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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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Linear Solvers for Collector Systems of Generalized Large-scale Inverter-Based Resources

Collector systems for inverter-based resources (IBRs) are typically represented by equivalent circuits for electromagnetic transient (EMT) simulations. Recent studies have revealed that modeling a detailed collector system is essential to accurately represent the behavior of IBRs, especially when dealing with partial tripping during external disturbances. However, there are several challenges in simulating a detailed EMT model of a collector system due to the time required to simulate such systems. Thus, this paper investigates the modeling of a detailed collector system, taking into account its configuration and components as defined in IEEE standard 2800. The configurations include the collector systems of generalized large-scale IBR plants. The components include the main IBR transformer, collector bus, and feeders with lines and/or cables. The EMT model of the collector system is represented by differential algebraic equations (DAEs) that are discretized to form linear equations that are solved using linear solvers. In this paper, linear solvers are proposed based on the Schur complement method, which are utilized for simulation of the EMT model of collector systems of generalized large-scale IBRs to accelerate simulation speed while maintaining the accuracy of the results. The proposed solvers are verified by comparing the performance to that of linear solvers provided in MATLAB.

Choi, Jongchan↗
DOE OSTI2026

Optimal Transfer Operators in Algebraic Two-Level Methods for Nonsymmetric and Indefinite Problems

Consider an algebraic two-level method applied to the 𝑛-dimensional linear system 𝐴⁢𝒙 = 𝒃 using fine-space preconditioner (i.e., “relaxation” or “smoother”) 𝑀, with 𝑀 ≈ 𝐴, restriction and interpolation 𝑅 and 𝑃, and algebraic coarse-space operator 𝐴 𝑐 : = 𝑅 ∗ ⁢𝐴⁢𝑃. Then, what are the best possible transfer operators 𝑅 and 𝑃 of a given dimension 𝑛 𝑐 < 𝑛? Brannick et al. [12] showed that when 𝐴 and 𝑀 are Hermitian positive definite (HPD), the optimal interpolation is such that its range contains the 𝑛 𝑐 smallest generalized eigenvectors of the matrix pencil (𝐴, 𝑀). Recently, in Ali et al. [5] we generalized this framework to the non-HPD setting, by considering both right (interpolation) and left (restriction) generalized eigenvectors of (𝐴, 𝑀) and defining corresponding nonsymmetric transfer operators {𝑅#, 𝑃#}. Tight convergence bounds for {𝑅#, 𝑃#} are derived in spectral radius, as well as a proof of pseudo-optimality. Note, {𝑅#, 𝑃#} are typically complex valued, which is not practical for real-valued problems. Here, in this work, we build on [5], first characterizing all inner products in which the coarse-space correction defined by {𝑅#, 𝑃#} is orthogonal. We then develop tight two-level convergence bounds in these norms, and prove that the underlying transfer operators {𝑅#, 𝑃#} are genuinely optimal. As a special case, our theory both recovers and extends the HPD results from [12]. Finally, we show how to construct optimal, real-valued transfer operators in the case of that 𝐴 and 𝑀 are real valued, but are not HPD. Numerical examples arising from a discretized advection-reaction equation, wave-equation, and Stokes equations are used to verify and illustrate the theory.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Time domain convergence properties of Lyapunov stable penalty methods

Linear hyperbolic partial differential equations are analyzed using standard techniques to show that a sequence of solutions generated by the Liapunov stable penalty equations approaches the solution of the differential-algebraic equations governing the dynamics of multibody problems arising in linear vibrations. The analysis does not require that the system be conservative and does not impose any specific integration scheme. Variational statements are derived which bound the error in approximation by the norm of the constraint violation obtained in the approximate solutions.

Kurdila, A. J.↗
NASA NTRS1976

The method of Ritz applied to the equation of Hamilton

Without any reference to the theory of differential equations, the initial value problem of the nonlinear, nonconservative double pendulum system is solved by the application of the method of Ritz to the equation of Hamilton. Also shown is an example of the reduction of the traditional eigenvalue problem of linear, homogeneous, differential equations of motion to the solution of a set of nonhomogeneous algebraic equations. No theory of differential equations is used. Solution of the time-space path of the linear oscillator is demonstrated and compared to the exact solution.

Bailey, C. D.↗
NASA NTRS1993

Linearization of manipulator dynamics using spatial operators

Linearized dynamics models for manipulators are useful in robot analysis, motion planning, and control applications. Techniques from the spatial operator algebra are used to obtain closed form operator expressions for two types of linearized dynamics models, the linearized inverse and forward dynamics models. Spatially recursive algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and coefficient matrices for the linearized inverse dynamics model are developed first. Subsequently, operator factorization and inversion identities are used to develop corresponding closed-form expressions for the linearized forward dynamics model (LFDM). Once again, these are used to develop algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and the coefficient matrices. The algorithms for the LFDM do not require the explicit computation of the mass matrix nor its numerical inversion and are also of lower complexity than the conventional O(n-cubed) algorithms.

Jain, A.↗
NASA NTRS1972

Finite group homomorphic sequential systems.

A class of finite-state sequential systems evolving in groups is considered. It represents a broader class of input-output relations than those found in linear system theory. The concepts of controllability, observability, minimality, realizability, and the isomorphism of minimal realizations are developed. Results that are analogous to, but differ in essential details from, those of linear system theory are derived. Algorithmic design and algebraic decoding may benefit from these results.

Brockett, R. W.↗
NASA NTRS1972

Equations of motion in the linear approximation.

Attempt to develop a gauge-invariant theory of the motion of singularities in an n-dimensional Riemannian space. A gauge-invariant theory is developed for a nongeodetic particle represented by a time-like world line in the linearized field theory. The solution of the basic algebraic and differential equations is to be constructed from the source line, the future null cones emanating from it, a scale factor, and nothing else, and the leading term of the solution is the Schwarzschild field. A class of possible solutions is examined, and it is shown that this class contains just one acceptable member - namely, a particle in constant acceleration.

Robinson, I.↗
NASA NTRS1987

Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting

This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.

Badavi, F. F.↗
NASA NTRS2000

Turbulence Model Predictions of Strongly Curved Flow in a U-Duct

The ability of three types of turbulence models to accurately predict the effects of curvature on the flow in a U-duct is studied. An explicit algebraic stress model performs slightly better than one- or two-equation linear eddy viscosity models, although it is necessary to fully account for the variation of the production-to-dissipation-rate ratio in the algebraic stress model formulation. In their original formulations, none of these turbulence models fully captures the suppressed turbulence near the convex wall, whereas a full Reynolds stress model does. Some of the underlying assumptions used in the development of algebraic stress models are investigated and compared with the computed flowfield from the full Reynolds stress model. Through this analysis, the assumption of Reynolds stress anisotropy equilibrium used in the algebraic stress model formulation is found to be incorrect in regions of strong curvature. By the accounting for the local variation of the principal axes of the strain rate tensor, the explicit algebraic stress model correctly predicts the suppressed turbulence in the outer part of the boundary layer near the convex wall.

Rumsey, Christopher L.↗
NASA NTRS2002

A Lightning Channel Retrieval Algorithm for the North Alabama Lightning Mapping Array (LMA)

A new multi-station VHF time-of-arrival (TOA) antenna network is, at the time of this writing, coming on-line in Northern Alabama. The network, called the Lightning Mapping Array (LMA), employs GPS timing and detects VHF radiation from discrete segments (effectively point emitters) that comprise the channel of lightning strokes within cloud and ground flashes. The network will support on-going ground validation activities of the low Earth orbiting Lightning Imaging Sensor (LIS) satellite developed at NASA Marshall Space Flight Center (MSFC) in Huntsville, Alabama. It will also provide for many interesting and detailed studies of the distribution and evolution of thunderstorms and lightning in the Tennessee Valley, and will offer many interesting comparisons with other meteorological/geophysical wets associated with lightning and thunderstorms. In order to take full advantage of these benefits, it is essential that the LMA channel mapping accuracy (in both space and time) be fully characterized and optimized. In this study, a new revised channel mapping retrieval algorithm is introduced. The algorithm is an extension of earlier work provided in Koshak and Solakiewicz (1996) in the analysis of the NASA Kennedy Space Center (KSC) Lightning Detection and Ranging (LDAR) system. As in the 1996 study, direct algebraic solutions are obtained by inverting a simple linear system of equations, thereby making computer searches through a multi-dimensional parameter domain of a Chi-Squared function unnecessary. However, the new algorithm is developed completely in spherical Earth-centered coordinates (longitude, latitude, altitude), rather than in the (x, y, z) cartesian coordinates employed in the 1996 study. Hence, no mathematical transformations from (x, y, z) into spherical coordinates are required (such transformations involve more numerical error propagation, more computer program coding, and slightly more CPU computing time). The new algorithm also has a more realistic definition of source altitude that accounts for Earth oblateness (this can become important for sources that are hundreds of kilometers away from the network). In addition, the new algorithm is being applied to analyze computer simulated LMA datasets in order to obtain detailed location/time retrieval error maps for sources in and around the LMA network. These maps will provide a more comprehensive analysis of retrieval errors for LMA than the 1996 study did of LDAR retrieval errors. Finally, we note that the new algorithm can be applied to LDAR, and essentially any other multi-station TWA network that depends on direct line-of-site antenna excitation.

Koshak, William↗
NASA NTRS2003

Analysis of Extensive Cross-Flow Separation using Higher-Order RANS Closure Models

The turbulent flow fields associated with the incompressible flow over a 6:1 prolate spheroid at high angle of attack, and the supersonic flow over an ogive cylinder are studied. Both these flows are characterized by large separation and vortical flow regions and therefore provide a challenging database for comparison of turbulent closure models. Of interest is the ability to predict the effects of separation and associated vortical motion common to both flows. Two turbulent models are investigated that each represent the class of linear eddy-viscosity models (LEVMs) and explicit algebraic stress models (EASMs). Since the EASM accounts for anisotropic effects, the in- fluence of these effects on flow field predictions can be assessed. The EASM model is shown to both improve the separation location prediction and pressure trough under the secondary vortex on the 6:1 prolate spheroid at high angle of attack and high Reynolds number, and improve the prediction of the separation location on a supersonic ogive cylinder.

Morison, J. H.↗
NASA NTRS2003

Analysis of Extensive Cross-Flow Separation using Higher-Order RANS Closure Models

The turbulent flow fields associated with the incompressible flow over a 6:1 prolate spheroid at high angle of attack, and the supersonic flow over an ogive cylinder are studied. Both these flows are characterized by large separation and vortical flow regions and therefore provide a challenging database for comparison of turbulent closure models. Of interest is the ability to predict the effects of separation and associated vortical motion common to both flows. Two turbulent models are investigated that each represent the class of linear eddy-viscosity models (LEVMs) and explicit algebraic stress models (EASMs). Since the EASM accounts for anisotropic effects, the influence of these effects on flow field predictions can be assessed. The EASM model is shown to both improve the separation location prediction and pressure trough under the secondary vortex on the 6:l prolate spheroid at high angle of attack and high Reynolds number, and improve the prediction of the separation location on a supersonic ogive cylinder.

Morrison, J. H.↗
NASA NTRS1985

Bounding solutions of geometrically nonlinear viscoelastic problems

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Stubstad, J. M.↗
NASA NTRS1986

Bounding solutions of geometrically nonlinear viscoelastic problems

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Stubstad, J. M.↗
NASA NTRS1984

Finite-analytic numerical method for unsteady two-dimensional Navier-Stokes equations

A finite analytic (FA) numerical solution is developed for unsteady two-dimensional Navier-Stokes equations. The FA method utilizes the analytic solution in a small local element to formulate the algebraic representation of partial differential equations. The combination of linear and exponential functions that satisfy the governing equation is adopted as the boundary function, thereby improving the accuracy of the finite analytic solution. Two flows, one a starting cavity flow and the other a vortex shedding flow behind a rectangular block, are solved by the FA method. The starting square cavity flow is solved for Reynolds number of 400, 1000, and 2000 to show the accuracy and stability of the FA solution. The FA solution for flow over a rectangular block (H x H/4) predicts the Strouhal number for Reynolds numbers of 100 and 500 to be 0.156 and 0.125. Details of the flow patterns are given. In addition to streamlines and vorticity distribution, rest-streamlines are given to illustrate the vortex motion downstream of the block.

Chen, C.-J.↗
NASA NTRS1990

Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations

The compressible Navier-Stokes equations are solved for a variety of two-dimensional inviscid and viscous problems by preconditioned conjugate gradient-like algorithms. Roe's flux difference splitting technique is used to discretize the inviscid fluxes. The viscous terms are discretized by using central differences. An algebraic turbulence model is also incorporated. The system of linear equations which arises out of the linearization of a fully implicit scheme is solved iteratively by the well known methods of GMRES (Generalized Minimum Residual technique) and Chebyschev iteration. Incomplete LU factorization and block diagonal factorization are used as preconditioners. The resulting algorithm is competitive with the best current schemes, but has wide applications in parallel computing and unstructured mesh computations.

Venkatakrishnan, V.↗