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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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

A Fast and Accurate Method of Radiation Hydrodynamics Calculation in Spherical Symmetry

We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation, and it is accurate for optically thin, thick, and intermediate systems. In the limit of a homogeneously distributed extinction coefficient, our method is very accurate and exceptionally fast. We combine this fast method with a slower but more generally applicable method to describe realistic problems. We perform various test calculations, including a simplified protostellar collapse simulation. We also discuss possible future improvements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Precision photon spectra for wino annihilation

We provide precise predictions for the hard photon spectrum resulting from neutral SU(2)W triplet (wino) dark matter annihilation. Our calculation is performed utilizing an effective field theory expansion around the endpoint region where the photon energy is near the wino mass. This has direct relevance to line searches at indirect detection experiments. We compute the spectrum at next-to-leading logarithmic (NLL) accuracy within the framework established by a factorization formula derived previously by our collaboration. This allows simultaneous resummation of large Sudakov logarithms (arising from a restricted final state) and Sommerfeld effects. Resummation at NLL accuracy shows good convergence of the perturbative series due to the smallness of the electroweak coupling constant — scale variation yields uncertainties on our NLL prediction at the level of 5%. We highlight a number of interesting field theory effects that appear at NLL associated with the presence of electroweak symmetry breaking, which should have more general applicability. We also study the importance of using the full spectrum as compared with a single endpoint bin approximation when computing experimental limits. Our calculation provides a state of the art prediction for the hard photon spectrum that can be easily generalized to other DM candidates, allowing for the robust interpretation of data collected by current and future indirect detection experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1986

Comparative accuracy of selected multiple scattering approximations

Doubling method computational results which have yielded plane albedo, total transmission and fractional absorption for plane-parallel atmospheres composed of cloud droplets are presently compared with data obtained with selected radiative transfer approximations. The relative and absolute accuracies of asymptotic theory for thick layers and delta-Eddington, Meador-Weaver (1980) and Coakley-Chylek (1975) approximations are compared as a function of optical thickness, solar zenith angle, and single scattering albedo. The delta-Eddington approximation is the most accurate for conservative scattering when the solar zenith angle is small, while Meador-Weaver is the most accurate for nonconservative scattering.

King, M. D.↗
DOE OSTI2018

The parameter choice rules for weighted Tikhonov regularization scheme

The well-known approach to solve the ill-posed problem is Tikhonov regularization scheme. But, the approximate solution of Tikhonov scheme may not contain all the details of the exact solution. To circumference this problem, weighted Tikhonov regularization has been introduced. In this article, we propose two a posteriori parameter choice rules to choose the regularization parameter for weighted Tikhonov regularization and establish the optimal rate of convergence O(δ{sup ((α+1)/(α+2))}) for the scheme based on these proposed rules. The numerical results are documented to demonstrate the significance of the theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Crank–Nicolson WSGI difference scheme with finite element method for multi-dimensional time-fractional wave problem

In this article, a second-order Crank–Nicolson weighted and shifted Grünwald integral (WSGI) time-discrete scheme combined with finite element method is studied for finding the numerical solution of the multi-dimensional time-fractional wave equation. The time-fractional wave equation with Caputo-fractional derivative is transformed into the time-fractional integral equation by integral technique, then the second-order Crank–Nicolson finite element scheme with a time second-order WSGI discrete approximation for fractional integral is formulated. The analysis of stability is made, then a priori error estimate is given by making use of the conversion technique between the WSGI formula and fractional integral. At the end of the article, some numerical examples covering two two-dimensional cases with rectangular element and triangular element and a three-dimensional case with tetrahedral element are shown to test and verify our theoretical results.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

A case study of view-factor rectification procedures for diffuse-gray radiation enclosure computations

The view factors which are used in diffuse-gray radiation enclosure calculations are often computed by approximate numerical integrations. These approximately calculated view factors will usually not satisfy the important physical constraints of reciprocity and closure. In this paper several view-factor rectification algorithms are reviewed and a rectification algorithm based on a least-squares numerical filtering scheme is proposed with both weighted and unweighted classes. A Monte-Carlo investigation is undertaken to study the propagation of view-factor and surface-area uncertainties into the heat transfer results of the diffuse-gray enclosure calculations. It is found that the weighted least-squares algorithm is vastly superior to the other rectification schemes for the reduction of the heat-flux sensitivities to view-factor uncertainties. In a sample problem, which has proven to be very sensitive to uncertainties in view factor, the heat transfer calculations with weighted least-squares rectified view factors are very good with an original view-factor matrix computed to only one-digit accuracy. All of the algorithms had roughly equivalent effects on the reduction in sensitivity to area uncertainty in this case study.

Taylor, Robert P.↗
DOE OSTI2018

Finite-Dimensional Approximations of the Steklov–Poincaré Operator for the Helmholtz Equation in Periodic Waveguides

We consider the Dirichlet and Neumann problems for the Laplace operator in periodic waveguides. Integro-differential connections between the solution and its normal derivative, interpreted as a finite-dimensional version of the Steklov–Poincaré operator, are imposed on the artificial face of the truncated waveguide. These connections are obtained from the orthogonality and normalization conditions for the Floquet waves which are oscillating incoming/outgoing, as well as exponentially decaying/growing in the periodic waveguide. Under certain conditions, we establish the unique solvability of the problem and obtain error estimates for the solution itself, as well as for scattering coefficients in the solution. We give examples of trapped waves in periodic waveguides.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Two-Sided Semi-Local Smoothing Splines

A semi-local smoothing spline of degree n and class C{sup p} is a function defined on an interval, having p continuous derivatives on that interval, and coinciding with a polynomial of degree n on the subintervals forming its partition. The domain of each polynomial is a subinterval on which m + 1 values of the approximated function are given, but in order to construct the polynomial, it is necessary to know M ≥ m + 1 values (m and M are determined by the class and the degree of the spline). The additional values can be borrowed from the adjacent subintervals. When constructing an S-spline in the periodic case, the problem of additional values is solved on the basis of periodicity, but in the nonperiodic case, one is expected to define the lacking values of a function beyond the domain. The present paper is aimed at nonperiodic two-sided S-splines whose construction does not require additional data.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

An extension of the Lighthill theory of jet noise to encompass refraction and shielding

A formalism for jet noise prediction is derived that includes the refractive 'cone of silence' and other effects; outside the cone it approximates the simple Lighthill format. A key step is deferral of the simplifying assumption of uniform density in the dominant 'source' term. The result is conversion to a convected wave equation retaining the basic Lighthill source term. The main effect is to amend the Lighthill solution to allow for refraction by mean flow gradients, achieved via a frequency-dependent directional factor. A general formula for power spectral density emitted from unit volume is developed as the Lighthill-based value multiplied by a squared 'normalized' Green's function (the directional factor), referred to a stationary point source. The convective motion of the sources, with its powerful amplifying effect, also directional, is already accounted for in the Lighthill format: wave convection and source convection are decoupled. The normalized Green's function appears to be near unity outside the refraction dominated 'cone of silence', this validates our long term practice of using Lighthill-based approaches outside the cone, with extension inside via the Green's function. The function is obtained either experimentally (injected 'point' source) or numerically (computational aeroacoustics). Approximation by unity seems adequate except near the cone and except when there are shrouding jets: in that case the difference from unity quantifies the shielding effect. Further extension yields dipole and monopole source terms (cf. Morfey, Mani, and others) when the mean flow possesses density gradients (e.g., hot jets).

Ribner, Herbert S.↗
DOE OSTI2018

On the convergence and convergence order of finite volume gradient schemes for oblique derivative boundary value problems

This work is an improvement of the previous note (Bradji in: Fuhrmann et al., Finite volumes for complex applications VII–methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, 2014) which dealt with the convergence analysis of a finite volume scheme for the Poisson’s equation with a linear oblique derivative boundary condition. The formulation of the finite volume scheme given in Bradji (in: Fuhrmann et al., Finite volumes for complex applications VII–methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, 2014) involves the discrete gradient introduced recently in Eymard et al. (IMA J Numer Anal 30(4):1009–1043, 2010). In this paper, we consider the convergence analysis of finite volume schemes involving the discrete gradient of Eymard et al. (IMA J Numer Anal 30(4):1009–1043, 2010) for elliptic and parabolic equations with linear oblique derivative boundary conditions. Linear oblique derivative boundary conditions arise for instance in the study of the motion of water in a canal, cf. Lesnic (Commun Numer Methods Eng 23(12):1071–1080, 2007). We derive error estimates in several norms which allow us to get error estimates for the approximations of the exact solutions and its first derivatives. In particular, we provide an error estimate between the gradient of the exact solutions and the discrete gradient of the approximate solutions. Convergence of the family of finite volume approximate solutions towards the exact solution under weak regularity assumption is also investigated. In the case of parabolic equations with oblique derivative boundary conditions, we develop a new discrete a priori estimate result. The proof of this result is based on the use of a discrete mean Poincaré–Wirtinger inequality. Thanks to the stated a priori estimate and to a comparison with an appropriately chosen auxiliary finite volume scheme, we derive the convergence results. This work can be viewed as a continuation of the previous work (Bradji and Gallouët in Int J Finite Vol 3(2):1–35, 2006) where a convergence analysis for a finite volume scheme, based on the admissible mesh of Eymard et al. (In: Ciarlet and Lions, Handbook of numerical analysis, North-Holland, Amsterdam, 2000), for the Poisson’s equation with a linear oblique derivative boundary conditions is given. The obtained convergence results do not require any relation between the mesh sizes of the spatial and time discretizations. Some numerical tests are presented for both elliptic and parabolic equations. In particular, we present three methods to compute the discrete solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Generalized trigonometric Fourier-series method with automatic time step control for non-linear point kinetics equations

The trigonometric Fourier-series method (TFS) is generalized to provide approximate solutions for non-linear point kinetics equations with feedback using varying step sizes. This method can provide a very stable solution against the size of the discrete time step allowing much larger step sizes to be used. Systems of the point kinetics equations are solved using Fourier-series expansion over a partition of the total time interval. The approximate solution requires determining the series coefficients over each time step in that partition. These coefficients are determined using the high-order derivatives of the solution vector at the beginning of the time step introducing a system of linear algebraic equations to be solved at each step. This system is similar to the Vandermonde system. Two successive orders of the partial sums are used to estimate the local truncation error. This error and some other constrains are used to produce the largest step size allowable at each step while keeping the error within a specific tolerance. The process of calculating suitable step sizes should be automatic and inexpensive. Convergence and stability of the proposed method are discussed and a new formula is introduced to maintain stability. The proposed method solves the general linear and non-linear kinetics problems. The method has been applied to five different types of reactivities including step/ramp insertions with temperature feedback. The method is seemed to be valid for larger time intervals than those used in the conventional numerical integration, and is thus useful in reducing computing time. Computational results are found to be consistent with the analysis, they demonstrate that the convergence of the iteration scheme can be accelerated and the resulting computing times can be greatly reduced while maintain computational accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Counting generations in birth and death processes with competing Erlang and exponential waiting times

Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not divide at all. If individual cells behave independently, then each cell can be imagined as sampling from a probability density of times to division and death. The exponential density is the most mathematically and computationally convenient choice. It has the advantage of satisfying the memoryless property, consistent with a Markov process, but it overestimates the probability of short division times. With the aim of preserving the advantages of a Markovian framework while improving the representation of experimentally-observed division times, we consider a multi-stage model of cellular division and death. We use Erlang-distributed (or, more generally, phase-type distributed) times to division, and exponentially distributed times to death. We classify cells into generations, using the rule that the daughters of cells in generation n are in generation n + 1. In some circumstances, our representation is equivalent to established models of lymphocyte dynamics. We find the growth rate of the cell population by calculating the proportions of cells by stage and generation. The exponent describing the late-time cell population growth, and the criterion for extinction of the population, differs from what would be expected if N steps with rate λ were equivalent to a single step of rate λ/N. We link with a published experimental dataset, where cell counts were reported after T cells were transferred to lymphopenic mice, using Approximate Bayesian Computation. In the comparison, the death rate is assumed to be proportional to the generation and the Erlang time to division for generation 0 is allowed to differ from that of subsequent generations. The multi-stage representation is preferred to a simple exponential in posterior distributions, and the mean time to first division is estimated to be longer than the mean time to subsequent divisions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Scattering Amplitudes in a Neighborhood of Limit Rays in Short-Wave Diffraction by Elongated Bodies of Revolution

In the paper, diffraction problems of a plane wave by smooth, convex, and elongated bodies of revolution are considered within the framework of short-wave approximation (axially symmetric cases). The scattering amplitudes are calculated in the direction of limit rays, and the influence of the elongation of the scatterers on the amplitudes behavior is investigated. Mathematical techniques of our approach are based on the Green’s formulas in the exterior of the scatterers and numerical calculations of the wave field current in the boundary layers in the vicinity of the light-shadow zone. It is established that the elongation of axially symmetric bodies relatively weakly affects the scattering amplitudes of the short-wave asymptotics. The main contribution to the amplitudes is made by the solution of the 2D diffraction problem by a convex, smooth curve in the cross section of the scatterers by a plane containing the rotation axis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Regularizing the linearly extrapolated BDF2 scheme for incompressible flows with time relaxation

This paper presents a highly-efficient finite element scheme for the time relaxation model (TRM). The efficiency is achieved through the second-order BDF2 time-stepping scheme with linear extrapolation (BDF2LE). The accuracy of the scheme is also greatly enhanced through the use of the divergence-free Scott-Vogeulis finite elements, and van Cittert approximate deconvolution. A complete finite element analysis is provided, which includes rigorous proofs for the stability, well-possessedness, and convergence of both velocity and pressure solutions. Furthermore, we also demonstrate that the inclusion of the linear time relaxation term preserves the long-time stability of the unregularized BDF2LE scheme. Finally, numerical experiments are presented that demonstrate the added stability and accuracy that time relaxation can provide.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Generalization of the Cauchy–Poisson Method and the Construction of Timoshenko-Type Equations

We consider a generalization of the Cauchy–Poisson method to the n-dimensional Euclidean space and its application to the construction of hyperbolic approximations. The presented investigation generalizes and supplements the results obtained earlier. In the Euclidean space, we introduce certain restrictions for the derivatives. The principle of hyperbolic degeneracy in terms of parameters is formulated and its realization in the form of necessary and sufficient conditions is presented. In a special case of fourdimensional space (in which the operators are preserved up to the sixth order), we obtain a generalized hyperbolic equation for the bending vibrations of plates with coefficients that depend only on the Poisson ratio. This equation includes, as special cases, the well-known Bernoulli–Euler, Kirchhoff, Rayleigh, and Timoshenko equations. As the development of Maxwell's and Einstein's investigations of the propagation of perturbations with finite velocity in continuous media, we can mention the nontrivial construction of Timoshenko’s equation for the bending vibrations of a beam.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Ensemble variational Fokker-Planck methods for data assimilation

Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itˆo process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itˆo process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean- Vlasov-Itˆo processes. Here, the effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz ’63, Lorenz ’96 and the quasi-geostrophic equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Multifidelity Approach to Sensitivity Estimation in Large-Eddy Simulation

A novel approach to compute affordable approximate sensitivities in a large-eddy simulation (LES) is proposed and assessed. The approach is based on solving a Reynolds-averaged Navier–Stokes (RANS) problem that has been linearized around the mean LES solution, with closure modeling required for the linearized changes in turbulent Reynolds stresses. In the present study, the closure modeling is based on a linearized algebraic turbulence model. The method is assessed for the flow over a NACA0012 airfoil at a fixed angle of attack, with the Reynolds number as the variable parameter. The results show that, provided an accurate linearized closure model, the method predicts the correct sensitivity of the skin friction coefficient and the mean velocity field at the cost of a linearized RANS, which provides an important proof-of-concept for this approach. Here, the linearized algebraic turbulence model with standard model coefficients produces a reasonably accurate sensitivity, but the results also suggest that accuracy could be gained from recalibrating the model coefficients for this new use of the model.

42 ENGINEERING↗
DOE OSTI2021

A minimally invasive, efficient method for propagation of full-field uncertainty in solid dynamics

In this work, we present a minimally invasive method for forward propagation of material property uncertainty to full-field quantities of interest in solid dynamics. Full-field uncertainty quantification enables the design of complex systems where quantities of interest, such as failure points, are not known a priori. The method, motivated by the well-known probability density function (PDF) propagation method of turbulence modeling, uses an ensemble of solutions to provide the joint PDF of desired quantities at every point in the domain. A small subset of the ensemble is computed exactly, and the remainder of the samples are computed with approximation of the evolution equations based on those exact solutions. Although the proposed method has commonalities with traditional interpolatory stochastic collocation methods applied directly to quantities of interest, it is distinct and exploits the parameter dependence and smoothness of the driving term of the evolution equations. The implementation is model independent, storage and communication efficient, and straightforward. We demonstrate its efficiency, accuracy, scaling with dimension of the parameter space, and convergence in distribution with two problems: a quasi-one-dimensional bar impact, and a two material notched plate impact. For the bar impact problem, we provide an analytical solution to PDF of the solution fields for method validation. With the notched plate problem, we also demonstrate good parallel efficiency and scaling of the method.

42 ENGINEERING↗