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Results for “Numerical Accuracy Improvement”

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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Lubrication of nonconformal contacts

Minimum film thickness results for piezoviscous-rigid regime of lubrication are developed for a compressible Newtonian fluid with Roelands viscosity. The results provide a basis for the analysis and design of a wide range of machine elements operating in the piezoviscous-rigid regime of lubrication. A new numerical method of calculating elastic deformation in contact stresses is developed using a biquadratic polynomial to approximate the pressure distribution on the whole domain analyzed. The deformation of every node is expressed as a linear combination of the nodal pressures whose coefficients can be combined into an influence coefficient matrix. This approach has the advantages of improved numerical accuracy, less computing time and smaller storage size required for influence matrix. The ideal elastohydrodynamic lubrication is extended to real bearing systems in order to gain an understanding of failure mechanisms in machine elements. The improved elastic deformation calculation is successfully incorporated into the EHL numerical scheme. Using this revised numerical technique and the flow factor model developed by Patir and Cheng (1978) the surface roughness effects on the elastohydrodynamic lubrication of point contact is considered. Conditions typical of an EHL contact in the piezoviscous-elastic regime entrained in pure rolling are investigated. Results are compared with the smooth surface solutions. Experiments are conducted to study the transient EHL effects in instrument ball bearings.

Jeng, Y. R.↗
DOE OSTI2025

ComPort: Rigorous Testing Methods to Safeguard Software Porting (Final Technical Report)

This is a technical report from the lead institution – University of Utah, Kahlert School of Computing – funded under the Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under award number DE-SC0022252. We summarize our work done over the three years of funding received. The relevant papers and software have already been uploaded at the DOE site.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Wing-Design And -Analysis Code

WINGDES2 computer program provides wing-design algorithm based on modified linear theory taking into account effects of attainable leading-edge thrust. Features improved numerical accuracy and additional capabilities. Provides analysis as well as design capability and applicable to both subsonic and supersonic flow. Replaces earlier wing-design code designated WINGDES (see LAR-13315). Written in FORTRAN V.

Darden, Christine M.↗
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 NTRS1975

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

Baldwin, B. S.↗
NASA NTRS1974

Time elements

Time elements are introduced for use with Sundman time transformations of the type dt = r(alpha)ds for satellite equations of motion. Two time elements are given, one providing maximum accuracy for alpha = 1, the other for alpha = 2. Time elements and time transformations reduce local truncation error and Liapunov (in track) instability, and provide analytical step size control. Numerical results show accuracy improvements of more than one order of magnitude when time elements are employed with time transformations in the numerical integration of the satellite equations, compared with using time transformations alone.

Nacozy, P. E.↗
NASA NTRS1975

Time elements

Time elements are introduced for use with Sundman time transformations for satellite equations of motion. Two time elements are presented, one providing maximum accuracy when the exponent of the governing equation equals 1, the other when the exponent equals 2. Time elements and time transformations reduce local truncation error and Liapunov (in-track) instability, and provide analytical step size control. Numerical results show accuracy improvements of more than one order of magnitude when time elements are employed with time transformations in the numerical integration of the satellite equations, compared with using time transformations alone.

Nacozy, P. E.↗
NASA NTRS1980

Investigation of transonic flow in a cascade using an adaptive mesh

The solution of two-dimensional full potential equation for the analysis of steady transonic flow through cascades is investigated. Finite element method is employed in the analysis. Accuracy and efficiency of the obtained numerical solutions are discussed in terms of the employed computational grid. Accurate modeling of subsonic and supersonic flow regions together with the shock is discussed. The choice of artificial viscosity and relaxation factors are examined and related to the design of a computational grid. Shock capturing and shock fitting procedures are compared for improved accuracy and efficiency. Numerical results include cascades of Gostelow and NACA 0012 airfoils.

Ecer, A.↗
DOE OSTI2025

An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture

This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We impose desirable structures on the DNN by employing manifold regularization, sparsity regularization, and physics-informed terms. We introduce a ε – δ – stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a ε – δ stability-promoting algorithm. Further, we also derive the necessary conditions for the trainability of a newly added layer and investigate the training saturation problem. In the second stage of the algorithm (post-processing), a sequence of shallow networks is employed to extract information from the residual produced in the first stage, thereby improving the prediction accuracy. Numerical investigations on prototype regression and classification problems demonstrate that the proposed approach can outperform fully connected DNNs of the same size. Moreover, by equipping the physics-informed neural network (PINN) with the proposed adaptive architecture strategy to solve partial differential equations, we numerically show that adaptive PINNs not only are superior to standard PINNs but also produce interpretable hidden layers with provable stability. As a result, we also apply our architecture design strategy to solve inverse problems governed by elliptic partial differential equations.

42 ENGINEERING↗
NASA NTRS1978

Modification of the Douglas Neumann program to improve the efficiency of predicting component interference and high lift characteristics

The Douglas Neumann method for low-speed potential flow on arbitrary three-dimensional lifting bodies was modified by substituting the combined source and doublet surface paneling based on Green's identity for the original source panels. Numerical studies show improved accuracy and stability for thin lifting surfaces, permitting reduced panel number for high-lift devices and supercritical airfoil sections. The accuracy of flow in concave corners is improved. A method of airfoil section design for a given pressure distribution, based on Green's identity, was demonstrated. The program uses panels on the body surface with constant source strength and parabolic distribution of doublet strength, and a doublet sheet on the wake. The program is written for the CDC CYBER 175 computer. Results of calculations are presented for isolated bodies, wings, wing-body combinations, and internal flow.

Bristow, D. R.↗
NASA NTRS1973

The use of the modified Cholesky decomposition in divergence and classification calculations

The use of the Cholesky decomposition technique is analyzed as applied to the feature selection and classification algorithms used in the analysis of remote sensing data (e.g. as in LARSYS). This technique is approximately 30% faster in classification and a factor of 2-3 faster in divergence, as compared with LARSYS. Also numerical stability and accuracy are slightly improved. Other methods necessary to deal with numerical stablity problems are briefly discussed.

Vanroony, D. L.↗
NASA NTRS1973

The use of the modified Cholesky decomposition in divergence and classification calculations

This report analyzes the use of the modified Cholesky decomposition technique as applied to the feature selection and classification algorithms used in the analysis of remote sensing data (e.g., as in LARSYS). This technique is approximately 30% faster in classification and a factor of 2-3 faster in divergence, as compared with LARSYS. Also numerical stability and accuracy are slightly improved. Other methods necessary to deal with numerical stability problems are briefly discussed.

Van Rooy, D. L.↗
DOE OSTI2025

A Geometric Volume of Fluid-Based Multiphase Flow Solver Extension to the Reacting Flow Solver, PeleLM

A new algorithm is presented to simulate multiphase flows with surface tension in a pathway for spray combustion simulation. The algorithm combines capabilities from two open-source packages, including the interface reconstruction library (IRL), a library of computational geometry routines to enable the volume of fluid (VOF) method, and PeleLM, a solver for the reacting Navier-Stokes equations. Additionally, surface tension is implemented using the continuum surface force (CSF) model with an improved height function technique in the volume fraction field. Spurious errors in volume fraction arising from our combined strategy are corrected through a topology-based method that improves both numerical stability and accuracy. Multiple validation simulations are conducted, including (i) translations and rotations of Zalesak's disk, (ii) a stationary circular droplet with surface tension, (iii) an oscillating elliptical droplet, and (iv) three-dimensional deformation of a spherical droplet. Results indicate that the combined scheme retains the favorable properties of each of the component algorithms.

42 ENGINEERING↗
DOE OSTI2025

Electromagnetic Transient Simulation of Large-Scale Inverter-Based Resources With High-Granularity

The power grid is undergoing a significant transformation with the rapid increase in inverter-based resources (IBRs), including large-scale photovoltaic (PV) plants. Ensuring reliable and resilient grid operation in this new paradigm necessitates high-granularity electromagnetic transient (EMT) modeling that accurately captures the behavior of individual inverters and their interactions within IBR plants. Central to this approach is the detailed representation of both the IBR plant’s collector system and the dynamics of individual inverters. To achieve this, a high-granularity EMT model of a large-scale PV plant has been developed using advanced simulation algorithms, including matrix splitting and the Schur complement. These proposed techniques significantly enhance simulation speed, numerical stability, and accuracy while improving the modularity and efficiency of the collector system’s representation. The effectiveness of the proposed methods is validated through simulations of a representative large-scale PV plant consisting of 125 individual PV inverters, 25 IBR unit transformers, and a 52-bus collector system.

Choi, Jongchan [Oak Ridge National Laboratory (ORN↗
NASA NTRS1975

Second-order non-iterative ADI solution of non-linear partial differential equations

A new method for the solution of non-linear partial differential equations by an ADI procedure is described. Although the method is second order accurate in time, it does not require either iterations or predictor corrector methods to overcome the nonlinearity of the equations. Thus the computational effort required for the solution of the non-linear problem becomes similar to that required for the linear case. The method is applied to a two-dimensional 'extended Burgers equation'. Linear stability is studied, and some numerical solutions obtained. The improved accuracy obtained by the 2nd order truncation error is clearly manifested.

Wolfshtein, M.↗
NASA NTRS1989

Calculating Dynamic Shear Moduli Of Polymers

Improved nonlinear mathematical model developed to fit experimental data on relaxation of stresses in viscoelastic materials. Developed specifically to study shear moduli of rubbery solid rocket propellants, also used to characterize polymers in general, other viscoelastic materials, and composites of viscoelastic materials. Facilitates and improves accuracy of analysis and numerical simulation of mechanical behavior of structural components (for example, tires) made of such materials.

Moore, Carleton J.↗
NASA NTRS1990

A turbulent two-phase flow model for nebula flows

A new and very efficient turbulent two-phase flow numericaly model is described to analyze the environment of a protoplanetary nebula at a stage prior to the formation of planets. Focus is on settling processes of dust particles in flattened gaseous nebulae. The model employs a perturbation technique to improve the accuracy of the numerical simulations of such flows where small variations of physical quantities occur over large distance ranges. The particles are allowed to be diffused by gas turbulence in addition to settling under gravity. Their diffusion coefficients is related to the gas turbulent viscosity by the non-dimensional Schmidt number. The gas turbulent viscosity is determined by the means of the eddy viscosity hypothesis that assumes the Reynolds stress tensor proportional to the mean strain rate tensor. Zero- and two-equation turbulence models are employed. Modeling assumptions are detailed and discussed. The numerical model is shown to reproduce an existing analytical solution for the settling process of particles in an inviscid nebula. Results of nebula flows are presented taking into account turbulence effects of nebula flows. Diffusion processes are found to control the settling of particles.

Champney, Joelle M.↗
NASA NTRS1986

Improved numerical methods for turbulent viscous recirculating flows

The objective of the present study is to improve both the accuracy and computational efficiency of existing numerical techniques used to predict viscous recirculating flows in combustors. A review of the status of the study is presented along with some illustrative results. The effort to improve the numerical techniques consists of the following technical tasks: (1) selection of numerical techniques to be evaluated; (2) two dimensional evaluation of selected techniques; and (3) three dimensional evaluation of technique(s) recommended in Task 2.

Vandoormaal, J. P.↗