Search NASA⌕ Search

SEARCH · Search NASA

Results for “splitting 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

A numerical method for predicting hypersonic flowfields

The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to chemically react and reach states in thermal nonequilibrium. The prediction of hypersonic flowfields requires a numerical method capable of solving the conservation equations of fluid flow, the chemical rate equations for specie formation and dissociation, and the transfer of energy relations between translational and vibrational temperature states. Because the number of equations to be solved is large, the numerical method should also be as efficient as possible. The proposed paper presents a fully implicit method that fully couples the solution of the fluid flow equations with the gas physics and chemistry relations. The method flux splits the inviscid flow terms, central differences of the viscous terms, preserves element conservation in the strong chemistry source terms, and solves the resulting block matrix equation by Gauss Seidel line relaxation.

Maccormack, Robert W.↗
NASA NTRS1989

The secondary flow and its stability for natural convection in a tall vertical enclosure

The multicellular flow between two vertical parallel plates is numerically simulated using a time-splitting pseudospectral method. The steady flow of air and the time-periodic flow of oil are investigated, and descriptions of these flows using both physical and spectral approaches are presented. The time dependence of the flow and temperature fields of oil are shown, and the dynamics of the process is discussed. The spectral transfer of energy among the axial modes comprising the flow is explored. The three-dimensional linear stabiltiy of the multicellular air flow is parametrically studied. The domain of stable two-dimensional cellular motion is found to be constrained by the Eckhaus instability and by two types of monotone instability. The two-dimensional multicellular flow is unstable above a Grashof number of about 8550.

Chait, Arnon↗
NASA NTRS1989

Land-surface temperature measurement from space - Physical principles and inverse modeling

To apply the multiple-wavelength (split-window) method used for satellite measurement of sea-surface temperature from thermal-infrared data to land-surface temperatures, the authors statistically analyze simulations using an atmospheric radiative transfer model. The range of atmospheric conditions and surface temperatures simulated is wide enough to cover variations in clear atmospheric properties and surface temperatures, both of which are larger over land than over sea. Surface elevation is also included in the simulation as the most important topographic effect. Land covers characterized by measured or modeled spectral emissivities include snow, clay, sands, and tree leaf samples. The empirical inverse model can estimate the surface temperature with a standard deviation less than 0.3 K and a maximum error less than 1 K, for viewing angles up to 40 degrees from nadir under cloud-free conditions, given satellite measurements in three infrared channels. A band in the region from 10.2 to 11.0 microns will usually give the most reliable single-band estimate of surface temperature. In addition, a band in either the 3.5-4.0-micron region or in the 11.5-12.6-micron region must be included for accurate atmospheric correction, and a band below the ozone absorption feature at 9.6 microns (e.g., 8.2-8.8 microns) will increase the accuracy of the estimate of surface temperature.

Wan, Zhengming↗
NASA NTRS1989

A multiple-time-scale turbulence model based on variable partitioning of the turbulent kinetic energy spectrum

A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.

Kim, S.-W.↗
NASA NTRS1993

Upwind MacCormack Euler solver with non-equilibrium chemistry

A computer code, designated UMPIRE, is currently under development to solve the Euler equations in two dimensions with non-equilibrium chemistry. UMPIRE employs an explicit MacCormack algorithm with dissipation introduced via Roe's flux-difference split upwind method. The code also has the capability to employ a point-implicit methodology for flows where stiffness is introduced through the chemical source term. A technique consisting of diagonal sweeps across the computational domain from each corner is presented, which is used to reduce storage and execution requirements. Results depicting one dimensional shock tube flow for both calorically perfect gas and thermally perfect, dissociating nitrogen are presented to verify current capabilities of the program. Also, computational results from a chemical reactor vessel with no fluid dynamic effects are presented to check the chemistry capability and to verify the point implicit strategy.

Sherer, Scott E.↗
NASA NTRS2020

Beam Propagation Through Atmospheric Turbulence Using an Altitude-Dependent Structure Profile with Non-Uniformly Distributed Phase Screens

For free-space optical communication systems, numerical wave optics simulations provide a useful technique for modeling turbulence-induced beam degradation when the analytical theory is insufficient for characterizing the atmospheric channel. Motivated by such applications we use a split-step method modeling the turbulence as a series of random phase screens using the Hufnagel-Valley turbulence profile. We employ a space-to-ground case study to examine the irradiance and phase statistics for uniformly and non-uniformly located screens and find better agreement with theory using a non-uniform discretization minimizing the contribution of each screen to the total scintillation. In this poster, we summarize the method and the results of the case study including a comparison to layered models used in astronomical imaging applications.

Chahine, Yousef K.↗
NASA NTRS2020

Beam Propagation Through Atmospheric Turbulence Using an Altitude-Dependent Structure Profile with Non-Uniformly Distributed Phase Screens

Modeling the effects of atmospheric turbulence on optical beam propagation is a key element in the design and analysis of free-space optical communication systems. Numerical wave optics simulations provide a particularly useful technique for understanding the degradation of the optical field in the receiver plane when the analytical theory is insufficient for characterizing the atmospheric channel. Motivated by such an application, we use a split-step method modeling the turbulence along the propagation path as a series of thin random phase screens with modified von Karman refractive index statistics using the Hufnagel-Valley turbulence profile to determine the effective structure constant for each screen. In this work, we employ a space-to-ground case study to examine the irradiance and phase statistics for both uniformly and non-uniformly spaced screens along the propagation path and compare to analytical results. We find that better agreement with the analytical theory is obtained using a non-uniform spacing with the effective structure constant for each screen chosen to minimize its contribution to the scintillation in the receiver plane. We evaluate this method as a flexible alternative to other standard layered models used in astronomical imaging applications.

Chahine, Yousef K.↗
NASA NTRS2019

Emissions Relationships in Western Forest Fire Plumes: I. Reducing the Effect of Mixing Errors on Emission Factors

Studies of emission factors from biomass burning using aircraft data complement the results of lab studies and extend them to conditions of immense hot conflagrations. We illustrate and discuss emission relationships for 422 individual samples from many forest-fire plumes in the Western US. The samples are from two NASA investigations: ARCTAS (Arctic Research of the Composition of the Troposphere from Aircraft and Satellites) and SEAC4RS (Studies of Emissions and Atmospheric Composition, Clouds, and Climate Coupling by Regional Surveys). This work provides sample-by-sample enhancement ratios (EnRs) for 23 gases and particulate properties. Many EnRs provide candidates for emission ratios (ERs, corresponding to the EnR at the source) when the origin and degree of transformation is understood and appropriate. From these, emission factors (EFs) can be estimated when the fuel dry mass consumed is known or can be estimated using the carbon mass budget approach. This analysis requires understanding the interplay of mixing of the plume with surrounding air. Some initial examples emphasize that measured C(tot) = CO2 + CO in a fire plume does not necessarily describe the emissions of the total carbon liberated in the flames, C(burn). Rather, it represents C(tot) = C(burn) + C(bkgd), which includes possibly varying background concentrations for entrained air. Consequently, we present a simple theoretical description for plume entrainment for multiple tracers from flame to hundreds of kilometers downwind and illustrate some intrinsic linear behaviors. The analysis suggests a Mixed Effects Regression Emission Technique (MERET), which can eliminate occasional strong biases associated with the commonly used normalized excess mixing ratio (NEMR) method. MERET splits C(tot) to reveal C(burn) by exploiting the fact that C(burn) and all tracers respond linearly to dilution, while each tracer has consistent EnR behavior (slope of tracer concentration with respect to C(burn)). The two effects are separable. Two or three or preferably more emission indicators are required as a minimum; here we used ten. Limited variations in the EnRs for each tracer can be incorporated and the variations and co-variations analyzed. The percentage CO yield (or the modified combustion efficiency) plays some role. Other co-relationships involving nitrogen and organic classes are more prominent; these have strong relationships to the C(burn) to O3 emission relationship. In summary, MERET allows fine spatial resolution (EnRs for individual observations) and comparison of similar plumes distant in time and space. Alkene ratios provide us with an approximate photochemical timescale. This allows discrimination and definition, by fire situation, of ERs, allowing us to estimate emission factors.

Chatfield, Robert B.↗
NASA NTRS1995

Design of High-Accuracy Multiple Flyby Trajectories Using Constrained Optimization

The trajectory optimization technique described in this paper provides several distinct advantages over previous formulations. First, fully numerically integrated trajectory modeling is used. That is, no approximations to the trajectory are made and the inclusion of any level of complicated force models desired is allowed. Second, only trajectory propagation is used so there is no requirement for optimization. This is accomplished by the novel method of splitting the trajectory into independent legs, which are then subjected to constrained optimization. Third, each of the trajectory legs may be specified by any convenient set of parameters particularly useful for that leg. Any of these parameters may then be subject to constraints. Fourth, the nonlinear optimization problem is solved by solving a sequence of linear problems which converges to the optimal nonlinear solution. Fifth, the robustness of this formulation requires little or no user interaction with the optimization once a feasible problem has been posed.

flyby↗
DOE OSTI2022

GANISP: A GAN-Assisted Importance Splitting Probability Estimator

Designing manufacturing processes with high yield and strong reliability relies on effective methods for rare event estimation. Genealogical importance splitting reduces the variance of rare event probability estimators by iteratively selecting and replicating realizations that are headed towards a rare event. The replication step is difficult when applied to deterministic systems where the initial conditions of the offspring realizations need to be modified. Typically, a random perturbation is applied to the offspring to differentiate their trajectory from the parent realization. However, this random perturbation strategy may be effective for some systems while failing for others, preventing variance reduction in the probability estimate. This work seeks to address this limitation using a generative model such as a Generative Adversarial Network (GAN) to generate perturbations that are consistent with the attractor of the dynamical system. The proposed GAN-assisted Importance SPlitting method (GANISP) improves the variance reduction for the system targeted. An implementation of the method is available in a companion repository (https://github.com/NREL/GANISP).

generative adversarial network↗
NASA NTRS1976

Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

Rizzi, Arthur W.↗
NASA NTRS1992

Development of new flux splitting schemes

Maximizing both accuracy and efficiency has been the primary objective in designing a numerical algorithm for computational fluid dynamics (CFD). This is especially important for solutions of complex three dimensional systems of Navier-Stokes equations which often include turbulence modeling and chemistry effects. Recently, upwind schemes have been well received for their capability in resolving discontinuities. With this in mind, presented are two new flux splitting techniques for upwind differencing. The first method is based on High-Order Polynomial Expansions (HOPE) of the mass flux vector. The second new flux splitting is based on the Advection Upwind Splitting Method (AUSM). The calculation of the hypersonic conical flow demonstrates the accuracy of the splitting in resolving the flow in the presence of strong gradients. A second series of tests involving the two dimensional inviscid flow over a NACA 0012 airfoil demonstrates the ability of the AUSM to resolve the shock discontinuity at transonic speed. A third case calculates a series of supersonic flows over a circular cylinder. Finally, the fourth case deals with tests of a two dimensional shock wave/boundary layer interaction.

Liou, Meng-Sing↗
NASA NTRS1985

Recent advances in computational transonic aerodynamics

The near-term prospects are discussed for calculation of viscous transonic flow fields about realistic configurations at full-scale Reynolds numbers. Three basic algorithms are considered: The central-difference, three-factor ADI method; the central-difference, explicit, multistep Runge-Kutta method with multigrid acceleration; and the relaxation method for the upwind-differenced, flux-split equations. Each method has distinct advantages and disadvantages regarding stability, convergence rate, and vectorizability. It appears that computation times can be 15 to 60 hours on the latest super computers unless 3D algorithms are improved to perform as well as current 2D algorithms.

South, J. C., Jr.↗
NASA NTRS1936

A method of estimating the aerodynamic effects of ordinary and split flaps of airfoils similar to the Clark Y

An empirical method is given for estimating the aerodynamic effect of ordinary and split flaps on airfoils similar to the Clark Y. The method is based on a series of charts that have been derived from an analysis of existing wind-tunnel data. Factors are included by which such variables as flap location, flap span, wing aspect ratio, and wing taper may be taken into account. A series of comparisons indicate that the method would be suitable for use in making preliminary performance calculations and in structural design.

Pearson, H A↗
NASA NTRS2011

Split-screen display system and standardized methods for ultrasound image acquisition and multi-frame data processing

A standardized acquisition methodology assists operators to accurately replicate high resolution B-mode ultrasound images obtained over several spaced-apart examinations utilizing a split-screen display in which the arterial ultrasound image from an earlier examination is displayed on one side of the screen while a real-time "live" ultrasound image from a current examination is displayed next to the earlier image on the opposite side of the screen. By viewing both images, whether simultaneously or alternately, while manually adjusting the ultrasound transducer, an operator is able to bring into view the real-time image that best matches a selected image from the earlier ultrasound examination. Utilizing this methodology, dynamic material properties of arterial structures, such as IMT and diameter, are measured in a standard region over successive image frames. Each frame of the sequence has its echo edge boundaries automatically determined by using the immediately prior frame's true echo edge coordinates as initial boundary conditions. Computerized echo edge recognition and tracking over multiple successive image frames enhances measurement of arterial diameter and IMT and allows for improved vascular dimension measurements, including vascular stiffness and IMT determinations.

Selzer, Robert H.↗
NASA NTRS1991

Automated cloud screening of AVHRR imagery using split-and-merge clustering

Previous methods to segment clouds from ocean in AVHRR imagery have shown varying degrees of success, with nighttime approaches being the most limited. An improved method of automatic image segmentation, the principal component transformation split-and-merge clustering (PCTSMC) algorithm, is presented and applied to cloud screening of both nighttime and daytime AVHRR data. The method combines spectral differencing, the principal component transformation, and split-and-merge clustering to sample objectively the natural classes in the data. This segmentation method is then augmented by supervised classification techniques to screen clouds from the imagery. Comparisons with other nighttime methods demonstrate its improved capability in this application. The sensitivity of the method to clustering parameters is presented; the results show that the method is insensitive to the split-and-merge thresholds.

Gallaudet, Timothy C.↗
DOE OSTI2021

A unified formulation of splitting-based implicit time integration schemes

Splitting-based time integration approaches such as fractional step, alternating direction implicit, operator splitting, and locally one dimensional methods partition the system of interest into components, and solve individual components implicitly in a cost-effective way. Here this work proposes a unified formulation of splitting time integration schemes in the framework of general-structure additive Runge–Kutta (GARK) methods. Specifically, we develop implicit-implicit (IMIM) GARK schemes, provide the order conditions for this class, and explain their application to partitioned systems of ordinary differential equations. We show that classical splitting methods belong to the IMIM GARK family, and therefore can be studied in this unified framework. New IMIM-GARK splitting methods are developed and tested using parabolic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗