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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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Nonlinear dynamics and numerical uncertainties in CFD

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.

Yee, H. C.↗
NASA NTRS1997

Dynamics of Numerics & Spurious Behaviors in CFD Computations

The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.

Yee, Helen C.↗
NASA NTRS1996

Some Aspects of Nonlinear Dynamics and CFD

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with examples of spurious behavior observed in CFD computations.

Yee, Helen C.↗
DOE OSTI2024

Stability of fractional Chern insulators with a non-Landau level continuum limit

The stability of fractional Chern insulators is widely believed to be predicted by the resemblance of their single-particle spectra to Landau levels. Here we investigate the scope of this geometric stability hypothesis by analyzing the stability of a set of fractional Chern insulators that explicitly do not have a Landau level continuum limit. By computing the many-body spectra of Laughlin states in a generalized Hofstadter model, we analyze the relationship between single-particle metrics, such as trace inequality saturation, and many-body metrics, such as the magnitude of the many-body and entanglement gaps. We show numerically that the geometric stability hypothesis holds for Chern bands that are not continuously connected to Landau levels, as well as conventional Chern bands, albeit often requiring larger system sizes to converge for these configurations.

2-dimensional systems↗
NASA NTRS1987

Stability and resonance in grooved-channel flows

Numerical simulation using the spectral element method is used to study the stability and resonant response of incompressible moderate-Reynolds-number flows in periodically-grooved channels. For Reynolds numbers below a critical value, the flow is shown to approach a stable steady-state, and the least stable modes resemble Tollmien-Schlichting channel waves. For Reynolds numbers greater than the critical value, self-sustained oscillations result. Oscillatory perturbation of the grooved-channel flow at the frequency of the least stable mode of the linearized system is found to result in subcritical resonant excitation as the critical Reynolds number is approached. The importance of nonhomogeneous geometry in the forced response of the flow is discussed.

Ghaddar, Nasreen K.↗
NASA NTRS1994

Dynamics and statics of nonaxisymmetric liquid bridges

We finished the construction of the experimental apparatus and the design and testing of some of the visualization and data acquisition techniques. Experimental work focused on three areas: force measurements, loss of stability to nonaxisymmetric bridges, and vibration behavior. The experimental work is summarized in section 2. Selected results from our force measurement experiments are outlined in section 3. In addition we worked on the theory of the dynamic stability of axisymmetric bridges and undertook numerical simulation of the effects of inclined gravity vectors on the minimum volume stability limit for static bridges. The results and status of our theoretical work and numerical simulation are described in section 4. Papers published and in preparation, conference presentations, etc., are described in section 5. Work planned for the third year is discussed in section 6. References cited in the report are listed in section 7.

Alexander, J. Iwan D.↗
NASA NTRS1992

On the numerical treatment of nonlinear source terms in reaction-convection equations

The objectives of this paper are to investigate how various numerical treatments of the nonlinear source term in a model reaction-convection equation can affect the stability of steady-state numerical solutions and to show under what conditions the conventional linearized analysis breaks down. The underlying goal is to provide part of the basic building blocks toward the ultimate goal of constructing suitable numerical schemes for hypersonic reacting flows, combustions and certain turbulence models in compressible Navier-Stokes computations. It can be shown that nonlinear analysis uncovers much of the nonlinear phenomena which linearized analysis is not capable of predicting in a model reaction-convection equation.

Lafon, A.↗
NASA NTRS2007

Initial Ares I Bending Filter Design

The Ares-I launch vehicle represents a challenging flex-body structural environment for control system design. Software filtering of the inertial sensor output will be required to ensure control system stability and adequate performance. This paper presents a design methodology employing numerical optimization to develop the Ares-I bending filters. The filter design methodology was based on a numerical constrained optimization approach to maximize stability margins while meeting performance requirements. The resulting bending filter designs achieved stability by adding lag to the first structural frequency and hence phase stabilizing the first Ares-I flex mode. To minimize rigid body performance impacts, a priority was placed via constraints in the optimization algorithm to minimize bandwidth decrease with the addition of the bending filters. The bending filters provided here have been demonstrated to provide a stable first stage control system in both the frequency domain and the MSFC MAVERIC time domain simulation.

Jang, Jiann-Woei↗
NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗
NASA NTRS1994

The stability of two-phase flow over a swept-wing

We use numerical and asymptotic techniques to study the stability of a two-phase air/water flow above a flat porous plate. This flow is a model of the boundary layer which forms on a yawed cylinder and can be used as a useful approximation to the air flow over swept wings during heavy rainfall. We show that the interface between the water and air layers can significantly destabilize the flow, leading to traveling wave disturbances which move along the attachment line. This instability occurs for lower Reynolds numbers than in the case of the absence of a water layer. We also investigate the instability of inviscid stationary modes. We calculate the effective wavenumber and orientation of the stationary disturbance when the fluids have identical physical properties. Using perturbation methods we obtain corrections due to a small stratification in viscosity, thus quantifying the interfacial effects. Our analytical results are in agreement with the numerical solution which we obtain for arbitrary fluid properties.

Coward, Adrian↗
NASA NTRS1986

Polynomial elimination theory and non-linear stability analysis for the Euler equations

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Kennon, S. R.↗
NASA NTRS2006

Stability of the Wave Bearing on an Elastic Support

Numerical computation predicts that an elastic support can substantially improve the stability of the wave bearing if the dynamic stiffness and damping of this support are in a specific range of values. To experimentally validate this prediction, the housing of a gas bearing was mounted on elastic O-rings and the threshold of sub-synchronous whirl motion was experimentally observed when the bearing runs unloaded with a rotating speed up to 30,000 RPM. The O-ring system was also dynamically characterized by measuring its stiffness and damping at various frequencies up to 500 Hz. Good correlation exists between the experimental data and numerical prediction.

Dimofte, Florin↗
DOE OSTI2025

A randomized sketching trust-region secant method for low-memory dynamic optimization

The numerical solution of dynamic optimization problems is often limited by the memory required to store the state trajectory, which is used to evaluate the objective function and its derivatives. Recently, [R. Muthukumar et al., SIAM Journal on Optimization 31(2), pp. 1242–1275 (2021)] introduced a trust-region method for dynamic optimization that employs randomized sketching to compress the state trajectory, resulting in inexact derivative computations. By adaptively learning the sketch rank, the trust-region algorithm achieves rigorous convergence guarantees. Here, we extend this approach to use secant Hessian approximations. Due to the randomness introduced by the sketch, the traditional secant update formulae can produce poor Hessian approximations. In particular, the difference of two gradients, computed from two different sketches, may be inconsistent. To overcome this, we employ a sketched approximation of the Hessian application, in lieu of computing the gradient difference. We numerically demonstrate the improved stability of this approach on an example from PDE-constrained optimization.

dynamic optimization↗
DOE OSTI2024

Properties of Nb x Ti (1–x) N thin films deposited on 300 mm silicon wafers for upscaling superconducting digital circuits

Scaling superconducting digital circuits requires fundamental changes in the current material set and fabrication process. The transition to 300 mm wafers and the implementation of advanced lithography are instrumental in facilitating mature CMOS processes, ensuring uniformity, and optimizing the yield. Here, this study explores the properties of Nb x Ti (1–x) N films fabricated by magnetron DC sputtering on 300 mm Si wafers. As a promising alternative to traditional Nb in device manufacturing, Nb x Ti (1–x) N offers numerous advantages, including enhanced stability and scalability to smaller dimensions, in both processing and design. As a ternary material, Nb x Ti (1–x) N allows engineering material parameters by changing deposition conditions. The engineered properties can be used to modulate device parameters through the stack and mitigate failure modes. We report characterization of Nb x Ti (1–x) N films at less than 2% thickness variability, 2.4% T c variability and 3% composition variability. Film resistivity (140–375 Ωcm) shows a strong correlation with the film oxygen content, while the critical temperature T c (4.6 K–14.1 K) is strongly affected by film stoichiometry and its microstructure has only a moderate effect on modifying T c . Our results offer insights about the interplay between film stoichiometry, film microstructure and critical temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1962

GENERAL INSTABILITY OF ORTHOGONALLY STIFFENED CYLINDRICAL SHELLS

Earlier research at the National Aeronautics Research Institute (N.L.R.), Amsterdam, which forms the basis of recent work is reviewed. This early work refers to 2 schemes: the orthotropic shell and, in view of buckling modes where the half wave length is of the order of the ring distance, the shell with continuously distributed stringers and discrete rings. Linear theory is considered to be adequate for these structures, where the imperfections are small in comparison to the height of the ring sections. Recent developments account for pressure difference in addition to axial compression, for the correct stiffness matrix of skin panels in the post-buckling stage and for stringer bending due to hoop stresses in the skin, which are of importance as has been shown by the investigation of the post-buckling behaviour. Numerical data for the stiffness matrix of skin panels have been established. Numerical evaluation of the stability equation has not been performed as yet.

SHELL STABILITY↗
NASA NTRS1973

Numerical studies of unsteady two dimensional subsonic flows using the ICE method

A numerical program was developed to compute transient compressible and incompressible laminar flows in two dimensions with multicomponent mixing and chemical reaction. The algorithm used the Los Alamos Scientific Laboratory ICE (Implicit Continuous-Fluid Eulerian) method as its base. The program can compute both high and low speed compressible flows. The numerical program incorporating the stabilization techniques was quite successful in treating both old and new problems. Detailed calculations of coaxial flow very close to the entry plane were possible. The program treated complex flows such as the formation and downstream growth of a recirculation cell. An implicit solution of the species equation predicted mixing and reaction rates which compared favorably with the literature.

Wieber, P. R.↗
NASA NTRS1975

Upwind second-order difference schemes and applications in unsteady aerodynamic flows

Explicit second-order upwind difference schemes in combination with spatially symmetric schemes can produce larger stability bounds and better numerical resolution than symmetric schemes alone. However, if conservation form is essential, a special operator is required for transition between schemes. An operational approach has been devised for deriving transition operators so that strict conservation and local consistency are maintained. Various aspects of hybrid schemes are studied numerically for model linear and nonlinear equations. To demonstrate the utility of combining two different algorithms, MacCormack's explicit, noncentered, second-order method is combined with a completely upwind version, and numerical solutions of the Euler equations are obtained for two-dimensional, transonic flows with embedded supersonic regions and shock waves. The general utility of the operational approach for combining schemes is emphasized by deriving a second-order conservative scheme for the steady transonic small-disturbance potential equation.

Warming, R. F.↗