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Results for “interpolating methods”

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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

A numerical method for approximating antenna surfaces defined by discrete surface points

A simple numerical method for the quadratic approximation of a discretely defined reflector surface is described. The numerical method was applied to interpolate the surface normal of a parabolic reflector surface from a grid of nine closest surface points to the point of incidence. After computing the surface normals, the geometrical optics and the aperture integration method using the discrete Fast Fourier Transform (FFT) were applied to compute the radiaton patterns for a symmetric and an offset antenna configurations. The computed patterns are compared to that of the analytic case and to the patterns generated from another numerical technique using the spline function approximation. In the paper, examples of computations are given. The accuracy of the numerical method is discussed.

Lee, R. Q.↗
NASA NTRS1991

Uniform high order spectral methods for one and two dimensional Euler equations

Uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics are discussed. Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods. The authors present numerical results for the inviscid Burgers' equation, and for the one dimensional Euler equations including the interactions between a shock wave and density disturbance, Sod's and Lax's shock tube problems, and the blast wave problem. The interaction between a Mach 3 two dimensional shock wave and a rotating vortex is simulated.

Cai, Wei↗
NASA NTRS1993

Uniform high-order spectral methods for one- and two-dimensional Euler equations

Uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics are discussed. Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods. The authors present numerical results for the inviscid Burgers' equation, and for the one-dimensional Euler equations including the interactions between a shock wave and density disturbance, Sod's and Lax's shock tube problems, and the blast wave problem. The interaction between a Mach 3 two-dimensional shock wave and a rotating vortex is simulated.

Cai, Wei↗
NASA NTRSDate not supplied

Total Variation Majorization Minimization (TV-MM) Approach to Radiometer Brightness Temperature Gridding and Reconstruction

This paper presents the implementation of an algorithm to enhance the image resolution of the Earth's surface brightness temperature (T B ) data measured by radiometers such as the one onboard of the Soil Moisture Active Passive (SMAP) mission. A key step in radiometer T B processing is the conversion of the swath-based calibrated antenna temperature (T A ) measurements to the Level 3 Earth-centered grid. The simplest algorithm to transform this data from swath to gridded format is called drop-in-the-bucket which simply averages surrounding noisy T A samples to form a T B value at the gridded location. This method reduces noise, however produces low resolution products. To obtain a higher resolution product, SMAP uses other techniques such the Backus-Gilbert (BG) algorithm, which is the conventional method used in microwave radiometry. Although this method performs the required interpolation, it is not effective in denoising and removing blurring effects due to antenna filtering of the radiometer image data. Our motivation for this development is to further improve the resolution through post-processing of the radiometer T B image, a highly cost-effective method of image enhancement. The approach adapted in this work is based on the minimization of the Total Variation (TV) regularized objective function that is used extensively in solving general ill-posed linear inverse problems in image processing. Since the TV-based objective function is convex but not everywhere differentiable, there exists many numerical algorithms that can estimate the solution and the one selected for this work is called Majorization- Minimization (MM). By applying this algorithm, simulation experiments were performed based on synthetic data from the Geophysical model as well as real SMAP data to demonstrate the effectiveness of the technique. Results were then compared against the BG method.

Wing Lee↗
NASA NTRS1984

ADS: A FORTRAN program for automated design synthesis, version 1.00

A new general-purpose optimization program for engineering design is described. ADS-1 (Automated Design Synthesis - Version 1) is a FORTRAN program for solution of nonlinear constrained optimization problems. The program is segmented into three levels, being strategy, optimizer, and one-dimensional search. At each level, several options are available so that a total of over 100 possible combinations can be created. Examples of available strategies are sequential unconstrained minimization, the Augmented Lagrange Multiplier method, and Sequential Linear Programming. Available optimizers include variable metric methods and the Method of Feasible Directions as examples and one-dimensional search options include polynomial interpolation and the Golden Section method as examples. Emphasis is placed on ease of use of the program. All information is transferred via a single parameter list. Default values are provided for all internal program parameters such as convergence criteria, and the user is given a simple means to over-ride these, if desired. The program is demonstrated with a simple structural design example.

Vanderplaats, G. N.↗
NASA NTRS1985

ADS: A FORTRAN program for automated design synthesis: Version 1.10

A new general-purpose optimization program for engineering design is described. ADS (Automated Design Synthesis - Version 1.10) is a FORTRAN program for solution of nonlinear constrained optimization problems. The program is segmented into three levels: strategy, optimizer, and one-dimensional search. At each level, several options are available so that a total of over 100 possible combinations can be created. Examples of available strategies are sequential unconstrained minimization, the Augmented Lagrange Multiplier method, and Sequential Linear Programming. Available optimizers include variable metric methods and the Method of Feasible Directions as examples, and one-dimensional search options include polynomial interpolation and the Golden Section method as examples. Emphasis is placed on ease of use of the program. All information is transferred via a single parameter list. Default values are provided for all internal program parameters such as convergence criteria, and the user is given a simple means to over-ride these, if desired.

Vanderplaats, G. N.↗
DOE OSTI2024

Ensuring Σ s Y s = 1 in transport of species mass fractions

When transporting species mass fractions in reacting flow simulations, there are physical constraints that must be met. Unfortunately, nonlinear transport schemes such as weighted essentially non-oscillatory (WENO) schemes do not ensure that the sum of mass fractions equals 1. In detonation simulations, errors in the sum of mass fractions are observed to worsen over time when the standard WENO scheme is used. To prevent this, typically one species is forced to absorb all or most of the error in the sum of mass fractions. Here, this work presents an alternative method for correcting the WENO-interpolated mass fractions such that inert species do not change. The method is demonstrated for both argon and nitrogen-diluted hydrogen detonations in one dimension. Using the modified WENO interpolations, the error in the sum is reduced significantly. In addition, the new approach is better able to capture the physical instability expected for nitrogen-diluted detonations.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS2019

Auralization of Unsteady Rotor Noise Using a Solution to the Ffowcs Williams-Hawkings Equation

Auralization of unsteady helicopter flight operations is needed to better understand the impact of maneuvers on community noise. Previous source sound synthesis methods were based on interpolated data, which may lead to artifacts in generating sound for helicopter maneuvers where sound pressure directivity may change rapidly. In this paper, the source sound is synthesized at every time sample using a solution to the Ffowcs Williams-Hawkings Equation along the path of the emission angle between the source and a ground observer. The synthesized sound is then propagated to the ground observer for auralization. Since no interpolation is performed, maneuvers with rapidly changing sound pressure directivities may be more accurately synthesized and auralized. The framework for accomplishing this synthesis and auralization is described, which couples the Fundamental Rotorcraft Acoustic Modeling from Experiments, the second-generation Aircraft NOise Prediction Program, and the NASA Auralization Framework. Synthesis of a hovering rotor is presented to compare with previous synthesis methods. Two examples with a periodic signals are then presented to demonstrate synthesis and auralization of unsteady rotor noise.

Krishnamurthy, Siddhartha↗
NASA NTRS1976

The Adams formulas for numerical integration of differential equations from 1st to 20th order

The Adams Bashforth predictor coefficients and the Adams Moulton corrector coefficients for the integration of differential equations are presented for methods of 1st to 20th order. The order of the method as presented refers to the highest order difference formula used in Newton's backward difference interpolation formula, on which the Adams method is based. The Adams method is a polynomial approximation method derived from Newton's backward difference interpolation formula. The Newton formula is derived and expanded to 20th order. The Adams predictor and corrector formulas are derived and expressed in terms of differences of the derivatives, as well as in terms of the derivatives themselves. All coefficients are given to 18 significant digits. For the difference formula only, the ratio coefficients are given to 10th order.

Kirkpatrick, J. C.↗
DOE OSTI2024

On the applicability of the Redlich-Kister framework for viscosity estimation of molten halide salt mixtures

For molten halide salt mixtures already being utilized or under consideration for carbon-free energy production systems, it is crucial that their viscosity is well understood so that system thermal hydraulics can be reliably assessed. Because of the difficulty in accurately measuring molten halide viscosity and the sheer size of the matrix of possible higher order salt mixtures that may be of interest to the energy industry, there are several gaps in the quantified understanding of molten halide viscosity across this matrix. As such, both first-principles and semi-empirical modeling techniques may be crucial for rapidly assessing this broad, complex compositional domain. Herein, the Redlich-Kister framework is applied to assess the feasibility of broadly interpolating and estimating the viscosity of several pseudobinary and pseudoternary molten halide salt systems that may be of key interest to the energy industry. The framework is based on the assumption that an ideal component and a nonideal component collectively describe the viscosity as a function of composition and temperature for a given molten halide system. Three different ideal models were considered for the ideal component, including Grunburg-Nissan, Katti-Chaudhri, and Gambill methods. Regarding the pseudobinary interpolations, the Redlich-Kister models with either the Grunburg-Nissan or Katti-Chaudhri models as the ideal component resulted in either highly (average error less than 5%) or reasonably (average error less than 15%) accurate interpolations of pseudobinary halide viscosity; BeF 2 - or UF 4 -bearing salts tended to result in reasonably accurate interpolations, whereas other pseudobinary mixtures tended to show high accuracy. Regarding the pseudoternary extrapolations, the Redlich-Kister framework shows reasonable success at estimating the extent to which a pseudoternary system may indicate deviations from ideal Grunburg-Nissan mixing, where discrepancies with comparative experimental data generally stay within 30%. Finally, the primary reasons identified for such discrepancies are (1) inaccuracy in the underlying experimental data, (2) different complexation behavior in the higher order systems compared to the pseudobinary subsystems, and (3) extrapolation into temperatures too far out of the domain, which is valid for the underlying experimental data feeding the Redlich-Kister model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2002

Aeroacoustic Flow Phenomena Accurately Captured by New Computational Fluid Dynamics Method

One of the challenges in the computational fluid dynamics area is the accurate calculation of aeroacoustic phenomena, especially in the presence of shock waves. One such phenomenon is "transonic resonance," where an unsteady shock wave at the throat of a convergent-divergent nozzle results in the emission of acoustic tones. The space-time Conservation-Element and Solution-Element (CE/SE) method developed at the NASA Glenn Research Center can faithfully capture the shock waves, their unsteady motion, and the generated acoustic tones. The CE/SE method is a revolutionary new approach to the numerical modeling of physical phenomena where features with steep gradients (e.g., shock waves, phase transition, etc.) must coexist with those having weaker variations. The CE/SE method does not require the complex interpolation procedures (that allow for the possibility of a shock between grid cells) used by many other methods to transfer information between grid cells. These interpolation procedures can add too much numerical dissipation to the solution process. Thus, while shocks are resolved, weaker waves, such as acoustic waves, are washed out.

Blech, Richard A.↗
NASA NTRS2011

Method and System for Temporal Filtering in Video Compression Systems

Three related innovations combine improved non-linear motion estimation, video coding, and video compression. The first system comprises a method in which side information is generated using an adaptive, non-linear motion model. This method enables extrapolating and interpolating a visual signal, including determining the first motion vector between the first pixel position in a first image to a second pixel position in a second image; determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image; determining a third motion vector between the first pixel position in the first image and the second pixel position in the second image, the second pixel position in the second image, and the third pixel position in the third image using a non-linear model; and determining a position of the fourth pixel in a fourth image based upon the third motion vector. For the video compression element, the video encoder has low computational complexity and high compression efficiency. The disclosed system comprises a video encoder and a decoder. The encoder converts the source frame into a space-frequency representation, estimates the conditional statistics of at least one vector of space-frequency coefficients with similar frequencies, and is conditioned on previously encoded data. It estimates an encoding rate based on the conditional statistics and applies a Slepian-Wolf code with the computed encoding rate. The method for decoding includes generating a side-information vector of frequency coefficients based on previously decoded source data and encoder statistics and previous reconstructions of the source frequency vector. It also performs Slepian-Wolf decoding of a source frequency vector based on the generated side-information and the Slepian-Wolf code bits. The video coding element includes receiving a first reference frame having a first pixel value at a first pixel position, a second reference frame having a second pixel value at a second pixel position, and a third reference frame having a third pixel value at a third pixel position. It determines a first motion vector between the first pixel position and the second pixel position, a second motion vector between the second pixel position and the third pixel position, and a fourth pixel value for a fourth frame based upon a linear or nonlinear combination of the first pixel value, the second pixel value, and the third pixel value. A stationary filtering process determines the estimated pixel values. The parameters of the filter may be predetermined constants.

Lu, Ligang↗
NASA NTRS1991

Characteristics-based methods applied to infinite Prandtl number thermal convection in the hard turbulent regime

Characteristics-based methods for the advection-diffusion equation are presented and directly applied to study thermal convection with extremely large Rayleigh number (Ra). It is shown that the operator-splitting method for advection-diffusion problems is very accurate for determining the advected field at extremely high Peclet number (Pe). The technique presented is considered to have great potential for solving advection-dominated problems, while the Langrangian method is more accurate for lower Pe. It is noted that the accuracy of these characteristics-based methods strongly depends on the quality of interpolation. The computational time for the operator-splitting method grows with the number of time steps employed. The Langrangian method was used for simulations of convection at very high Ra, up to 3 x 10 to the 9th, and time-dependent, thermal convection solutions were obtained for infinite Prandtl number.

Malevsky, A. V.↗
NASA NTRS1991

Comparison of three atmospheric correction models for a vegetated airborne visible/infrared imaging spectrometer (AVIRIS) scene

Current atmospheric correction models applied to imaging spectroscopy data include such methods as residual or scene average, flat field correction, regression method or empirical line algorithm, the continuum interpolated band ratio (CIBR) derivation and the LOWTRAN 7 method. Due to the limitations of using residual and flat field corrections on vegetated scenes, three methods will be compared: regression, CIBR derivation and LOWTRAN 7. Field-measured bright and dark targets taken at the time of the 13 April, 1989 AVIRIS overflight of Jasper Ridge, California were used to formulate the regression method atmospheric correction. Using this corrected scene as 'ground truth', the CIBR derivation and the LOWTRAN 7 method with both input models are compared on the vegetated Jasper Ridge scene. Although representing a qualitative approach, this is a first approximation and shows the need for more quantitative analysis.

Van Den Bosch, J. M.↗
DOE OSTI2025

Data-driven reduced-order models for port-Hamiltonian systems with operator inference

Hamiltonian operator inference has been developed in Sharma et al. (2022) to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method constructs a low-dimensional model using only data and knowledge of the functional form of the Hamiltonian. The resulting ROMs preserve the intrinsic structure of the system, ensuring that the mechanical and physical properties of the system are maintained. In this work, we extend this approach to port-Hamiltonian systems, which generalize Hamiltonian systems by including energy dissipation, external input, and output. Based on snapshots of the system’s state and output, together with the information about the functional form of the Hamiltonian, reduced operators are inferred through optimization and are then used to construct data-driven ROMs. To further alleviate the complexity of evaluating nonlinear terms in the ROMs, a hyper-reduction method via discrete empirical interpolation is applied. Accordingly, we derive error estimates for the ROM approximations of the state and output. Lastly, we demonstrate the structure preservation, as well as the accuracy of the proposed port-Hamiltonian operator inference framework, through numerical experiments on a linear mass–spring-damper problem and a nonlinear Toda lattice problem.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

Interpolation in numerical optimization

The present work discusses the generation of the cubic-spline interpolator in numerical optimization methods which use a variable-step integrator with step size control based on local relative truncation error. An algorithm for generating the cubic spline with successive over-relaxation is presented which represents an improvement over that given by Ralston and Wilf (1967). Rewriting the code reduces the number of N-vectors from eight to one. The algorithm is formulated in such a way that the solution of the linear system set up yields the first derivatives at the nodal points. This method is as accurate as other schemes but requires the minimum amount of storage.

Hall, K. R.↗
NASA NTRS1976

Investigations with satellite data temperature retrievals

A method is presented for using satellite measurements to interpolate vertical temperature soundings between radiosonde stations. The method finds a set of coefficients, which when multiplied by corresponding measured radiance quantities, yield zero temperature error at a radiosonde station. This derived set of coefficients is then applied to satellite radiance measurements at places between radiosonde stations. The computations show, for example, that the average absolute error in the layer 1000-800 mbs is only 0.3K when the corresponding 'minimum-information' method error was 2.9K. The method may be most applicable to measurements from geostationary satellites, but should also be applicable to measurements from polar orbiting satellites under certain conditions.

Fritz, S.↗
NASA NTRS1982

Computation of consistent boundary quantities in finite element thermal-fluid solutions

The consistent boundary quantity method for computing derived quantities from finite element nodal variable solutions is investigated. The method calculates consistent, continuous boundary surface quantities such as heat fluxes, flow velocities, and surface tractions from nodal variables such as temperatures, velocity potentials, and displacements. Consistent and lumped coefficient matrix solutions for such problems are compared. The consistent approach may produce more accurate boundary quantities, but spurious oscillations may be produced in the vicinity of discontinuities. The uncoupled computations of the lumped approach provide greater flexibility in dealing with discontinuities and provide increased computational efficiency. The consistent boundary quantity approach can be applied to solution boundaries other than those with Dirichlet boundary conditions, and provides more accurate results than the customary method of differentiation of interpolation polynomials.

Thornton, E. A.↗