward flow that theoretically occurs before the right turn in a supercell track and causes contraction and spin-up.

Supercell thunderstorm↗

NASA NTRS2002

Definition of Contravariant Velocity Components

In this paper we have reviewed the basics of tensor analysis in an attempt to clarify some misconceptions regarding contravariant and covariant vector components as used in fluid dynamics. We have indicated that contravariant components are components of a given vector expressed as a unique combination of the covariant base vector system and, vice versa, that the covariant components are components of a vector expressed with the contravariant base vector system. Mathematically, expressing a vector with a combination of base vector is a decomposition process for a specific base vector system. Hence, the contravariant velocity components are decomposed components of velocity vector along the directions of coordinate lines, with respect to the covariant base vector system. However, the contravariant (and covariant) components are not physical quantities. Their magnitudes and dimensions are controlled by their corresponding covariant (and contravariant) base vectors.

Hung, Ching-moa↗

NASA NTRS1974

Physical effects in cavitating flows

The microscopic and macroscopic aspects of the physical effects of cavitating flows are discussed. The microscopic features are related to the properties of nuclei in liquids and to the moderate tensile strengths which are usually encountered in flows. The macroscopic features are concerned with the growth of vapor or gaseous cavities from a small initial size and with their eventual collapse. Mathematical models are developed to analyze the characteristics of: (1) tensile strength in liquids, (2) growth of vapor bubbles, and (3) collapse of vapor bubbles.

Plesset, M. S.↗

NASA NTRS1979

Recent advances in the solution of three-dimensional flow over wings with leading edge vortex separation

Recent advances in a panel method for the solution of three-dimensional flow about wing and wing-body combinations with leading-edge vortex separation are presented. These advances were achieved as part of an ultimately successful assault on two shortcomings of the method, namely convergence failures in seemingly random cases, and overprediction of lift coefficient for high aspect-ratio wings. Advances include the implementation of improved panel numerics for the purpose of eliminating the highly non-linear effects of ring vortices around doublet panel edges, and the development of a least squares procedure for damping vortex sheet geometry update instabilities. A variety of cases generated by the computer program implementing the method are presented. These cases are of two types. The first type consists of numerical studies, which verify the underlying mathematical assumptions of the method and moreover show that the results are strongly invariant with respect to such user dependent input as wing panel layout, initial sheet shape, sheet rollup, etc. The second type consists of cases run for the purpose of comparing computed results with experimental data, and these comparisons verify the underlying physical assumptions made by the method.

Johnson, F. T.↗

NASA NTRS1980

A theoretical model of phase changes of a klystron due to variation of operating parameters

A mathematical model for phase changes of the VA-876 CW klystron amplifier output is presented and variations of several operating parameters are considered. The theoretical approach to the problem is based upon a gridded gap modeling with inclusion of a second order correction term so that actual gap geometry is reflected in the formulation. Physical measurements are contrasted to theoretical calculations.

Kupiszewski, A.↗

NASA NTRS1991

Sensitivity analysis and optimization issues in NASTRAN

The purpose is to develop procedures to extract sensitivity analysis information from COSMIC/NASTRAN and to couple it with a mathematical optimization package. At present, the analysis will be limited to stress, displacement, and frequency constraints with structures modeled with membrane elements, rods, and bar elements. Two types of sensitivity analysis are discussed: an adjoint variable approach which is most effective when the number of active constraints is significantly less than the number of physical variables, and an approach based on a first order approximation of a Taylor series. The latter approach is more effective when the number of independent design variables is significantly less than the number of active constraints.

Tischler, V. A.↗

NASA NTRS1973

Earth and Ocean Physics Applications Program /EOPAP/

Abbreviated description of the objectives, experiments, spacecraft, and required schedules of a proposed NASA program blending geophysics, oceanography, and space technology in order to facilitate the prediction of earthquakes, storm surges, tidal waves, and the condition of ocean surfaces. Relevant measurements from space will be carried out by LAGEOS, SAESATS-1, GEOPAUSE, GRAVSAT, and SEASATS-2 satellites contributing data on earth dynamics, sea surface states, satellite dynamics, and earth gravity. The development of suitable mathematical models for predicting events on earth on the basis of satellite data is considered.

Vonbun, F. O.↗

NASA NTRS1989

An airfoil pitch apparatus-modeling and control design

The study of dynamic stall of rapidly pitching airfoils is being conducted at NASA Ames Research Center. Understanding this physical phenomenon will aid in improving the maneuverability of fighter aircraft as well as civilian aircraft. A wind tunnel device which can linearly pitch and control an airfoil with rapid dynamic response is needed for such tests. To develop a mechanism capable of high accelerations, an accurate model and control system is created. The model contains mathematical representations of the mechanical system, including mass, spring, and damping characteristics for each structural element, as well as coulomb friction and servovalve saturation. Electrical components, both digital and analog, linear and nonlinear, are simulated. The implementation of such a high-performance system requires detailed control design as well as state-of-the-art components. This paper describes the system model, states the system requirements, and presents results of its theoretical performance which maximizes the structural and hydraulic aspects of this system.

Andrews, Daniel R.↗