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NASA NTRSDate not supplied

Continuum Covariance Propagation for Understanding Variance Loss in Advective Systems

We demonstrate for state dynamics governed by the continuity equation and related hyperbolic partial differential equations that significant, spurious variance loss occurs during covariance propagation by traditional methods used in data assimilation, even at full rank. This inaccurate variance evolution is caused not by numerical dissipation, but rather by a discontinuous change in the continuum covariance dynamics as correlation lengths tend to zero.

Shay Gilpin↗

NASA NTRS1990

Dynamics of groups around interacting double ellipticals: Measuring dark matter haloes

Binary galaxies, as binary stars, are important to measure masses, as suggested by Page (1952). Because three orbit parameters are measurable for galaxies at one instant of time, severe uncertainties remain in the orbit and mass determinations. These uncertainties can partly be overcome by statistical studies of selected samples and/or n-body simulations. Close double galaxies (and isolated galaxies) could also be useful to estimate dynamical masses if we can find test particles around them. Interacting elliptical pairs or dumb-bell galaxies are found with a large range, between 0-1200 km s(exp -1), of relative radial velocities. Standard 2-body orbit calculations, highly uncertain due to projection factors, suggest for the largest velocity differences very large galaxy masses, if the systems are bound and stationary. However, recent n-body simulations model these binaries as galaxies captured from hyperbolic orbits, requiring masses of order a few times 10(exp 11) solar maximum (Borne et al. 1988), but producing systems that are short lived. A different picture appears when we study observationally the dynamical mass of interacting double ellipticals using faint satellite galaxies. These satellites contribute little luminosity and, presumably, little mass to the system. The authors present results of two such groups, basically forming systems of test particles, around the dumb-bells NGC 4782/3 and IC 5049. They also briefly discuss the satellite group around the central dumb-bell in the cluster Sersic 40/6. Apparently, they detect large quantities of dark matter in the vicinity of these dumb-bell galaxies, because the system masses of approx. 4.5 times 10(exp 13) solar mass and 8 times 10(exp 13) solar mass for NGC 4782/3 and IC 5049, respectively, are quite high. Likewise, the mass of the Sersic 40/6 inner core is 7 times 10(exp 13) solar mass. The possibility that a common massive dark matter halo increases the merging times of these types of galaxies is suggested. Here, the authors assume H sub o = 100 km s (exp -1) Mpc(exp -1).

Quintana, H.↗

NASA NTRS1987

Factorization and the synthesis of optimal feedback kernels for differential-delay systems

A combination of ideas from the theories of operator Riccati equations and Volterra factorizations leads to the derivation of a novel, relatively simple set of hyperbolic equations which characterize the optimal feedback kernel for the finite-time regulator problem for autonomous differential-delay systems. Analysis of these equations elucidates the underlying structure of the feedback kernel and leads to the development of fast and accurate numerical methods for its computation. Unlike traditional formulations based on the operator Riccati equation, the gain is characterized by means of classical solutions of the derived set of equations. This leads to the development of approximation schemes which are analogous to what has been accomplished for systems of ordinary differential equations with given initial conditions.

Milman, Mark M.↗

NASA NTRS2018

Exergy Efficiency of Interplanetary Transfer Vehicles

In order to optimize systems, systems engineers require some sort of measure with which to compare vastly different system components. One such measure is system exergy, or the usable system work. Exergy balance analysis models provide a comparison of different system configurations, allowing systems engineers to compare different systems configuration options. This paper presents the exergy efficiency of several Mars transportation system configurations, using data on the interplanetary trajectory, engine performance, and vehicle mass. The importance of the starting and final parking orbits is addressed in the analysis, as well as intermediate hyperbolic escape and entry orbits within Earth and Mars' spheres of influence (SOIs). Propulsion systems analyzed include low-enriched uranium (LEU) nuclear thermal propulsion (NTP), high-enriched uranium (HEU) NTP, LEU methane (CH4) NTP, and liquid oxygen (LOX)/liquid hydrogen (LH2) chemical propulsion.

Owen, Sean T.↗

NASA NTRS2018

Exergy Efficiency of Interplanetary Transfer Vehicles

Owen, Sean T.↗

NASA NTRS2018

Exergy Efficiency of Interplanetary Transfer Vehicles

Owen, Sean T.↗

NASA NTRS1986

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: An eigenvalue analysis

A hyperbolic initial-boundary-value problem can be approximated by a system of ordinary differential equations (ODEs) by replacing the spatial derivatives by finite-difference approximations. The resulting system of ODEs is called a semidiscrete approximation. A complication is the fact that more boundary conditions are required for the spatially discrete approximation than are specified for the partial differential equation. Consequently, additional numerical boundary conditions are required and improper treatment of these additional conditions can lead to instability. For a linear initial-boundary-value problem (IBVP) with homogeneous analytical boundary conditions, the semidiscrete approximation results in a system of ODEs of the form du/dt = Au whose solution can be written as u(t) = exp(At)u(O). Lax-Richtmyer stability requires that the matrix norm of exp(At) be uniformly bounded for O less than or = t less than or = T independent of the spatial mesh size. Although the classical Lax-Richtmyer stability definition involves a conventional vector norm, there is no known algebraic test for the uniform boundedness of the matrix norm of exp(At) for hyperbolic IBVPs. An alternative but more complicated stability definition is used in the theory developed by Gustafsson, Kreiss, and Sundstrom (GKS). The two methods are compared.

Warming, Robert F.↗

NASA NTRS1995

Where Are the Interstellar Comets?

The existing theories of comet dynamics held that large numbers of comets are ejected to interstellar space and that other stellar systems would do the same; however, no comet on a hyperbolic orbit has ever been observed. Calculations developed by Duncan et al. are used to show that most comets thought to be ejected would actually be captured by the Oort Cloud.

comets interstellar comets Oort Cloud orbital dyna↗

NASA NTRS1993

On the global dynamics of adaptive systems - A study of an elementary example

The inherent nonlinear character of adaptive systems poses serious theoretical problems for the analysis of their dynamics. On the other hand, the importance of their dynamic behavior is directly related to the practical interest in predicting such undesirable phenomena as nonlinear oscillations, abrupt transients, intermittence or a high sensitivity with respect to initial conditions. A geometrical/qualitative description of the phase portrait of a discrete-time adaptive system with unmodeled disturbances is given. For this, the motions in the phase space are referred to normally hyperbolic (structurally stable) locally invariant sets. The study is complemented with a local stability analysis of the equilibrium point and periodic solutions. The critical character of adaptive systems under rather usual working conditions is discussed. Special emphasis is put on the causes leading to intermittence. A geometric interpretation of the effects of some commonly used palliatives to this problem is given. The 'dead-zone' approach is studied in more detail. The predicted dynamics are compared with simulation results.

Espana, Martin D.↗

NASA NTRS1980

Pioneer Venus Orbiter neutral gas mass spectrometer experiment

The Pioneer Venus Orbiter Neutral Mass Spectrometer (ONMS) is designed to measure the vertical and horizontal density variations of the major neutral constituents in the upper atmosphere of Venus. The mass spectrometer sensor includes a retarding potential ion source, hyperbolic quadrupole rod analyzer, and electron multiplier detector. The supporting electronic system consists of hybrid integrated circuits to reduce weight and power. The ONMS instrument was launched aboard the Pioneer Venus Orbiter on May 20, 1978, and turned on in orbit around Venus on December 4, 1978. It has operated flawlessly for over a Venus year (243 earth days) and has returned data of the composition of the major constituents in the Venus atmosphere between the altitudes of 150 and 350 km.

Niemann, H. B.↗

NASA NTRS1994

Magnetobraking: Use of tether electrodynamic drag for Earth return from Mars

It has often been proposed that a vehicle returning from Mars will use aerobraking in the Earth's atmosphere to dissipate hyperbolic excess velocity to capture into Earth orbit. Here a different system for dissipating excess velocity without expenditure of reaction mass, magnetobraking, is proposed. Magnetobraking uses the force on an electrodynamic tether in the Earth's magnetic field to produce thrust. An electrodynamic tether is deployed from the spacecraft as it approaches the Earth. The Earth's magnetic field produces a force on electrical current in the tether. If the tether is oriented perpendicularly to the Earth's magnetic field and to the direction of motion of the spacecraft, force produced by the Earth's magnetic field can be used to either brake or accelerate the spacecraft without expenditure of reaction mass. The peak acceleration on the Mars return is 0.007 m/sq sec, and the amount of braking possible is dependent on the density and current-carrying capacity of the tether, but is independent of length. A superconducting tether is required. The required critical current is shown to be within the range of superconducting technology now available in the laboratory.

Landis, Geoffrey A.↗

NASA NTRS2018

Closed Loop Guidance Trade Study for Space Launch System Block-1B Vehicle

NASA is currently building the Space Launch System (SLS) Block-1 launch vehicle for the Exploration Mission 1 (EM-1) test flight. The design of the next evolution of SLS, Block-1B, is well underway. The Block-1B vehicle is more capable overall than Block-1; however, the relatively low thrust-to-weight ratio of the Exploration Upper Stage (EUS) presents a challenge to the Powered Explicit Guidance (PEG) algorithm used by Block-1. To handle the long burn durations (on the order of 1000 seconds) of EUS missions, two algorithms were examined. An alternative algorithm, OPGUID, was introduced, while modifications were made to PEG. A trade study was conducted to select the guidance algorithm for future SLS vehicles. The chosen algorithm needs to support a wide variety of mission operations: ascent burns to LEO, apogee raise burns, trans-lunar injection burns, hyperbolic Earth departure burns, and contingency disposal burns using the Reaction Control System (RCS). Additionally, the algorithm must be able to respond to a single engine failure scenario. Each algorithm was scored based on pre-selected criteria, including insertion accuracy, algorithmic complexity and robustness, extensibility for potential future missions, and flight heritage. Monte Carlo analysis was used to select the final algorithm. This paper covers the design criteria, approach, and results of this trade study, showing impacts and considerations when adapting launch vehicle guidance algorithms to a broader breadth of in-space operations.

Von der Porten, Paul↗

NASA NTRS1986

Property of radially quadratic reflector systems

This report shows that when considered in terms of optical geometry, radially parabolic and radially hyperbolic mirrors used as mirrors for Cassegrain and parabolic antennas possess values similar to common conical horn reflector antennas.

Mizusawa, M.↗

NASA NTRS1976

Conformal coordinates associated with uniformly accelerated motion

Specific problems in the theory of relativity are often simplified by an appropriate choice of the coordinate system. Restricted conformal coordinates provide an especially simple analysis of motion with uniform acceleration, known as hyperbolic motion. Conformal coordinates x', t' may be obtained from Cartesian coordinates x, t by the transformation x'+ct'=F(x+ct) and x'-ct'=G(x-ct), where c is the velocity of light. A variable motion of the x' system is determined by the choice of the functions F and G.

Jones, R. T.↗

NASA NTRS1999

A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow

A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.

Xu, Kun↗

NASA NTRSDate not supplied

Automation of Overset Structured Mesh Generation onBoundary Representation Geometries

A scheme is presented for the automatic generation of structured overset meshes ongeometries that are defined by Boundary Representation (BRep) solids. The surface meshsystem consists of face, edge and node meshes corresponding to the three respective basicBRep entity types. A cut-cell method is introduced to improve robustness of the on-geometrydetermination test for a face mesh grid point. A geometric component tagging scheme is utilizedto enhance local grid point distribution on a configuration with a large range of geometricscales. A cap grid topology is automatically utilized around the trailing edge of wing and tailtips to enhance mesh quality and to enable more effective surface coverage. Robustness of thehyperbolic surface marching method is improved by replacing the point projection scheme witha walking scheme. Relaxation of surface grid spacing at concave corners enables automatedhigh quality hyperbolic volume mesh creation. Domain connectivity is automatically performedon the surface mesh system. A variety of test cases are presented including a re-entry capsule,two models of the Juncture Flow Experiment wing-body, five rotorcraft concept vehicles, andvarious components of the High-Lift Common Research Model from the High-Lift PredictionWorkshop 4.

TTT↗

NASA NTRS1982

LORAN-C, an overview

LORAN-C a highly accurate radio navigation positioning system which operates at an assigned frequency of 10 kHz, and provides phase-coded pulses to develop hyperbolic time-difference lines-of-position (LOP's) was evaluated. LORAN-C provides precise time and time interval to within plus or minus 5 microseconds of UTC. The steps taken to plan, install, operate, and maintain the LORAN-C system up to the year 2000 are discussed. Topics included in the discussion were: theory of operation, timing, chain lanning, group repetition interval, coding delay versus emission delay, chain calibration, chart verification, system accuracy, signal reliability, and future developments.

Thrall, W. J.↗

NASA NTRS1996

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

Molenaar, J.↗