Search NASA⌕ Search

SEARCH · Search NASA

Results for “Taylor approximation”

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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A weighted Shifted Boundary Method for free surface flow problems

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods and was recently introduced for the Poisson, linear advection/diffusion, Stokes, Navier-Stokes, acoustics, and shallow-water equations. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we extend the SBM to the simulation of incompressible Navier-Stokes flows with moving free-surfaces, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach prevents spurious pressure oscillations in time, which would otherwise be produced if the total active fluid volume were to change abruptly over a time step. In fact, the proposed weighted SBM method induces small mass (i.e., volume) conservation errors, which converge quadratically in the case of piecewise-linear finite element interpolations, as the grid is refined. Finally, we present an extensive set of two- and three-dimensional tests to demonstrate the robustness and accuracy of the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1997

Application of AWE Along with a Combined FEM/MoM Technique to Compute RCS of a Cavity-Backed Aperture in an Infinite Ground Plane Over a Frequency Range

A hybrid Finite Element Method (FEM)/Method of Moments (MoM) technique in conjunction with the Asymptotic Waveform Evaluation (AWE) technique is applied to obtain radar cross section (RCS) of a cavity-backed aperture in an infinite ground plane over a frequency range. The hybrid FEM/MoM technique when applied to the cavity-backed aperture results in an integro-differential equation with electric field as the unknown variable, the electric field obtained from the solution of the integro-differential equation is expanded in Taylor series. The coefficients of the Taylor series are obtained using the frequency derivatives of the integro-differential equation formed by the hybrid FEM/MoM technique. The series is then matched via the Pade approximation to a rational polynomial, which can be used to extrapolate the electric field over a frequency range. The RCS of the cavity-backed aperture is calculated using the electric field at different frequencies. Numerical results for a rectangular cavity, a circular cavity, and a material filled cavity are presented over a frequency range. Good agreement between AWE and the exact solution over the frequency range is obtained.

Reddy, C.J.↗
DOE OSTI2024

Towards natural and realistic E 7 GUTs in F-theory

We consider phenomenological aspects of a natural class of Standard Model-like supersymmetric F-theory vacua realized through flux breaking of rigid E 7 gauge factors. Three generations of Standard Model matter are realized in many of these vacua. We further find that many other Standard Model-like features are naturally compatible with these constructions. For example, dimension-4 and 5 terms associated with proton decay are ubiquitously suppressed. Many of these features are due to the group theoretical structure of E 7 and associated F-theory geometry. In particular, a set of approximate global symmetries descends from the E 7 group, leading to exponential suppression of undesired couplings.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1988

Nonlinearities in spacecraft structural dynamics

In considering nonlinearities in spacecraft structural dynamics, the following are examined: (1) SCOLE Configuration-Equations of Motion; (2) Modeling Error Sources; (3) Approximate Solutions; (4) Comparison of Model Accuracy; (5) Linear and Nonlinear Damping; (6) Experimental Results; and, (7) Future Work.

Taylor, Larry↗
DOE OSTI2020

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗
DOE OSTI2019

A Framework for Distributed Approximation of Moments with Higher-Order Derivatives through Automatic Differentiation

We present a framework for the distributed approximation of moments, enabling the evaluation of the uncertainty in a dynamical system. The first and second moment, mean, and variance are computed with up to third-order Taylor series expansion. The required derivatives for the expansion are generated automatically by automatic differentiation and propagated through an implicit time stepper. The computational kernels are the accumulation of the derivatives (Jacobian, Hessian, tensor) and the covariance matrix. We apply distributed parallelism to the Hessian or third-order tensor, and the user merely has to provide a function for the differential equation, thus achieving similar ease of use as Monte Carlo-based methods. We demonstrate our approach using with benchmarks on Theta, a KNL-based system at the Argonne Leadership Computing Facility.

Automatic Differentiation↗
NASA NTRS1992

Structure of a swirling turbulent mixing layer

A single-stream swirling turbulent mixing layer was produced in which the angular momentum instability acts over most of the layer for most of its development length. The instability is associated with a large increase in the level of the conventional Reynolds stresses over those in an unswirled mixing layer. This paper presents measurements of the three-dimensionality of the mean flow at one axial location well downstream of the origin. The output of a fixed hot-wire probe was ensemble-averaged to produce an approximation to the mean flow field that would be seen by a rotating observer. The main goals of this study were to establish the presence or absence of Taylor-Goertler vortices found in unstable laminar boundary layers. The variations in the mean velocities and Reynolds stresses are generally consistent with a bodily 'wrinkling' of the mixing layer, without a significant variation in the layer thickness. The wrinkling is most probably a result of circumferential variations in the initial boundary layer, which in turn originate at the swirl generator.

Wood, D. H.↗
DOE OSTI2024

A weighted shifted boundary method for immersed moving boundary simulations of Stokes' flow

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. The surrogate domain is constructed so as to avoid cut cells and the associated problematic implementation and numerical integration issues. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions: hence the name of the method, that shifts the location and values of the boundary conditions. Here, in this article, we extend the SBM to the simulation of incompressible Stokes flow, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach allows to drastically reduce spurious pressure oscillations in time, which are produced if the total volume of active fluid were to change abruptly over a time step. The proposed Weighted SBM (W-SBM) exactly preserves states of hydrostatic equilibrium, and induces small mass and momentum conservation errors, which converge as the grid is refined. This is in analogy to cutFEMs and related unfitted approaches, which rely on an affine representation of cut boundaries. We demonstrate the robustness and accuracy of the proposed method with an extensive suite of two-dimensional tests.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

NONLINEAR EVOLUTION OF RAYLEIGH-TAYLOR INSTABILITY IN A RADIATION-SUPPORTED ATMOSPHERE

The nonlinear regime of Rayleigh-Taylor instability (RTI) in a radiation supported atmosphere, consisting of two uniform fluids with different densities, is studied numerically. We perform simulations using our recently developed numerical algorithm for multi-dimensional radiation hydrodynamics based on a variable Eddington tensor (VET) as implemented in Athena, focusing on the regime where scattering opacity greatly exceeds absorption opacity. We find that the radiation field can reduce the growth and mixing rate of RTI, but this reduction is only significant when radiation pressure significantly exceeds gas pressure. Small-scale structures are also suppressed in this case. In the nonlinear regime, dense fingers sink faster than rarefied bubbles can rise, leading to asymmetric structures about the interface. By comparing the calculations that use a VET versus the Eddington approximation, we demonstrate that anisotropy in the radiation field can affect the nonlinear development of RTI significantly. We also examine the disruption of a shell of cold gas being accelerated by strong radiation pressure, motivated by models of radiation driven outflows in ultraluminous infrared galaxies. We find that when the growth timescale of RTI is smaller than acceleration timescale, the amount of gas that would be pushed away by the radiation field is reduced due to RTI.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution

This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally managed to satisfy water demand while improving power grid operations; {for the power network, an AC optimal power flow formulation is augmented to accommodate the controllability of water pumps.} Unfortunately, the physics governing the operation of the two infrastructures and coupling constraints lead to a nonconvex (and, in fact, NP-hard) problem; however, after reformulating OWPF as a nonconvex, quadratically-constrained quadratic problem, a feasible point pursuit-successive convex approximation approach is used to identify feasible and optimal solutions. In addition, a distributed solver based on the alternating direction method of multipliers enables water and power operators to pursue individual objectives while respecting the couplings between the two networks. The merits of the proposed approach are demonstrated for the case of a distribution feeder coupled with a municipal water distribution network.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2015

Self-focusing of Hermite-Gaussian laser beam with relativistic nonlinearity

This paper presents an investigation of self-focusing of Hermite-Gaussian laser beams in plasma considering relativistic nonlinearity. The differential equations for beam width parameters are obtained using the usual Wentzel–Kramers–Brillouin and paraxial approximations. The nonlinearity in the dielectric constant is assumed to be aroused mainly due to the relativistic mass correction of electron. To highlight the nature of focusing, graphical results of the behavior of beam-width parameters with the dimensionless distance of propagation is presented. The numerical computation is completed by using Taylor series method. The present work is helpful to understand issues related to the beam propagation in laser plasma interaction experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

DOE Workshop at Tapia Conference

The DE-SC0013568 DOE Grant, in the amount of $11,822.79, was used to support five doctoral students from underrepresented groups to attend the 2015 Richard Tapia Celebration of Diversity in Computing Conference, held February 18-21 in Boston, MA. Each scholarship was approximately $1200 to cover conference registration, travel, and lodging for the duration of the conference. The remaining $5,822.79 was used to support a DOE Breakfast Workshop during breakfast on Thursday, February 19. The Breakfast supported approximately 140 graduate students from underrepresented groups to learn about the different career opportunities at the different DOE National Laboratories.

99 GENERAL AND MISCELLANEOUS↗
NASA NTRS1975

Analysis of liquid rocket combustion chamber turbulence levels from diffusion data

The intensity of turbulence and the Lagrangian correlation coefficient in a liquid-rocket combustion chamber have been analytically determined from an analysis of experimental diffusion data obtained in a small rocket engine which operated at 300-psia chamber pressure and produced approximately 250 pounds thrust. Results of gas-sample measurements obtained by Orsat and gas-chromatograph techniques to determine helium-concentration profiles were analyzed on the basis of Taylor's (1921) turbulent diffusion theory to obtain turbulence flow-field parameters. The results of the analysis indicate that turbulent diffusion in a combustion chamber can be adequately modeled by the one-dimensional Taylor theory, which assumes that the intensity of turbulence is a function only of axial distance in the chamber and that the Lagrangian correlation coefficient is expressed by a power law. The results indicate a higher intensity of turbulence and lower correlation than previously expected.

Smith, L. O., Jr.↗
NASA NTRS2002

Decoupling the Role of Particle Inertia and Gravity on Particle Dispersion

Particle dispersion and the influence that particle momentum exchange has on the properties of a turbulent carrier flow in micro-gravity environments challenge present understanding and predictive schemes. The objective of this effort has been to develop and assess high-fidelity simulation tools for predicting particle transport within micro-gravity environments suspended in turbulent flows. The computational technique is based on Direct Numerical Simulation (DNS) of the incompressible Navier-Stokes equations. The particular focus of the present work is on the class of dilute flows in which particle volume fractions and inter-particle collisions are negligible. Particle motion is assumed to be governed by drag with particle relaxation times ranging from the Kolmogorov scale to the Eulerian timescale of the turbulence and particle mass loadings up to one. The velocity field was made statistically stationary by forcing the low wavenumbers of the flow. The calculations were performed using 96(exp 3) collocation points and the Taylor-scale Reynolds number for the stationary flow was 62. The effect of particles on the turbulence was included in the Navier-Stokes equations using the point-force approximation in which 96(exp 3) particles were used in the calculations. DNS results show that particles increasingly dissipate fluid kinetic energy with increased loading, with the reduction in kinetic energy being relatively independent of the particle relaxation time. Viscous dissipation in the fluid decreases with increased loading and is larger for particles with smaller relaxation times. Fluid energy spectra show that there is a non-uniform distortion of the turbulence with a relative increase in small-scale energy. The non-uniform distortion significantly affects the transport of the dissipation rate, with the production and destruction of dissipation exhibiting completely different behaviors. The spectrum of the fluid-particle energy exchange rate shows that the fluid drags particles at low wavenumbers while the converse is true at high wavenumbers for small particles. A spectral analysis shows that the increase of the high wavenumber portion of the fluid energy spectrum can be attributed to transfer of the fluid-particle covariance by the fluid turbulence. This in turn explains the relative increase of small-scale energy caused by small particles observed in the present simulations as well as those of others.

Squires, Kyle D.↗
NASA NTRS2006

A Method for Calculating Viscosity and Thermal Conductivity of a Helium-Xenon Gas Mixture

A method for calculating viscosity and thermal conductivity of a helium-xenon (He-Xe) gas mixture was employed, and results were compared to AiResearch (part of Honeywell) analytical data. The method of choice was that presented by Hirschfelder with Singh's third-order correction factor applied to thermal conductivity. Values for viscosity and thermal conductivity were calculated over a temperature range of 400 to 1200 K for He-Xe gas mixture molecular weights of 20.183, 39.94, and 83.8 kg/kmol. First-order values for both transport properties were in good agreement with AiResearch analytical data. Third-order-corrected thermal conductivity values were all greater than AiResearch data, but were considered to be a better approximation of thermal conductivity because higher-order effects of mass and temperature were taken into consideration. Viscosity, conductivity, and Prandtl number were then compared to experimental data presented by Taylor.

Johnson, Paul K.↗
DOE OSTI2019

Arbitrary-order time-accurate semi-Lagrangian spectral approximations of the Vlasov–Poisson system

The Vlasov–Poisson system, modeling the evolution of non-collisional plasmas in the electrostatic limit, is approximated by a semi-Lagrangian technique. Spectral methods of periodic type are implemented through a collocation approach. Groups of particles are represented by the Fourier Lagrangian basis and evolve, for a single timestep, along a high-order accurate representation of the local characteristic lines. The time-advancing technique is based on truncated Taylor series that can be, in principle, of any order of accuracy. A variant is obtained by coupling the phase space discretization with high-order accurate Backward Differentiation Formulas (BDF). At each timestep, particle displacements are reinterpolated and expressed in the original basis to guarantee the order of accuracy in all the variables at relatively low costs. Thus, these techniques combine the excellent features of spectral approximations with high-order time integration. The resulting method has excellent conservation properties. Indeed, it can be proven that the total number of particles, proportional to the total mass and charge, is conserved up to the machine precision. Series of numerical experiments are performed in order to assess the real performance. In particular, comparisons with standard benchmarks are examined.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1971

Mathematical models of the open magnetosphere - Application to dayside auroras.

Two static mathematical models of the open or Dungey model of the magnetosphere are constructed. The process of construction is similar to that for early closed magnetosphere models, such as the Taylor-Hones model. The first model in fact is simply an addition of an interplanetary field in arbitrary direction to a Taylor-Hones image dipole model. In order to preserve the shape of the magnetosphere at high latitudes, and to partially exclude the exterior field, another model is constructed with the magnetopause approximated by a diamagnetic sphere. We find that there are some interplanetary field lines connected to the earth for all orientations of the interplanetary field other than strictly northward, and that the maximum number of connected field lines occurs with a due southward field. For an average spiral hose angle of the interplanetary field, the dayside neutral point occurs on the magnetopause at about 10 o'clock local time. Dayside auroras, convection patterns, and other phenomena may exhibit symmetry about this local time. For a positive (negative) interplanetary field sector, energetic, anisotropic particle fluxes should have direct access to the northern (southern) polar caps, as is supported by many recent observations.

Forbes, T. G.↗
NASA NTRS2000

The Dynamics of Miscible Interfaces: A Space Flight Experiment

Experiments as well as accompanying simulations are described that serve in preparation of a space flight experiment to study the dynamics of miscible interfaces. The investigation specifically addresses the importance of both nonsolenoidal effects as well as nonconventional Korteweg stresses in flows that give rise to steep but finite concentration gradients. The investigation focuses on the flow in which a less viscous fluid displaces one of higher viscosity and different density within a narrow capillary tube. The fluids are miscible in all proportions. An intruding finger forms that occupies a fraction of the total tube diameter. Depending on the flow conditions, as expressed by the Peclet number, a dimensionless viscosity ratio, and a gravity parameter, this fraction can vary between approximately 0.9 and 0.2. For large Pe values, a quasi-steady finger forms, which persists for a time of O(Pe) before it starts to decay, and Poiseuille flow and Taylor dispersion are approached asymptotically. Depending on the specific flow conditions, we observe a variety of topologically different streamline patterns, among them some that leak fluid from the finger tip. For small Pe values, the flow decays from the start and asymptotically reaches Taylor dispersion after a time of O(Pe). Comparisons between experiments and numerical simulations based on the 'conventional' assumption of solenoidal velocity fields and without Korteweg stresses yield poor agreement as far as the Pe value is concerned that distinguishes these two regimes. As one possibility, we attribute this lack of agreement to the disregard of these terms. An attempt is made to use scaling arguments in order to evaluate the importance of the Korteweg stresses and of the assumption of solenoidality. While these effects should be strongest in absolute terms when steep concentration fronts exist, i.e., at large Pe, they may be relatively most important at lower values of Pe. We subsequently compare these conventional simulations to more complete simulations that account for nonvanishing divergence as well as Korteweg stresses. While the exact value of the relevant stress coefficients are not known, ballpark numbers do exist, and their use in the simulations indicates that these stresses may indeed be important. We plan to evaluate these issues in detail by means of comparing a space experiment with corresponding simulations, in order to extract more accurate Korteweg stress coefficients, and to confirm or deny the importance of such stresses.

Maxworthy, Tony↗