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At least 991 records · Page 55

A Strong Stability Preserving Analysis for Explicit Multistage Two-Derivative Time-Stepping Schemes Based on Taylor Series Conditions

High-order strong stability preserving (SSP) time discretizations are usually needed to ensure the nonlinear (and sometimes non-inner-product) strong stability properties of spatial discretizations specially designed for the solution of hyperbolic PDEs. Multi-derivative time-stepping methods have recently been increasingly used for evolving hyperbolic PDEs, and the strong stability properties of these methods are of interest. In our prior work we explored time discretizations that preserve the strong stability properties of spatial discretizations coupled with forward Euler and a second-derivative formulation. Yet, many spatial discretizations do not satisfy strong stability properties when coupled with this second-derivative formulation, but rather with a more natural Taylor series formulation. Here, we demonstrate sufficient conditions for an explicit two-derivative multistage method to preserve the strong stability properties of spatial discretizations in a forward Euler and Taylor series formulation. We call these strong stability preserving Taylor series (SSP-TS) methods. We also prove that the maximal order of SSP-TS methods is p=6, and define an optimization procedure that allows us to find such SSP methods. Several types of these methods are presented and their efficiency compared. Finally, these methods are tested on several PDEs to demonstrate the benefit of SSP-TS methods, the need for the SSP property, and the sharpness of the SSP time-step in many cases.

97 MATHEMATICS AND COMPUTING↗

An analytical method for ride quality of flexible airplanes

A new and easily used method of aircraft ride quality analysis is developed, and its use is illustrated by a numerical example using DC-8 airplane equations of motion. The method readily allows any type of stability augmentation system to be included for good handling qualities. A particularly powerful method of specifying and achieving all roots of a desired closed-loop characteristic equation by use of full state variable feedback is described and applied to the DC-8 example.

Swaim, R. L.↗

Solar ultraviolet spectral irradiance monitor experiment on OSS-1

The need to improve the accuracy of measurement of the absolute solar flux within the wavelength range 120 nm to 400 nm requires an extensive effort in contamination control and in tracking the instruments' stability. The techniques used in the solar ultraviolet irradiance monitor are described. These methods resulted in very high calibration stability as proved by preflight and postflight calibration. In-flight calibrating and the pointing accuracy provided by the shuttle attitude control system are discussed.

Vanhossier, M. E.↗

The measurement system of pulse modulated carrier frequency stability and timing jitter

The definition of pulse modulated carrier frequency stability and timing jitter as well as the configuration and synchronous acquisition measurement method of its measurement system. Frequency stability of the pulse modulated carrier is measured with a discrimination technique. The pulse modulated carrier under testing is mixed with a reference frequency synthesizer. A delay line is used to convert the frequency fluctuation mixed IF signal to the voltage fluctuation. The system has the capability to make the phase noise measurement of two port devices on a pulsed carrier using a phase bridge. The noise voltage mentioned above is applied to the data acquisition and processing unit by PC to realize stability measurement. The data acquisition is in the form of pulse synchronization so that the measurement system accuracy is increased. The pulse width is more than 0.3 microseconds. The phase fluctuation variance, sigma, is less than 0.017. The time interval measuring system with high resolution is used to make interpulse timing and pulse width jitters automatic measurement. The pulse width is less than 0.2 ns. The resolution is 0.1 ns. The system is successfully applied to radar measurement.

Li Cheng-Fu↗

The measurement of aircraft performance and stability and control after flight through natural icing conditions

The effects of airframe icing on the performance and stability and control of a twin-engine commuter-class aircraft were measured by the NASA Lewis Research Center. This work consisted of clear air tests with artificial ice shapes attached to the horizontal tail, and natural icing flight tests in measured icing clouds. The clear air tests employed static longitudinal flight test methods to determine degradation in stability margins for four simulated ice shapes. The natural icing flight tests employed a data acquisition system, which was provided under contract to NASA by Kohlman Systems Research Incorporated. This system used a performance modeling method and modified maximum likelihood estimation (MMLE) technique to determine aircraft performance degradation and stability and control. Flight test results with artificial ice shapes showed that longitudinal, stick-fixed, static margins are reduced on the order of 5 percent with flaps up. Natural icing tests with the KSR system corroborated these results and showed degradation in the elevator control derivatives on the order of 8 to 16 percent depending on wing flap configuration. Performance analyses showed the individual contributions of major airframe components to the overall degration in lift and drag.

Ranaudo, R. J.↗

The measurement of aircraft performance and stability and control after flight through natural icing conditions

The effects of airframe icing on the performance and stability and control of a twin-engine commuter-class aircraft were measured by the NASA Lewis Research Center. This work consisted of clear air tests with artificial ice shapes attached to the horizontal tail, and natural icing flight tests in measured icing clouds. The clear air tests employed static longitudinal flight test methods to determine degradation in stability margins for four simulated ice shapes. The natural icing flight tests employed a data acquisition system, which was provided under contract to NASA by Kohlman Systems Research Incorporated. This system used a performance modeling method and modified maximum likelihood estimation (MMLE) technique to determine aircraft performance degradation and stability and control. Flight test results with artificial ice shapes showed that longitudinal, stick-fixed, static margins are reduced on the order of 5 percent with flaps up. Natural icing tests with the KSR system corroborated these results and showed degradation in the elevator control derivatives on the order of 8 to 16 percent depending on wing flap configuration. Performance analyses showed the individual contributions of major airframe components to the overall degradation in lift and drag.

Ranaudo, R. J.↗

Practical Methodology for the Inclusion of Nonlinear Slosh Damping in the Stability Analysis of Liquid-Propelled Space Vehicles

A method is presented that allows for the prediction of the magnitude of limit cycles due to adverse control-slosh interaction in liquid propelled space vehicles using non-linear slosh damping. Such a method is an alternative to the industry practice of assuming linear damping and relying on: mechanical slosh baffles to achieve desired stability margins; accepting minimal slosh stability margins; or time domain non-linear analysis to accept time periods of poor stability. Sinusoidal input describing functional analysis is used to develop a relationship between the non-linear slosh damping and an equivalent linear damping at a given slosh amplitude. In addition, a more accurate analytical prediction of the danger zone for slosh mass locations in a vehicle under proportional and derivative attitude control is presented. This method is used in the control-slosh stability analysis of the NASA Space Launch System.

Ottander, John A.↗

Low-iridium stabilized ruthenium oxide anode catalyst for durable proton-exchange membrane water electrolysis

While mixing iridium (Ir) with ruthenium oxide (RuO 2 ) has proven to be an effective strategy for reducing Ir loading in anode catalysts for proton-exchange membrane (PEM) water electrolysers, achieving industrially relevant long-term stability typically requires an Ir-rich, Ru-lean combination. Here, in this study, by combining density functional theory with Metropolis Monte Carlo methods, we discovered that sufficient stabilization in the RuO 2 lattice could be achieved with less than 50 at.% of Ir, and that Ir in the first subsurface layer plays a critical role. By effectively dispersing Ir dopants within the RuO 2 lattice, we demonstrated an Ir:Ru atomic ratio of only 1:6 that exhibited exceptional stability for over 1,500 h of continuous water electrolysis at 2 A cm −2 . Our Ru 6 IrO x catalyst has the potential to reduce Ir loading by 80% compared with current commercial PEM water electrolysers, and its stability was further validated under industrial testing conditions in a 25-cm 2 PEM electrolyser.

36 MATERIALS SCIENCE↗

Semi-Implicit Computation of Fast Modes in a Scheme Integrating Slow Modes by a Leapfrog Method Based on a Selective Implicit Time Filter

Abstract A scheme for integration of atmospheric equations containing terms with differing time scales is developed. The method employs a filtered leapfrog scheme utilizing a fourth-order implicit time filter with one function evaluation per time step to compute slow-propagating phenomena such as advection and rotation. The terms involving fast-propagating modes are handled implicitly with an unconditionally stable method that permits application of larger time steps and faster computations compared to fully explicit treatment. Implementation using explicit and recurrent formulation is provided. Stability analysis demonstrates that the method is conditionally stable for any combination of frequencies involved in the slow and fast terms as they approach the origin. The implicit filter used in the method damps the computational modes without noticeably sacrificing the accuracy of the physical mode. TheO[(Δt 4 )] accuracy for amplitude errors achieved by the implicitly filtered leapfrog is preserved in applications where terms responsible for fast propagation are integrated with a semi-implicit method. Detailed formulation of the method for soundproof nonhydrostatic anelastic equations is provided. Procedures for implementation in global spectral shallow-water models are also given. Examples comparing numerical and analytical solutions for linear gravity waves demonstrate the accuracy of the scheme. The performance is also shown in more practical nonlinear applications, where numerical solutions accomplished by the method are evaluated against those computed from a scheme where the slow terms are handled by the third-order Runge–Kutta scheme. It demonstrates that the method is able to accurately resolve fine-scale dynamics of Kelvin–Helmholtz shear instabilities, the evolution of density current, and nonlinear drifts of twin tropical cyclones.

Meteorology & Atmospheric Sciences↗

A Comparison of Two Path Planners for Planetary Rovers

The paper presents two path planners suitable for planetary rovers. The first is based on fuzzy description of the terrain, and genetic algorithm to find a traversable path in a rugged terrain. The second planner uses a global optimization method with a cost function that is the path distance divided by the velocity limit obtained from the consideration of the rover static and dynamic stability. A description of both methods is provided, and the results of paths produced are given which show the effectiveness of the path planners in finding near optimal paths. The features of the methods and their suitability and application for rover path planning are compared

Tarokh, M.↗

Determination of lateral-stability derivatives and transfer-function coefficients from frequency-response data for lateral motions

A method is presented for determining the lateral-stability derivatives, transfer-function coefficients, and the modes for lateral motion from frequency-response data for a rigid aircraft. The method is based on the application of the vector technique to the equations of lateral motion, so that the three equations of lateral motion can be separated into six equations. The method of least squares is then applied to the data for each of these equations to yield the coefficients of the equations of lateral motion from which the lateral-stability derivatives and lateral transfer-function coefficients are computed. Two numerical examples are given to demonstrate the use of the method.

Donegan, James J↗

Early Oscillation Detection for DC/DC Converter Fault Diagnosis

The electrical power system of a spacecraft plays a very critical role for space mission success. Such a modern power system may contain numerous hybrid DC/DC converters both inside the power system electronics (PSE) units and onboard most of the flight electronics modules. One of the faulty conditions for DC/DC converter that poses serious threats to mission safety is the random occurrence of oscillation related to inherent instability characteristics of the DC/DC converters and design deficiency of the power systems. To ensure the highest reliability of the power system, oscillations in any form shall be promptly detected during part level testing, system integration tests, flight health monitoring, and on-board fault diagnosis. The popular gain/phase margin analysis method is capable of predicting stability levels of DC/DC converters, but it is limited only to verification of designs and to part-level testing on some of the models. This method has to inject noise signals into the control loop circuitry as required, thus, interrupts the DC/DC converter's normal operation and increases risks of degrading and damaging the flight unit. A novel technique to detect oscillations at early stage for flight hybrid DC/DC converters was developed.

Wang, Bright L.↗

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting

Fully implicit Runge--Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic preconditioning framework for solving the systems of equations that arise from IRK methods applied to linear numerical PDEs (without algebraic constraints). Additionally, this framework also naturally applies to discontinuous Galerkin discretizations in time. Under quite general assumptions on the spatial discretization that yield stable time integration, the preconditioned operator is proven to have condition number bounded by a small, order-one constant, independent of the spatial mesh and time-step size, and with only weak dependence on number of stages/polynomial order; for example, the preconditioned operator for 10th-order Gauss IRK has condition number less than two, independent of the spatial discretization and time step. The new method can be used with arbitrary existing preconditioners for backward Euler-type time-stepping schemes and is amenable to the use of three-term recursion Krylov methods when the underlying spatial discretization is symmetric. The new method is demonstrated to be effective on various high-order finite-difference and finite element discretizations of linear parabolic and hyperbolic problems, demonstrating fast, scalable solution of up to 10th-order accuracy. The new method consistently outperforms existing block preconditioning approaches, and in several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications and wallclock time as required using standard diagonally IRK methods.

97 MATHEMATICS AND COMPUTING↗

On an efficient and accurate method to integrate restricted three-body orbits

This work is a quantitative analysis of the advantages of the Bulirsch-Stoer (1966) method, demonstrating that this method is certainly worth considering when working with small N dynamical systems. The results, qualitatively suspected by many users, are quantitatively confirmed as follows: (1) the Bulirsch-Stoer extrapolation method is very fast and moderately accurate; (2) regularization of the equations of motion stabilizes the error behavior of the method and is, of course, essential during close approaches; and (3) when applicable, a manifold-correction algorithm reduces numerical errors to the limits of machine accuracy. In addition, for the specific case of the restricted three-body problem, even a small eccentricity for the orbit of the primaries drastically affects the accuracy of integrations, whether regularized or not; the circular restricted problem integrates much more accurately.

Murison, Marc A.↗