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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

High precision computing with charge domain devices and a pseudo-spectral method therefor

The present invention enhances the bit resolution of a CCD/CID MVM processor by storing each bit of each matrix element as a separate CCD charge packet. The bits of each input vector are separately multiplied by each bit of each matrix element in massive parallelism and the resulting products are combined appropriately to synthesize the correct product. In another aspect of the invention, such arrays are employed in a pseudo-spectral method of the invention, in which partial differential equations are solved by expressing each derivative analytically as matrices, and the state function is updated at each computation cycle by multiplying it by the matrices. The matrices are treated as synaptic arrays of a neural network and the state function vector elements are treated as neurons. In a further aspect of the invention, moving target detection is performed by driving the soliton equation with a vector of detector outputs. The neural architecture consists of two synaptic arrays corresponding to the two differential terms of the soliton-equation and an adder connected to the output thereof and to the output of the detector array to drive the soliton equation.

Barhen, Jacob↗
NASA NTRS1985

Topics in spectral methods

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

Gottlieb, D.↗
NASA NTRS1987

An adaptive pseudo-spectral method for reaction diffusion problems

The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions.

Bayliss, A.↗
NASA NTRS1989

An adaptive pseudo-spectral method for reaction diffusion problems

The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions.

Bayliss, A.↗
NASA NTRS1991

Spectral methods for the Euler equations - The blunt body problem revisited

The present use of the Chebyshev spectral collocation method, in conjunction with shock-fitting, to solve the blunt-body problem gives attention to the boundary and the shock-acceleration equations. The crux of these procedures is the use of the characteristic compatibility relations to compute the body pressure and shock velocity. It is shown that converged solutions are obtainable without artificial smoothing, and that spectral accuracy is achieved.

Kopriva, David A.↗
NASA NTRS1991

Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions

The time-dependent, 3D incompressible Navier-Stokes equations in (1) boundary layers, the semiinfinite domain, and (2) mixing layers or wakes, the fully infinite domain, are respectively solved by two numerical methods which employ rapidly decaying spectral basis functions to approximate the vertical dependence of the solutions. These functions are then combined with one, for method (1), and two, for method (2), slowly decaying 'extra functions' for each wave vector. Each extra function can exactly represent the solution's irrotational component at large distances. The two methods have been applied to extensive direct-numerical simulation of transition and turbulence.

Spalart, Philippe R.↗
NASA NTRS1991

Spectral Method For Simulation Of Vortex Rings

Method of computation relying on spectral basis functions developed especially for simulation of axisymmetric vortex rings in incompressible, viscous fluid with quiescent far field. Contributes to understanding of flows in and around vortex rings during long propagation times, including such theoretically and practically important phenomena as drift and expansion of ring, "leapfrogging" and coalescence of two rings, and shedding of vorticity into wake of propagating ring.

Stanaway, S. K.↗
NASA NTRS1997

Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

Loulou, Patrick↗
NASA NTRS1981

Generalized Dufort-Frankel spectral methods

An explicit time-advancing scheme for the spectral solution of parabolic equations is presented. Several two-dimensional examples are considered, including convection-diffusion and nonlinear problems, under various boundary conditions. Numerical evidence demonstrates the efficiency and accuracy of the spectral approach.

Lustman, L.↗
DOE OSTI2024

Anti-symmetric and positivity preserving formulation of a spectral method for Vlasov-Poisson equations

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Comparative Evaluation of Spectral Methods for Robust Reactor Noise Estimation

Reactor noise analysis provides a noninvasive means to determine neutron kinetic parameters from stochastic fluctuations in detector signals. However, standard cross-power spectral density (CPSD) analyses can be sensitive to numerical processing choices, which may introduce processing-dependent systematic shifts in estimates of the prompt neutron decay constant (α) and limit reproducibility. This study uses a hybrid multitaper–Welch spectral estimator to analyze subcritical noise measurements from a fast-spectrum critical assembly. The decay constant α was extracted using three frequency-domain methods: the CPSD, the magnitude-squared coherence (MSC), and the generalized magnitude-squared coherence (GMSC). These coherence-based estimators normalize detector auto-spectral structure and are expected to reduce the sensitivity of fitted α values to processing parameters. A Sobol global sensitivity analysis identified which numerical inputs most strongly influence the fitted values of α. All estimators produced a linear dependence of α on inverse count rate, with delayed-critical extrapolations near 1.7 × 10 4 s −1 , in agreement within 8% of MCNP6.3 KOPTS benchmark calculations. Sensitivity results show that while the CPSD depends on both time-bin width and taper selection, the MSC and GMSC are dominated by time-bin width alone, indicating reduced parameter coupling and greater robustness to processing variability. These findings demonstrate the feasibility and practical value of coherence-based spectral estimators for extracting α from reactor noise and support their broader application to multi-detector and irregular datasets in subcritical system characterization.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Enhancing photoionization rate calculations in low-temperature plasmas using spectral methods

Photoionization plays a central role in the development of streamer discharges and other non-equilibrium plasma phenomena. It creates seed electrons, which are essential for positive streamer propagation, allowing the ionization front to move forward. Because of this, accurate modeling of photoionization is very important for predicting streamer behavior and plasma evolution. The photoionization process in air (N 2 – O 2 mixture) is often described by the Zheleznyak model (1982). This model is usually solved through Helmholtz-type equations that approximate the Zheleznyak photoionization model (Zheleznyak et al. 1982) as Partial Differential Equations (PDEs). Conventional numerical methods, such as the Finite Difference Method (FDM) or Finite Volume Method (FVM), are widely used to solve these equations. Although they are prevalent, the computational cost of these methods due to their need for matrix operations and iterative solver is demanding. To address this challenge, this work develops a spectral solver based on the Fast Fourier Transform (FFT) combined with Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) to calculate the photoionization rate efficiently in an axisymmetric cylindrical domain. This method naturally satisfies the boundary conditions used in the model and converts the PDE into algebraic ones in spectral space. Thus, avoids the need for iterative matrix solvers. When compared with FDM results, it is demonstrated that the new solver not only maintains accuracy, but also reduces the computational cost, showing a performance increase of approximately 100 compared to FDM over a wide range of problem sizes. The method is parallelized using Message Passing Interface (MPI) and has been integrated into a fluid plasma model for streamer simulation. Here, this FFT-based approach provides a fast and reliable alternative for calculating photoionization in fluid models, helping large-scale plasma simulations run faster and efficiently, and allows higher-resolution simulation without extra computational cost.

Axisymmetric system↗
NASA NTRS1954

A study of the application of power-spectral methods of generalized harmonic analysis to gust loads on airplanes

The applicability of some results from the theory of generalized harmonic analysis (or power-spectral analysis) to the analysis of gust loads on airplanes in continuous rough air is examined. The general relations for linear systems between power spectrums of a random input disturbance and an output response are used to relate the spectrum of airplane load in rough air to the spectrum of atmospheric gust velocity. The power spectrum of loads is shown to provide a measure of the load intensity in terms of the standard deviation (root mean square) of the load distribution for an airplane in flight through continuous rough air. For the case of a load output having a normal distribution, which appears from experimental evidence to apply to homogeneous rough air, the standard deviation is shown to describe the probability distribution of loads or the proportion of total time that the load has given values. Thus, for airplane in flight through homogeneous rough air, the probability distribution of loads may be determined from a power-spectral analysis. In order to illustrate the application of power-spectral analysis to gust-load analysis and to obtain an insight into the relations between loads and airplane gust-response characteristics, two selected series of calculations are presented. The results indicate that both methods of analysis yield results that are consistent to a first approximation.

Press, Harry↗
NASA NTRS1987

Coupling finite element and spectral methods: First results

A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.

Bernardi, Christine↗
NASA NTRS1990

Coupling finite element and spectral methods - First results

A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.

Bernardi, Christine↗
NASA NTRS1973

A multi-spectral method for estimating cirrus cloud top heights

A two-channel method has been developed to estimate the altitude of cirrus clouds over ocean areas with an expected altitude error less than or equal to plus or minus 50 mb. Reflected radiation is used to estimate cirrus emissivity in the 10- to 11-micron spectral interval. The cirrus altitude is determined from the emissivity estimate, a registered 10- to 11-micron measurement, and a vertical temperature profile. Nimbus 3 medium-resolution infrared radiometer measurements were used to establish the relationship between reflectance and 11-micron cirrus emissivity.

Shenk, W. E.↗
NASA NTRS1987

The convergence of spectral methods for nonlinear conservation laws

The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows.

Tadmor, Eitan↗