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Results for “Accuracy and stability”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Accuracy and stability of fringe measurements in SIM

In order to identify habitable planets beyond our solar system it is necessary to determine their masses. SIM PlanetQuest is the only space mission which can discover and measure planets as small and cool as those in our solar system. This mission, however, requires unprecedented accuracy of angular rneasurements to the level of a microarcsecond, which are three orders of magnitude better than accuracy of the recent space astrometric missions. For microarcsecond accuracy of astrometric measurements the corresponding fringe delay must be determined to the accuracy of picometers, and it is a challenging task to measure fringe delays to this level of precision.

interferometer↗
NASA NTRS1972

NASA hydrogen maser accuracy and stability in relation to world standards

Frequency comparisons were made among five NASA hydrogen masers to a precision of one part in 10 to the 13th power. Frequency comparisons were also made between these masers and the cesium-beam ensembles of several international standards laboratories. The hydrogen maser frequency stabilities as related to the international time scale (IAT) were comparable to the frequency stabilities of individual time scales with respect to IAT. The relative frequency variations among the NASA masers were 2 plus or minus 2 parts in 10 to the 13th power after a three year interval. Charts are developed to show the results of the accuracy tests.

Peters, H. E.↗
NASA NTRS1981

Accuracy and stability of finite element schemes for the duct transmission problem

An investigation is conducted regarding the feasibility of approaches for improving the efficiency and stability of existing finite element method (FEM) schemes, taking into account both analytical and numerical studies. Of the four schemes considered for the 'steady' problem, the Hermitian Galerkin formulation appears to be the most efficient and therefore the most suitable scheme for futher full scale implementation. The Hermitian residual least squares (RLS) scheme although comparable in accuracy for the cases considered exhibits a slight tendency to cumulative errors. The performance of both the Lagrangian element schemes considered compares poorly with that of their Hermitian element counterparts. This is particularly true of the Lagrangian RLS scheme. The presence of internal oscillatory components is an inevitable consequence of all Galerkin schemes irrespective of element type.

Astley, R. J.↗
NASA NTRS1973

NASA hydrogen maser accuracy and stability in relation to world standards

Frequency comparisons were made among five NASA hydrogen masers in 1969 and again in 1972 to a precision of one part in 10 to the 13th power. Frequency comparisons were also made between these masers and the cesium-beam ensembles of several international standards laboratories. The hydrogen maser frequency stabilities as related to IAT were comparable to the frequency stabilities of individual time scales with respect to IAT. The relative frequency variations among the NASA masers, measured after the three-year interval, were 2 + or - 2 parts in 10 to the 13th power. Thus time scales based on hydrogen masers would have excellent long-term stability and uniformity.

Peters, H. E.↗
NASA NTRS1979

Explicit numerical formulas of improved stability and accuracy for the solution of parabolic equations

A class of explicit numerical formulas which involve next nearest neighbor as well as nearest neighbor points are explored in this paper. These formulas are formal approximations to the linear parabolic partial-differential equation of first order in time and second order in distance. It was found that some of these formulas can employ time steps as much as four times that for the conventional explicit technique without becoming unstable. Others showed improved accuracy for a given time step and spatial grid spacing. One formula achieved a steady-state solution of specified accuracy for an example problem in less than 4 percent of the total computational time required by the conventional explicit technique.

Olstad, W. B.↗
NASA NTRS1981

Accuracy and stability of time-split finite-difference schemes

In a recently published work by Abarbanel and Gottlieb (1980), a new class of explicit time-split algorithms designed for application to the compressible Navier-Stokes equations was developed. These algorithms, which utilize locally-one-dimensional (LOD) spatial steps, were shown to possess stability characteristics superior to those of other time-split schemes. In the present work, the properties of an implicit LOD method, analogous to the Abarbanel-Gottlieb algorithm, are examined using the two-dimensional heat conduction equation as the test problem. Both temporal and spatial inconsistencies inherent in the scheme are identified, and a new consistent, implicit splitting approach is developed and applied to the linear Burgers' equation. The relationship between this new method and other time-split implicit schemes is explained and stability problems encountered with the method in three dimensions are discussed.

Dwoyer, D. L.↗
NASA NTRS2011

Cryogenic Behavior of the High Temperature Crystal Oscillator PX-570

Microprocessors, data-acquisition systems, and electronic controllers usually require timing signals for proper and accurate operation. These signals are, in most cases, provided by circuits that utilize crystal oscillators due to availability, cost, ease of operation, and accuracy. Stability of these oscillators, i.e. crystal characteristics, is usually governed, amongst other things, by the ambient temperature. Operation of these devices under extreme temperatures requires, therefore, the implementation of some temperature-compensation mechanism either through the manufacturing process of the oscillator part or in the design of the circuit to maintain stability as well as accuracy. NASA future missions into deep space and planetary exploration necessitate operation of electronic instruments and systems in environments where extreme temperatures along with wide-range thermal swings are countered. Most of the commercial devices are very limited in terms of their specified operational temperature while very few custom-made and military-grade parts have the ability to operate in a slightly wider range of temperature. Thus, it is becomes mandatory to design and develop circuits that are capable of operation efficiently and reliably under the space harsh conditions. This report presents the results obtained on the evaluation of a new (COTS) commercial-off-the-shelf crystal oscillator under extreme temperatures. The device selected for evaluation comprised of a 10 MHz, PX-570-series crystal oscillator. This type of device was recently introduced by Vectron International and is designed as high temperature oscillator [1]. These parts are fabricated using proprietary manufacturing processes designed specifically for high temperature and harsh environment applications [1]. The oscillators have a wide continuous operating temperature range; making them ideal for use in military and aerospace industry, industrial process control, geophysical fields, avionics, and engine control. They exhibit low jitter and phase noise, consume little power, and are suited for high shock and vibration applications. The unique package design of these crystal oscillators offers a small ceramic package footprint, as well as providing both through-hole mounting and surface mount options.

Patterson, Richard↗
DOE OSTI2020

High-order partitioned spectral deferred correction solvers for multiphysics problems

We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1], [2], which used implicit-explicit Runge-Kutta methods (IMEX) to build high-order, partitioned multiphysics solvers. We consider a generic multiphysics problem modeled as a system of coupled ordinary differential equations (ODEs), coupled through coupling terms that can depend on the state of each subsystem; therefore the method applies to both a semi-discretized system of partial differential equations (PDEs) or problems naturally modeled as coupled systems of ODEs. The sufficient conditions to build arbitrarily high-order partitioned SDC schemes are derived. Based on these conditions, various of partitioned SDC schemes are designed. The stability of the first-order partitioned SDC scheme is analyzed in detail on a coupled, linear model problem. We show that the scheme is conditionally stable, and under conditions on the coupling strength, the scheme can be unconditionally stable. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems with moderate coupling strength. They include a stiff linear system of ODEs, advection-diffusion-reaction systems, and fluid-structure interaction problems with both incompressible and compressible flows, where we verify the design order of the SDC schemes and study various stability properties. We also directly compare the accuracy, stability, and cost of the proposed partitioned SDC solver with the partitioned IMEX method in [1], [2] on this suite of test problems. The results suggest that the high-order partitioned SDC solvers are more robust than the partitioned IMEX solvers for the numerical examples considered in this work, while the IMEX methods require fewer implicit solves.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1997

Future Laser-Cooled Microwave Clock Performance

Limitations to the performance of laser-cooled earth and space-based Cs clocks will be critically discussed. The most significant limitation to the stability and accuracy of laser-cooled atomic clocks is the frequency shift due to cold collisions. Because of it, laser-cooled Cs clocks must be operated at low density and this implies that space based Cs clock performance will not be significantly better than earth based. To regain some of the high accuracy and stability lost to the low density, clocks can be designed to multiply launch (or juggle) atoms. Clocks based on other atoms, in particular Rb-87 or possibly Rb-85, may have much smaller cold collision frequency shifts and therefore be capable of higher stability and accuracy, especially in a space environment.

Gibble, Kurt↗
DOE OSTI2023

Lack of robustness and accuracy of many numerical schemes for phase-field simulations

In this paper, we study the stability, accuracy and convergence behavior of various numerical schemes for phase-field modeling through a simple ODE model. Both theoretical analysis and numerical experiments are carried out on this ODE model to demonstrate the limitation of most numerical schemes that have been used in practice. One main conclusion is that the first-order fully implicit scheme is the only robust algorithm for phase-field simulations while all other schemes (that have been analyzed) may have convergence issue if the time step size is not exceedingly small. More specifically, by rigorous analysis in most cases, we have the following conclusions: (i) The first-order fully implicit scheme converges to the correct steady state solution for all time step sizes. In the case of multiple solutions, one of the solution branches always converges to the correct steady state solution. (ii) The first-order convex splitting scheme, which is equivalent to the first-order fully implicit scheme with a different time scaling, always converges to the correct steady state solution but may seriously lack numerical accuracy for transient solutions. (iii) For the second-order fully implicit and convex splitting schemes, for any time step size $δt > 0$, there exists an initial condition $u_0$ , with $|u_0| > 1$, such that the numerical solution converges to the wrong steady state solution. (iv) For $|u_0|$ ≤ 1, all second-order schemes studied in this paper converge to the correct steady state solution although severe numerical oscillations occur for most of them if the time step size is not sufficiently small. (v) An unconditionally energy-stable scheme (such as the modified Crank–Nicolson scheme) is not necessarily better than a conditionally energy-stable scheme (such as the Crank–Nicolson scheme). Finally, most, if not all, of the above conclusions are expected to be true for more general Allen–Cahn and other phase-field models.

97 MATHEMATICS AND COMPUTING↗