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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Using High-Order Methods on Lower-Order Geometries

The desire to obtain acoustic information from the numerical solution of a nonlinear system of equations is a demanding proposition for a computational algorithm. High-order accuracy is required for the propagation of high-frequency, low-amplitude waves. The accuracy of an algorithm can be compromised by low-order errors that naturally occur in the solution of a particular problem. Such errors arise from two sources: the presence of discontinuities in the flow field or because the geometry on which the problem is defined is not everywhere smooth to the order of the scheme. The performance of high-order accurate essentially non-oscillatory (ENO) schemes on piecewise smooth solutions is well documented. Herein, the performance of these methods on smooth solutions defined on piecewise smooth geometries is investigated. The propagation of sound in a quasi-one-dimensional nozzle is considered as a test case. Some of the issues involved in the extension to two spatial dimensions are discussed.

Casper, Jay↗
NASA NTRS2009

The a(4) Scheme-A High Order Neutrally Stable CESE Solver

The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a nondissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To provide a solid foundation for a systematic CESE development of high order schemes, in this paper we describe a new high order (4-5th order) and neutrally stable CESE solver of a 1D advection equation with a constant advection speed a. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and two points at the lower time level. Because it is associated with four independent mesh variables (the numerical analogues of the dependent variable and its first, second, and third-order spatial derivatives) and four equations per mesh point, the new scheme is referred to as the a(4) scheme. As in the case of other similar CESE neutrally stable solvers, the a(4) scheme enforces conservation laws in space-time locally and globally, and it has the basic, forward marching, and backward marching forms. Except for a singular case, these forms are equivalent and satisfy a space-time inversion (STI) invariant property which is shared by the advection equation. Based on the concept of STI invariance, a set of algebraic relations is developed and used to prove the a(4) scheme must be neutrally stable when it is stable. Numerically, it has been established that the scheme is stable if the value of the Courant number is less than 1/3

Chang, Sin-Chung↗
NASA NTRS2002

Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

A stable high-order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy-splitting approach splits the inviscid flux derivatives into conservative and nonconservative portions. The spatial difference operators satisfy a summation-by-parts condition, leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier–Stokes equations is used to ensure that any tendency to odd–even decoupling associated with central schemes can be countered by the fluid viscosity. The resulting methods are able to minimize the spurious high-frequency oscillations associated with pure central schemes, especially for long time integration applications such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at low values of friction Mach number, where reference turbulence data bases exist. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with published channel data. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.

N.D. Sandham↗
NASA NTRS1990

Formulation and validation of high-order linearized models of helicopter flight mechanics

A high-order linearized model of helicopter flight dynamics is extracted from a nonlinear time domain simulation. The model has 29 states that describe the fuselage rigid body degrees of freedom, the flap and lag dynamics in a nonrotating coordinate system, the inflow dynamics, the delayed entry of the horizontal tail into the main rotor wake, and, approximately, the blade torsion dynamics. The nonlinear simulation is obtained by extensively modifying the GENHEL computer program. The results indicate that the agreement between the linearized and the nonlinear model is good for small perturbations, and deteriorates for large amplitude maneuvers.

Kim, Frederick D.↗
NASA NTRS1998

Cascade Error Projection with Low Bit Weight Quantization for High Order Correlation Data

In this paper, we reinvestigate the solution for chaotic time series prediction problem using neural network approach. The nature of this problem is such that the data sequences are never repeated, but they are rather in chaotic region. However, these data sequences are correlated between past, present, and future data in high order. We use Cascade Error Projection (CEP) learning algorithm to capture the high order correlation between past and present data to predict a future data using limited weight quantization constraints. This will help to predict a future information that will provide us better estimation in time for intelligent control system. In our earlier work, it has been shown that CEP can sufficiently learn 5-8 bit parity problem with 4- or more bits, and color segmentation problem with 7- or more bits of weight quantization. In this paper, we demonstrate that chaotic time series can be learned and generalized well with as low as 4-bit weight quantization using round-off and truncation techniques. The results show that generalization feature will suffer less as more bit weight quantization is available and error surfaces with the round-off technique are more symmetric around zero than error surfaces with the truncation technique. This study suggests that CEP is an implementable learning technique for hardware consideration.

Duong, Tuan A.↗
NASA NTRS2004

Adaptive Numerical Dissipative Control in High Order Schemes for Multi-D Non-Ideal MHD

The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea 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 of numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multi-resolution wavelets (WAV) (for the above types of flow feature). These filter approaches also provide a natural and efficient way for the minimization of Div(B) numerical error. The filter scheme consists of spatially sixth order or higher non-dissipative spatial difference operators as the base scheme for the inviscid flux derivatives. If necessary, a small amount of high order linear dissipation is used to remove spurious high frequency oscillations. For example, an eighth-order centered linear dissipation (AD8) might be included in conjunction with a spatially sixth-order base scheme. The inviscid difference operator is applied twice for the viscous flux derivatives. After the completion of a full time step of the base scheme step, the solution is adaptively filtered by the product of a 'flow detector' and the 'nonlinear dissipative portion' of a high-resolution shock-capturing scheme. In addition, the scheme independent wavelet flow detector can be used in conjunction with spatially compact, spectral or spectral element type of base schemes. The ACM and wavelet filter schemes using the dissipative portion of a second-order shock-capturing scheme with sixth-order spatial central base scheme for both the inviscid and viscous MHD flux derivatives and a fourth-order Runge-Kutta method are denoted.

Yee, H. C.↗
DOE OSTI2021

High-Order Multipole and Binary Love Number Universal Relations

Using a data set of approximately 2 million phenomenological equations of state consistent with observational constraints, we construct new equation-of-state-insensitive universal relations that exist between the multipolar tidal deformability parameters of neutron stars, Λ l , for several high-order multipoles (l = 5,6,7,8), and we consider finite-size effects of these high-order multipoles in waveform modeling. We also confirm the existence of a universal relation between the radius of the 1.4M ⊙ NS, R 1.4 and the reduced tidal parameter of the binary, Λ˜, and the chirp mass. We extend this relation to a large number of chirp masses and to the radii of isolated NSs of different mass M, R M . We find that there is an optimal value of M for every M such that the uncertainty in the estimate of R M is minimized when using the relation. We discuss the utility and implications of these relations for the upcoming LIGO O4 run and third-generation detectors.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Nonreflective boundary conditions for high-order methods

A different approach to nonreflective boundary conditions for the Euler equations is presented. This work is motivated by a need for in and outflow boundary conditions that do not limit the useful accuracy of high-order accurate methods. The primary interest is in the propagation and convection of continuous acoustic and convective waves. This new approach employs the exact solution to finite waves to relate interior values and ambient conditions to boundary values. The method is first presented in one dimension and then generalized to multidimensions. Grid refinement studies are used to demonstrate high-order convergence for both one-dimensional and two-dimensional flows.

Atkins, H. L.↗
NASA NTRS1994

Nonreflective boundary conditions for high-order methods

A different approach to nonreflective boundary conditions for the Euler equations is presented. This work is motivated by a need for inflow and outflow boundary conditions that do not limit the useful accuracy of high-order accurate methods. The primary interest is in the propagation and convection of continuous acoustic and convective waves. This new approach employs the exact solution to finite waves to relate interior values and ambient conditions to boundary values. The method is first presented in one dimension and then generalized to multidimensions. Grid refinement studies are used to demonstrate high-order convergence for both one-dimensional and two-dimensional flows.

Atkins, H.↗
NASA NTRS1986

Uniformly high order accurate essentially non-oscillatory schemes 3

In this paper (a third in a series) the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws are presented. Also presented is a hierarchy of high order accurate schemes which generalizes Godunov's scheme and its second order accurate MUSCL extension to arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is derived from a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear.

Harten, A.↗
DOE OSTI2024

Stabilized bases for high-order, interpolation semi-Lagrangian, element-based tracer transport

In a computational fluid model of the atmosphere, the advective transport of trace species, or tracers, can be computationally expensive. For efficiency, models often use semi-Lagrangian advection methods. High-order interpolation semi-Lagrangian (ISL) methods, in particular, can be extremely efficient, if the problem of property preservation specific to them can be addressed. Atmosphere models often use geometrically and logically nonuniform grids for efficiency and, as a result, element-based discretizations. Such grids and discretizations make stability a particular problem for ISL methods. Generally, high-order, element-based ISL methods that use the natural polynomial interpolant associated with a nodal finite-element discretization are unstable. Here, we derive new bases having order of accuracy up to nine, with positive nodal weights, that stabilize the element-based ISL method. We use these bases to construct the linear advection operator in the property-preserving Interpolation Semi-Lagrangian Element-based Transport (Islet) method. Then we discuss key software implementation details. Finally, we show performance results for the Energy Exascale Earth System Model's atmosphere dynamical core, comparing the original and new transport methods. These simulations used up to 27,600 Graphical Processing Units (GPU) on the Oak Ridge Leadership Computing Facility's Summit supercomputer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Ultrafast and selective gas transport through highly ordered black phosphorene nanochannels

Two-dimensional (2D) materials bring a great opportunity to fabricate molecular sieving membranes that can potentially break the permeability-selectivity trade-off. Although 2D laminar membranes with interlayer nanochannels as molecular sieving channel were widely studied, for most of reported 2D laminar membranes, it is of a great challenge to fabricate highly ordered interlayer nanochannels for mass transport. Herein, we report a novel kind of black phosphorene membrane which is made from the stacking of highly ordered 2D black phosphorene nanoflakes. The as prepared black phosphorene membrane shows H 2 permeance > 1000 GPU and H 2 /CO 2 selectivity > 100 for H 2 /CO 2 mixed gas, demonstrating an extremely high gas separation performance. The DFT calculation results demonstrate that the interlayer galleries in the black phosphorene membrane allow the H 2 passing through easily while block the other gases with bigger kinetic diameters, matching well with the experimental findings. In conclusion, the present results indicate that the interlayer galleries in the black phosphorene membrane can be applied as molecular sieving channels for gas separation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1992

Laboratory for Engineering Man/Machine Systems (LEMS): System identification, model reduction and deconvolution filtering using Fourier based modulating signals and high order statistics

Several important problems in the fields of signal processing and model identification, such as system structure identification, frequency response determination, high order model reduction, high resolution frequency analysis, deconvolution filtering, and etc. Each of these topics involves a wide range of applications and has received considerable attention. Using the Fourier based sinusoidal modulating signals, it is shown that a discrete autoregressive model can be constructed for the least squares identification of continuous systems. Some identification algorithms are presented for both SISO and MIMO systems frequency response determination using only transient data. Also, several new schemes for model reduction were developed. Based upon the complex sinusoidal modulating signals, a parametric least squares algorithm for high resolution frequency estimation is proposed. Numerical examples show that the proposed algorithm gives better performance than the usual. Also, the problem was studied of deconvolution and parameter identification of a general noncausal nonminimum phase ARMA system driven by non-Gaussian stationary random processes. Algorithms are introduced for inverse cumulant estimation, both in the frequency domain via the FFT algorithms and in the domain via the least squares algorithm.

Pan, Jianqiang↗
DOE OSTI2022

Calculation of collisionless pitch-angle scattering of runaway electrons with synchrotron radiation via high-order guiding-centre equation

Recently, the collisionless pitch-angle scattering for relativistic runaway electrons (REs) in toroidal geometries such as tokamaks was discovered through a full orbit simulation approach (Liu et al., Nucl. Fusion, vol. 56, 2016, p. 064002), and it was then theoretically investigated that a new expression for the magnetic moment, including the second-order corrections, could essentially reproduce the so-called collisionless pitch-angle scattering process (Liu et al., Nucl. Fusion, vol. 58, 2018, p. 106018). In this paper, with synchrotron radiation, extensive numerical verification of the validity of the high-order guiding-centre theory is given for simulations involving REs by incorporating such an expression for the magnetic moment into our particle tracing code. A high-order guiding-centre simulation approach with synchrotron radiation (HGSA) is applied. Synchrotron radiation plays an essential role in the life cycle of REs. The energy of REs first increases and then becomes saturated until the electric field acceleration is balanced by the radiation dissipation. Unfortunately, the process cannot be simulated accurately with the standard guiding-centre model, i.e. the first-order guiding-centre model. Remarkably, it is found that the HGSA can effectively produce the fundamental process of REs. Since the time scale of the energy saturation of REs is close to seconds, the computational cost becomes significant. In order to save costs, it is necessary to estimate the time of energy saturation. An analytical estimate is derived for the time it takes for synchrotron drag to balance an accelerating electric field and the provided formula has been numerically verified. Finally, test calculations reveal that HGSA is favourable for exploiting the dynamics of REs in tokamak plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

High order filtering methods for approximating hyperbolic systems of conservation laws

The essentially nonoscillatory (ENO) schemes, while potentially useful in the computation of discontinuous solutions of hyperbolic conservation-law systems, are computationally costly relative to simple central-difference methods. A filtering technique is presented which employs central differencing of arbitrarily high-order accuracy except where a local test detects the presence of spurious oscillations and calls upon the full ENO apparatus to remove them. A factor-of-three speedup is thus obtained over the full-ENO method for a wide range of problems, with high-order accuracy in regions of smooth flow.

Lafon, F.↗
NASA NTRSDate not supplied

Updating High-Order Aeroservoelastic Models from Low-Order System Identification Results

Estimating aircraft models from test data requires several simplifying assumptions that introduce biases into the parameter estimates. In this paper, these biases are defined and a method for estimating the biases is discussed. Having an estimate of the bias allows the parameters estimated from test to be integrated into a high-order model. The Integrated Adaptive Wing Technology Maturation (IAWTM) wind tunnel model is discussed and the bias is demonstrated for one of the testing configurations. The methodology was able to estimate these biases and apply corrections to high-order aeroelastic models to improve the fit to test data. The consideration of the biases allows more meaningful comparisons and avoids the erroneous differences between pretest predictions and the fitted model.

Jeffrey Ouellette↗