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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1989

Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Freund, Roland↗
NASA NTRS1988

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

Freund, Roland↗
NASA NTRS1969

An Encke-type special perturbation method.

Encke type analytical-numerical integration for solving differential equations of modified set of Lagrange planetary equations, obtaining satellite ephemeris for orbit prediction

Born, G. H.↗
NASA NTRS1972

A multispectral cloud type identification method using Nimbus 3 MRIR measurements.

Using Nimbus 3 medium resolution infrared radiometer measurements, a multispectral cloud type identification method is developed. This method includes a fourth spectral region (20-23 microns), the use of radiative transfer theory, and a semiquantitative evaluation of satellite cloud type estimates with concurrent high resolution photography from aircraft flights.

Shenk, W. E.↗
NASA NTRS1973

Data storage, image tube type

Method and apparatus for the storage of digital or analog electrical signals are provided by a memory storage system employing a conventional vidicon tube. At the beginning of an operating cycle, the vidicon is conditioned to accept electrical data input by exposing its photosensitive target to a short, high intensity light flash. A first electron beam scan of the photosensitive surface then sets up a charge pattern on the photosensitive target. A second electron beam scan of the photosensitive surface by an unmodulated electron beam then develops an output signal across an output resistor by using capacitive currents. The conditioning and scanning steps are operated repetitively at high speed using conventional television camera scan, sync, and power supply circuitry to provide a low cost data storage system.

Lipoma, P. C.↗
NASA NTRS1976

A multispectral cloud type identification method developed for tropical ocean areas with Nimbus-3 MRIR measurements

A four-channel multispectral cloud type identification technique is developed on the basis of Nimbus-3 Resolution Infrared Radiometer (MRIR) measurements, with the four channels being spectrally located at 0.2-4.0, 6.5-7, 10-11, and 20-23 microns. The technique requires the use of a radiative transfer model with information on the vertical temperature and moisture profiles and climatological knowledge of the upper boundaries of cloud surfaces associated with expected cloud types within a given area. Experimental verification of the technique indicates that deletion of the 20-23 micron channel has no adverse effect on method capability, and that the 6.5-7 micron channel alone is well suited for successful mapping of the areas where cirrus is reasonably dense, while indicating the regions where cirrus is not present.

Shenk, W. E.↗
NASA NTRS1985

Topics in spectral methods

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

Gottlieb, D.↗
DOE OSTI2023

Cauchy-type integral method for solving the linearized one-dimensional Vlasov-Poisson equation

Here, we present a method for solving the linearized Vlasov-Poisson equation, based on analyticity properties of the equilibrium and initial condition through Cauchy-type integrals, that produces algebraic expressions for the distribution and field, i.e., the solution is expressed without integrals. Standard extant approaches involve deformations of the Bromwich contour that give erroneous results for certain physically reasonable configurations or eigenfunction expansions that are misleading as to the temporal structure of the solution. Our method is more transparent, lacks these defects, and predicts previously unrecognized behavior.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2016

Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review

A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di erential equations (ODEs) is undertaken. The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods. Over 20 important aspects of DIRKtype methods are reviewed. A design study is then conducted on DIRK-type methods having from two to seven implicit stages. From this, 15 schemes are selected for general purpose application. Testing of the 15 chosen methods is done on three singular perturbation problems. Based on the review of method characteristics, these methods focus on having a stage order of two, sti accuracy, L-stability, high quality embedded and dense-output methods, small magnitudes of the algebraic stability matrix eigenvalues, small values of aii, and small or vanishing values of the internal stability function for large eigenvalues of the Jacobian. Among the 15 new methods, ESDIRK4(3)6L[2]SA is recommended as a good default method for solving sti problems at moderate error tolerances.

Kennedy, Christopher A.↗
DOE OSTI2024

Trifluoromethylation of 2D Transition Metal Dichalcogenides: A Mild Functionalization and Tunable p‐Type Doping Method

Chemical modification is a powerful strategy for tuning the electronic properties of 2D semiconductors. Here, in this study, we report the electrophilic trifluoromethylation of 2D WSe2 and MoS 2 under mild conditions using the reagent trifluoromethyl thianthrenium triflate (TTT). Chemical characterization and density functional theory calculations reveal that the trifluoromethyl groups bind covalently to surface chalcogen atoms as well as oxygen substitution sites. Trifluoromethylation induces p-type doping in the underlying 2D material, enabling the modulation of charge transport and optical emission properties in WSe 2 . This work introduces a versatile and efficient method for tailoring the optical and electronic properties of 2D transition metal dichalcogenides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Slater transition methods for core-level electron binding energies

Methods for computing core-level ionization energies using self-consistent field (SCF) calculations are evaluated and benchmarked. These include a “full core hole” (or “ΔSCF”) approach that fully accounts for orbital relaxation upon ionization, but also methods based on Slater’s transition concept in which the binding energy is estimated from an orbital energy level that is obtained from a fractional-occupancy SCF calculation. A generalization that uses two different fractional-occupancy SCF calculations is also considered. The best of the Slater-type methods afford mean errors of 0.3–0.4 eV with respect to experiment for a dataset of K-shell ionization energies, a level of accuracy that is competitive with more expensive many-body techniques. An empirical shifting procedure with one adjustable parameter reduces the average error below 0.2 eV. Here, this shifted Slater transition method is a simple and practical way to compute core-level binding energies using only initial-state Kohn–Sham eigenvalues. It requires no more computational effort than ΔSCF and may be especially useful for simulating transient x-ray experiments where core-level spectroscopy is used to probe an excited electronic state, for which the ΔSCF approach requires a tedious state-by-state calculation of the spectrum. As an example, we use Slater-type methods to model x-ray emission spectroscopy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1983

Finite element methods for nonlinear elastostatic problems in rubber elasticity

A number of finite element methods for the analysis of nonlinear problems in rubber elasticity are outlined. Several different finite element schemes are discussed. These include the augmented Lagrangian method, continuation or incremental loading methods, and associated Riks-type methods which have the capability of incorporating limit point behavior and bifurcations. Algorithms for the analysis of limit point behavior and bifurcations are described and the results of several numerical experiments are presented. In addition, a brief survey of some recent work on modelling contact and friction in elasticity problems is given. These results pertain to the use of new nonlocal and nonlinear friction laws.

Oden, J. T.↗
NASA NTRS2005

NASALIFE - Component Fatigue and Creep Life Prediction Program

NASALIFE is a life prediction program for propulsion system components made of ceramic matrix composites (CMC) under cyclic thermo-mechanical loading and creep rupture conditions. Although the primary focus was for CMC components, the underlying methodologies are equally applicable to other material systems as well. The program references empirical data for low cycle fatigue (LCF), creep rupture, and static material properties as part of the life prediction process. Multiaxial stresses are accommodated by Von Mises based methods and a Walker model is used to address mean stress effects. Varying loads are reduced by the Rainflow counting method or a peak counting type method. Lastly, damage due to cyclic loading and creep is combined with Minor s Rule to determine damage due to cyclic loading, damage due to creep, and the total damage per mission and the number of potential missions the component can provide before failure.

Gyekenyesi, John Z.↗
NASA NTRS2014

NASALIFE - Component Fatigue and Creep Life Prediction Program

NASALIFE is a life prediction program for propulsion system components made of ceramic matrix composites (CMC) under cyclic thermo-mechanical loading and creep rupture conditions. Although the primary focus was for CMC components, the underlying methodologies are equally applicable to other material systems as well. The program references empirical data for low cycle fatigue (LCF), creep rupture, and static material properties as part of the life prediction process. Multiaxial stresses are accommodated by Von Mises based methods and a Walker model is used to address mean stress effects. Varying loads are reduced by the Rainflow counting method or a peak counting type method. Lastly, damage due to cyclic loading and creep is combined with Minor's Rule to determine damage due to cyclic loading, damage due to creep, and the total damage per mission and the number of potential missions the component can provide before failure.

CMC Vane↗
DOE OSTI2025

Constrained or unconstrained? Neural-network-based equation discovery from data

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or the accurate resolution of their solutions may be intractable. Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations (PDEs), on a spectrum of interpretability. The success of these strategies is often contingent upon the correct identification of representative equations from noisy observations of state variables and, as importantly and intertwined with that, the mathematical strategies utilized to enforce those equations. Specifically, the latter has been commonly addressed via unconstrained optimization strategies. Representing the PDE as a neural network, we propose to discover the PDE (or the associated operator) by solving a constrained optimization problem and using an intermediate state representation similar to a physics-informed neural network (PINN). The objective function of this constrained optimization problem promotes matching the data, while the constraints require that the discovered PDE is satisfied at a number of spatial collocation points. We present a penalty method and a widely used trust-region barrier method to solve this constrained optimization problem, and we compare these methods on numerical examples. Our results on several example problems demonstrate that the latter constrained method outperforms the penalty method, particularly for higher noise levels or fewer collocation points. This work motivates further exploration into using sophisticated constrained optimization methods in scientific machine learning, as opposed to their commonly used, penalty-method or unconstrained counterparts. For both of these methods, we solve these discovered neural network PDEs with classical methods, such as finite difference methods, as opposed to PINNs-type methods relying on automatic differentiation. Here, we briefly highlight how simultaneously fitting the data while discovering the PDE improves the robustness to noise and other small, yet crucial, implementation details.

Data-driven discovery↗