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NASA NTRS2004

On controlling nonlinear dissipation in high order filter methods for ideal and non-ideal MHD

The newly developed adaptive numerical dissipation control in spatially high order filter schemes for the compressible Euler and Navier-Stokes equations has been recently extended to the ideal and non-ideal magnetohydrodynamics (MHD) equations. These filter schemes are applicable to complex unsteady MHD high-speed shock/shear/turbulence problems. They also provide a natural and efficient way for the minimization of Div(B) numerical error. The adaptive numerical dissipation mechanism consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is very general. The objective of this paper is to investigate the performance of three commonly used types of nonlinear numerical dissipation for both the ideal and non-ideal MHD.

Yee, H. C.↗

NASA NTRS2004

Nonlinear filtering and limiting in high order methods for ideal and non-ideal MHD

The various filtering mechanisms and base scheme options of the newly developed adaptive numerical dissipation control in spatially high order filter schemes for the ideal and non-ideal magnetohydrodynamics (MHD) equations are investigated. These filter schemes are applicable to complex unsteady MHD high-speed shock/shear/turbulence problems. They also provide a natural and efficient way for the minimization of Div(B) numerical error. The type of spatial base scheme to be used in conjunction with our filter idea is very general. For example, spectral, compact and non-compact spatially central finite difference schemes are possible candidates. The adaptive numerical dissipation mechanism consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and to leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is also very general. The objective of this paper is to investigate the performance of using compact and non-compact central base schemes in conjunction with three commonly used types of nonlinear numerical dissipation for both the ideal and non-ideal MHD. This extended abstract shows the performance of three nonlinear filters in conjunction with a sixth-order non-compact spatial central base scheme. In the final paper, the high order compact spatial central base scheme will be illustrated and compared with the non-compact base scheme. The reason for the investigation of the high order compact spatial central base scheme over the non-compact base scheme is to evaluate if additional accuracy can be gained in regions of fine scale turbulence that are away from shocks/shears.

Yee,H. C.↗

NASA NTRS1968

Visible CW parametric oscillator.

Tunable optical continuous wave parametric oscillator using 5145 angstrom Ar laser pump and lithium niobate as nonlinear material, noting large oscillation bandwidth

Byer, R. L.↗

NASA NTRS1971

Dynamic responses of railroad car models to vertical and lateral rail inputs

Simplified dynamic models were applied in a study of vibration in a high-speed railroad car. The mathematical models used were a four-degree-of-freedom model for vertical responses to vertical rail inputs and a ten-degree-of-freedom model for lateral response to lateral or rolling (cross-level) inputs from the rails. Elastic properties of the passenger car body were represented by bending and torsion of a uniform beam. Rail-to-car (truck) suspensions were modeled as spring-mass-dashpot oscillators. Lateral spring nonlinearities approximating certain complicated truck mechanisms were introduced. The models were excited by displacement and, in some cases, velocity inputs from the rails by both deterministic (including sinusoidal) and random input functions. Results were obtained both in the frequency and time domains. Solutions in the time domain for the lateral model were obtained for a wide variety of transient and random inputs generated on-line by an analog computer. Variations in one of the damping properties of the lateral car suspension gave large fluctuations in response over a range of car speeds for a given input. This damping coefficient was significant in reducing lateral car responses that were higher for nonlinear springs for three different inputs.

Sewall, J. L.↗

NASA NTRS1982

On the origin of solar spicules

The nonlinear evolution of vertical motions on intense solar magnetic flux tubes is considered. It is shown that a quasi-impulsive source in the photosphere can excite a train of upward-propagating rebound shocks in the chromosphere. The rebound shock train is the nonlinear development of oscillations of the atmosphere at its natural frequency. The rebound shocks impinge on the transition region and thrust the underlying chromosphere upward. It is found that the rebound shock train leads naturally to structures which can be identified with the solar spicules.

Hollweg, J. V.↗

NASA NTRS1983

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

Yee, H. C.↗

NASA NTRS1983

Implicit total variation diminishing (TVD) schemes for steady-state calculations

Yee, H. C.↗

NASA NTRS1985

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The novel implicit and unconditionally stable, high resolution Total Variation Diminishing (TVD) scheme whose application to steady state calculations is presently examined is a member of a one-parameter family of implicit, second-order accurate systems developed by Harten (1983) for the computation of weak solutions for one-dimensional hyperbolic conservation laws. The scheme will not generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments for a quasi-one-dimensional nozzle problem show that the experimentally determined stability limit correlates exactly with the theoretical stability limit for the nonlinear scalar hyberbolic conservation laws.

Yee, H. C.↗

NASA NTRS1991

Line narrowing of AgGaSe2 optical parametric oscillator by injection seeding

Solid-state lasers are developed for atmospheric applications. Optical parametric oscillators (OPO) are being investigated as sources of tunable radiation in the 2.5-12 micron range where development of conventional lasers is subject to numerous difficulties. Parametric oscillation is a nonlinear optical technique for converting laser output to longer wavelengths. Incident photons, typically from a pulsed pump laser, are converted into two photons of longer wavelength, while satisfying energy conservation. The particular split of energy is determined by momentum conservation; the wavelength of interest is usually selected by angle orientation of the nonlinear material with respect to the direction of propagation of the pump beam. An OPO based on AgGaSe2 was considered.

Watson, George H.↗

NASA NTRS1999

Super Photon Counters

The perfect photon detector would measure the arrival time, the energy, the polarization, and the position of every arriving quantum, but that is easier said than done. Two groups have now succeeded in doing time-resolved spectroscopy on the Crab Nebula pulsar, measuring everything but the polarization, with reports from Romani et al. at Stanford and from Perryman et al. at ESTEC. Both groups use superconducting detectors to gain the necessary speed and sensitivity. The photon can heat the electrons in a superconductor biased in the middle of its resistive transition, or break bound superconducting electron-hole pairs, which can then be collected. Three years ago, Peacock et al. reported that they had detected single optical photons with a superconducting tunnel junction (STJ), and Paresce wrote a News and Views article. A tunnel junction uses two pieces of conductive material, separated by a tiny gap of insulating material or even vacuum. If the gap is thin enough, electrons can tunnel across anyway, and if the conductors are superconductors, the junction displays very useful quantum mechanical properties and electrical nonlinearities. Amplifiers, detectors, oscillators, and computer circuits can all be made from them. Their special advantage is that they operate at very low temperatures, dissipate very little power, operate very fast, and are very small.

Mather, John↗

NASA NTRS1981

Chaotic /strange/ and periodic behavior in instability saturation by the oscillating two-stream instability

The nonlinear Schroedinger equation with linear growth and damping is truncated to three waves. The resulting system of nonlinear ordinary differential equations describes the excitation of linearly damped waves by the oscillating two-stream instability driven by a linearly unstable pump wave. This system represents a simple model for the nonlinear saturation of a linearly unstable wave. The model is examined analytically and numerically as a function of the dimensionless parameters of the system. It is found that the model can exhibit a wealth of characteristic dynamical behavior including stationary equilibria, Hopf bifurcations to periodic orbits, period doubling bifurcations, chaotic solutions characteristic of a strange attractor, tangent bifurcations from chaotic to periodic solutions, transient chaos, and hysteresis. Many of these features are shown to be explainable on the basis of one-dimensional maps. In the case of chaotic solutions, evidence for the presence of a strange attractor is provided by demonstrating Cantor set-like structure (i.e., scale invariance) in the surface of section.

Russell, D. A.↗

NASA NTRS1983

On the analytical modeling of the nonlinear vibrations of pretensioned space structures

Pretensioned structures are receiving considerable attention as candidate large space structures. A typical example is a hoop-column antenna. The large number of preloaded members requires efficient analytical methods for concept validation and design. Validation through analyses is especially important since ground testing may be limited due to gravity effects and structural size. The present investigation has the objective to present an examination of the analytical modeling of pretensioned members undergoing nonlinear vibrations. Two approximate nonlinear analysis are developed to model general structural arrangements which include beam-columns and pretensioned cables attached to a common nucleus, such as may occur at a joint of a pretensioned structure. Attention is given to structures undergoing nonlinear steady-state oscillations due to sinusoidal excitation forces. Three analyses, linear, quasi-linear, and nonlinear are conducted and applied to study the response of a relatively simple cable stiffened structure.

Housner, J. M.↗

NASA NTRS1991

Linear and nonlinear aspects of the tropical 30-60 day oscillation: A modeling study

The scientific problem focused on study of the tropical 30-60 day oscillation and explanation for this phenomenon is discussed. The following subject areas are covered: the scientific problem (the importance of low frequency oscillations; suggested mechanisms for developing the tropical 30-60 day oscillation); proposed research and its objective; basic approach to research; and results (satellite data analysis and retrieval development; thermodynamic model of the oscillation; the 5-level GCM).

Stevens, Duane E.↗

NASA NTRS1972

Nonlinearity of Helmholtz resonators

Consideration of the nonlinear damping of pressure oscillations by means of acoustic liners consisting of a perforated plate communicating with a volume or of individual Helmholtz resonators. A nonlinear analysis leads to a modified first-order theory; in particular, some second-order damping effects (due to the formation of jets through the orifices) are considered, while other less important damping effects (of second order) are neglected. The effect of the vena contracta in the orifice flow is also taken into account, and the conditions of maximum damping are discussed. A determination is made of the orifice velocity, the cavity pressure, the admittance coefficient, the resistance, and the reactance, and good agreement is found between the theoretically determined resistance and orifice velocity and the pertinent experimental data.

Sirignano, W. A.↗

NASA NTRS1989

A seven-month solar cycle observed with the Langmuir probe on Pioneer Venus Orbiter

Data collected by the Langmuir probe aboard the Pioneer Venus orbiter (PVO) over the years 1979 though 1987 were normalized to remove the long-period 11-year solar maximum to minimum trend and were analyzed for periodicity. Results yield evidence for the existence of an approximately 7-month solar cycle, which was also observed from SME Lyman alpha and 2800-MHz radio flux measurements carried out from an earth-based platform. This coincidence suggests that the cycle is an intrinsic periodicity in the solar output. The cycle has a frequency independent of the orbital frequency of the PVO and is distinct from a 'rotating beacon' cycle whose period depends on the orbital motion of the PVO about the sun. The second most dominant cycle discovered was a 5-month period. Results of an oscillation model of solar periodicity indicate that the 7-month and 5-month cycles are caused by long-lived flux enhancements from nonlinear interactions of global oscillation modes in the sun's convective envelope (r modes) and radiative interior (g modes).

Hoegy, W. R.↗

NASA NTRS1999

Simulation of Non-Linear Transonic Aeroelastic Behavior on the B-2

At high subsonic flight speeds, large flexible aircraft begin to encounter unsteady airloads which are not predicted by most currently available aerodynamic analysis and design methods. With increasing speed and the development of transonic flow and shocks, viscous effects quickly become very important, and flow separation can occur. The Northrop Grumman USAF B-2 Bomber encountered a nonlinear aeroelastic Residual Pitch Oscillation (RPO) under these conditions. Simulation studies were performed with the Computational Aeroelasticity Program-Transonic Small Disturbance, Viscous (CAPTSDv) computer program to evaluate its ability to predict these nonlinear aeroelastic responses. Open and closed loop simulations were performed to assess the participation of the flight control system. Control, system actuator hysteresis characteristics were modeled and found to be a significant participant in the RPO phenomenon. Simulations were also performed for varying Mach numbers and altitudes to establish the stability boundaries and compare with flight test data. These CAPTSDv simulations compared well with flight data and revealed many potential further modeling enhancements.

Residual pitch oscillation↗

NASA NTRS2002

Resonantly enhanced interaction of light and microwaves via whispering gallery modes

We propose a scheme of a resonant cw microwave-optical parametric oscillator based on high-Q whispering gallery modes excited in a nonlinear dielectric cavity. Such an oscillator has an extremely low threshold and stable operation, and may be used in spectroscopy and metrology.

whispering gallery modes spectroscopy metrology↗

NASA NTRS1994

Control-nonlinear-nonstationary structural response and radiation near a supersonic jet

This paper is on the control of nonlinear-nonstationary vibration of a frame-stringer structure resulting from high levels of excitation from a nearby supersonic jet exhaust. The structure exhibits periodic, chaotic, or random behaviors when forced by high-intensity sound from a supersonic jet exhaust with 'shock' loading superimposed on a broadband response. The time history of the pressure, showing the rotation and flapping of the shock structure in the jet column due to large-scale instabilities, indicates that the response is not only nonlinear but also nonstationary. The acoustic pressure radiated by the structure also contains shocks and the formation of harmonics with distance. Control of the structural response is achieved by actively forcing the structure with an actuator at the shock oscillation frequency whose amplitude is locked into a self-control cycle. Results show that the peak power level is reduced by a factor of 63, or 18 dB. As a result, new broadband components emerge with at least four harmonics. At accelerating and decelerating supersonic speeds, the exhaust from the jet induces higher transient loading on the nearby flexible structure due to the occurrence of multiple shock from the jet.

TRT-EXPERIMENTAL↗