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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 541 records · Page 30

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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.↗

NASA NTRS1986

Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics

The inverse and forward dynamics problems for multi-link serial manipulators are solved by using recursive techniques from linear filtering and smoothing theory. The pivotal step is to cast the system dynamics and kinematics as a two-point boundary-value problem. Solution of this problem leads to filtering and smoothing techniques identical to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The solutions prescribe an inward filtering recursion to compute a sequence of constraint moments and forces followed by an outward recursion to determine a corresponding sequence of angular and linear accelerations. In addition to providing techniques to compute joint accelerations from applied joint moments (and vice versa), the report provides an approach to evaluate recursively the composite multi-link system inertia matrix and its inverse. The report lays the foundation for the potential use of filtering and smoothing techniques in robot inverse and forward dynamics and in robot control design.

Rodriguez, G.↗

DOE OSTI2020

τ-SIMPLE Algorithm for the closure problem in homogenization of stokes flows

Estimation of the permeability tensor is crucial for many natural and industrial porous media applications. Homogenization provides a rigorous framework to calculate effective parameters from pore-scale images of a representative unit cell of the porous medium by solving a boundary value problem, also known as closure problem, subject to global constraints. However, the latter are hard to satisfy for arbitrarily complex geometries. We have developed a novel computational algorithm to calculate rigorously the permeability tensor. The approach, here referred to as τ-SIMPLE, is based on introducing an artificial time scale τ to satisfy the global constraint within the SIMPLE iteration. Here, we show that the proposed algorithm has high accuracy for both two-dimensional and three-dimensional periodically arranged geometries.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1981

Development of a linear unsteady aerodynamic analysis for finite-deflection subsonic cascades

A linear unsteady potential flow analysis, which accounts for the effects of blade geometry and steady turning, is being developed to predict the aerodynamic response to blade vibrations in the fan, compressor or turbine stages of modern jet engines. In previous work numerical solutions were restricted to cascades of sharp-edged blades aligned with the mean flow. Under the present effort the solution procedure has been extended to treat blades with rounded or blunt edges. As part of this effort an analytical model-problem study has been conducted to clarify the behavior of first-order perturbation solutions in the vicinity of airfoil edges. Further, a numerical approximation using concepts from singular perturbation theory has been developed to resolve the unsteady boundary value problem for cascades of blunt leading-edged blades. Numerical results for NACA 0012 cascades, including detailed results in the vicinity of a blade leading edge, are presented and evaluated.

Verdon, J. M.↗

NASA NTRS1985

Overheated Open Coronal Regions

The physics of compact, hydrostatic coronal shells formed from the collapse of overheated coronae is addressed. A large number of hydrostatic shells was computed for the usual exponential heating law with constant damping length. The boundary conditions were that on both sides of a shell the conductive flux at chromospheric temperatures is small. The boundary value problem was solved with a shooting technique. The main goal of the calculations was to determine the dependence of the shells on coronal heating flux (F sub Mo) and damping length (L); and in particular, to localize the boundary line in the parameter space (F sub Mo, L) that separates normal extended coronae from coronal shells.

Hammer, R.↗

NASA NTRS1973

Boundary-integral methods in elasticity and plasticity

Recently developed methods that use boundary-integral equations applied to elastic and elastoplastic boundary value problems are reviewed. Direct, indirect, and semidirect methods using potential functions, stress functions, and displacement functions are described. Examples of the use of these methods for torsion problems, plane problems, and three-dimensional problems are given. It is concluded that the boundary-integral methods represent a powerful tool for the solution of elastic and elastoplastic problems.

Mendelson, A.↗

NASA NTRS1988

Minimum-time pointing control of a two-link manipulator

Minimum-time pointing control for the end-effector of a planar, two-link manipulator is developed. Minimum-time pointing control is a new area of research for multilink manipulators, which can be applied to rapid retargeting control of a multibody spacecraft. The minimum-time control problem of aligning the second link of the two-link manipulator with a given target point is considered. A numerical method called the minimizing-boundary-condition method is used to determine optimal solutions for the two-point boundary-value problem associated with first-order necessary conditions. Minimum-time solutions for different models of pointing systems are compared. The results of the comparison show that a two-link manipulator with two degree-of-freedom performs better than a conventional one-link system for minimum-time pointing.

Wie, Bong↗

DOE OSTI2022

Investigation of fracture in porous materials: a phase-field fracture study informed by ReaxFF

Microscopic features (e.g, pore shapes, sizes, and distribution) in porous material substantially affect the overall mechanical properties such as stiffness and strength. In turn, these material properties determine the macroscopic behaviors of fracture in the porous material. In certain cases, macroscopic properties can be derived from the porous skeleton and void ratio (i.e., porosity), but in many other cases, such derivation is a challenging task. This paper presents a numerical investigation of microporosity and micropore shapes effect on the macrofracture behavior in porous amorphous silica. For this study, we extend the recently-proposed combined molecular dynamic (MD) and phase-field (PF) fracture modeling approach by including different pore shapes in the atomistic domain. In the MD simulations, we adopt ReaxFF to evaluate the material properties, where four different micropore cases are considered. Based on the material properties derived from MD simulations, the macrofracture propagation of porous media is studied using hybrid PF simulation. In the characterization of the pore structure, the concept of pore ligament is proposed to relate the pore shape and the critical energy release rate. Two classical fracture problems were used to evaluate the effect of pore shape on the macrofracture behavior. The results of the case study show that although the micropore shapes change the macrofracture behaviors, these effects vary with the geometry and loading conditions of macroscopic boundary value problems. Furthermore, the case study also shows that the influence of micropore structure can be captured at the macroscopic level through the material properties derived from the MD simulations.

42 ENGINEERING↗

NASA NTRS2020

Multi-Impulse to Time Optimal Finite Burn Trajectory Conversion

A novel conversion algorithm is presented that combines the fidelity of indirect optimization methods with the generality of direct methods to more easily solve time-optimal, finite-burn pseudo-rendezvous problems. An algorithm is described that converts a set of multiple-impulses, representing the entirety or a portion of a high- or low-thrust maneuver, to an exact time optimal finite-burn trajectory for a thrust limited, constant exhaust velocity spacecraft. A pseudo-rendezvous problem is one that yields a solution whose final time, position and velocity state is equal to that of the original post-impulsive trajectory. An iterative adjoint-control transformation is used to initialize the optimal control two-point boundary value problem. Examples are shown for both high and low-thrust non-coplanar Earth orbit transfers, as well as a low-thrust Hohmann-type Earth-Mars transfer.

Fogel, J.↗

DOE OSTI2018

On the strength of transversely isotropic rocks: On the strength of transversely isotropic rocks

Accurate prediction of strength in rocks with distinct bedding planes requires knowledge of the bedding plane orientation relative to the load direction. Thermal softening adds complexity to the problem since it is known to have significant influence on the strength and strain localization properties of rocks. In this paper, we utilize a recently proposed thermoplastic constitutive model appropriate for rocks exhibiting transverse isotropy in both the elastic and plastic responses to predict their strength and strain localization properties. Recognizing that laboratory-derived strengths can be influenced by material and geometric inhomogeneities of the rock samples, we consider both stress-point and boundary-value problem simulations of rock strength behavior. Both plane strain and 3D loading conditions are considered. Results of the simulations of the strength of a natural Tournemire shale and a synthetic transversely isotropic rock suggest that the mechanical model can reproduce the general U-shaped variation of rock strength with bedding plane orientation quite well. We show that this variation could depend on many factors, including the stress loading condition (plane strain versus 3D), degree of anisotropy, temperature, shear-induced dilation versus shear-induced compaction, specimen imperfections, and boundary restraints, among others.

42 ENGINEERING↗

NASA NTRS1989

Optimal aeroassisted coplanar orbital transfer using an energy model

The atmospheric portion of the trajectories for the aeroassisted coplanar orbit transfer was investigated. The equations of motion for the problem are expressed using reduced order model and total vehicle energy, kinetic plus potential, as the independent variable rather than time. The order reduction is achieved analytically without an approximation of the vehicle dynamics. In this model, the problem of coplanar orbit transfer is seen as one in which a given amount of energy must be transferred from the vehicle to the atmosphere during the trajectory without overheating the vehicle. An optimal control problem is posed where a linear combination of the integrated square of the heating rate and the vehicle drag is the cost function to be minimized. The necessary conditions for optimality are obtained. These result in a 4th order two-point-boundary-value problem. A parametric study of the optimal guidance trajectory in which the proportion of the heating rate term versus the drag varies is made. Simulations of the guidance trajectories are presented.

Halyo, Nesim↗

NASA NTRS1994

Fourth order difference methods for hyperbolic IBVP's

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

Gustafsson, Bertil↗

DOE OSTI2021

Hyperbolic three-string vertex

We begin developing tools to compute off-shell string amplitudes with the recently proposed hyperbolic string vertices of Costello and Zwiebach. Exploiting the relation between a boundary value problem for Liouville’s equation and a monodromy problem for a Fuchsian equation, we construct the local coordinates around the punctures for the generalized hyperbolic three-string vertex and investigate their various limits. This vertex corresponds to the general pants diagram with three boundary geodesics of unequal lengths. We derive the conservation laws associated with such vertex and perform sample computations. We note the relevance of our construction to the calculations of the higher-order string vertices using the pants decomposition of hyperbolic Riemann surfaces.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Manufactured Solutions for Solid Mechanics Code Verification -- Hyperelastic Material Case

Increased emphasis on computational simulation for NW qualification merits a corresponding increased diligence in verifying our codes. A manufactured solution process (implemented in Mathematica) for finite deformation, hyperelastic problems is presented that has been used to verify Sierra/SM for this class of problems. The process "manufactures a problem" given either a displacement field or motion map. Four test problems are examined; two provide sanity checks on symbolically calculated results, and two provide code verification results. While simple solutions from linear elasticity can be used to "seed" a manufactured solution, one from beam theory is shown to yield a n unexpectedly complex boundary value problem. The last problem combines two approaches that can significantly simplify the solution of some hypoelasticity problems, which require integration over time; a semi-manufactured approach is proposed and examined that yields the same observed rates of convergence as the classical approach at significantly reduced analytical effort.

42 ENGINEERING↗

NASA NTRS1986

Computation of multi-dimensional viscous supersonic jet flow

A new method has been developed for two- and three-dimensional computations of viscous supersonic flows with embedded subsonic regions adjacent to solid boundaries. The approach employs a reduced form of the Navier-Stokes equations which allows solution as an initial-boundary value problem in space, using an efficient noniterative forward marching algorithm. Numerical instability associated with forward marching algorithms for flows with embedded subsonic regions is avoided by approximation of the reduced form of the Navier-Stokes equations in the subsonic regions of the boundary layers. Supersonic and subsonic portions of the flow field are simultaneously calculated by a consistently split linearized block implicit computational algorithm. The results of computations for a series of test cases relevant to internal supersonic flow is presented and compared with data. Comparison between data and computation are in general excellent thus indicating that the computational technique has great promise as a tool for calculating supersonic flow with embedded subsonic regions. Finally, a User's Manual is presented for the computer code used to perform the calculations.

Kim, Y. N.↗

NASA NTRS1986

Computation of multi-dimensional viscous supersonic flow

A method has been developed for two- and three-dimensional computations of viscous supersonic jet flows interacting with an external flow. The approach employs a reduced form of the Navier-Stokes equations which allows solution as an initial-boundary value problem in space, using an efficient noniterative forward marching algorithm. Numerical instability associated with forward marching algorithms for flows with embedded subsonic regions is avoided by approximation of the reduced form of the Navier-Stokes equations in the subsonic regions of the boundary layers. Supersonic and subsonic portions of the flow field are simultaneously calculated by a consistently split linearized block implicit computational algorithm. The results of computations for a series of test cases associated with supersonic jet flow is presented and compared with other calculations for axisymmetric cases. Demonstration calculations indicate that the computational technique has great promise as a tool for calculating a wide range of supersonic flow problems including jet flow. Finally, a User's Manual is presented for the computer code used to perform the calculations.

Buggeln, R. C.↗

DOE OSTI2019

PRISMS-Plasticity: An open-source crystal plasticity finite element software

An open-source parallel 3-D crystal plasticity finite element (CPFE) software package PRISMS-Plasticity is presented here as a part of PRISMS integrated framework. A highly efficient rate-independent crystal plasticity algorithm is implemented along with developing its algorithmic tangent modulus. Additionally, a twin activation mechanism is incorporated into the framework based on an integration point sensitive scheme. The integration of the software as a part of the PRISMS framework is demonstrated. To do so, the integration of the PRISMS-Plasticity software with experimental characterization techniques such as electron backscatter diffraction (EBSD) and synchrotron X-ray diffraction using available open source software packages of DREAM.3D and Neper is elaborated. The integration of the PRISMS-Plasticity software with the information repository of Materials Commons is also presented. The parallel performance of the software is characterized which demonstrates that it scales well for large problems running on hundreds of processors. Various examples of polycrystalline metals with face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) crystals structures are presented to show the capability of the software to efficiently solve crystal plasticity boundary value problems, in addition to integration with preprocessing and postprocessing tools. PRISMS-Plasticity is an important activity within the broader PRISMS Center and future enhancements to PRISMS-Plasticity are planned and will be described.

36 MATERIALS SCIENCE↗

NASA NTRS1996

New Nonlinear Multigrid Analysis

The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.

Xie, Dexuan↗