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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 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Simplified computational methods for elastic and elastic-plastic fracture problems

This paper presents an overview of some of the recent (1984-1991) developments in computational/analytical methods in the mechanics of fracture: (i) analytical solutions for elliptical or circular cracks embedded in isotropic or transversely isotropic solids (the crack-plane being at an arbitrary angle to the axis of transverse isotropy), with crack-faces being subjected to arbitrary tractions; (ii) finite-element or boundary-element alternating methods for two- and three-dimensional crack problems; (iii) a "direct-stiffness" method for stiffened panels with flexible fasteners and with multiple cracks, using the alternating method; (iv) multiplesite-damage near a row of fastener holes; (v) analysis of cracks with bonded repair patches; (vi) methods for generation of weight-functions for 2- and 3-D crack problems, and (vii) domain-integral methods for elastic-plastic or inelastic crack mechanics.

Aging Aircraft↗
NASA NTRS1978

On least squares approximations to indefinite problems of the mixed type

A least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The method retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency, i.e., the resulting matrix system is always symmetric and positive definite. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.

Fix, G. J.↗
NASA NTRS1978

Computerized symbolic manipulation in structural mechanics Progress and potential

Status and recent applications of computerized symbolic manipulation to structural mechanics problems are summarized. The applications discussed include; (1) generation of characteristic arrays of finite elements; (2) evaluation of effective stiffness and mass coefficients of continuum models for repetitive lattice structures; and (3) application of Rayleigh-Ritz technique to free vibration analysis of laminated composite elliptic plates. The major advantages of using computerized symbolic manipulation in each of these applications are outlined. A number of problem areas which limit the realization of the full potential of computerized symbolic manipulation in structural mechanics are examined and some of the means of alleviating them are discussed.

Noor, A. K.↗
DOE OSTI2015

A hyperbolic-equation system approach for magnetized electron fluids in quasi-neutral plasmas

A new approach using a hyperbolic-equation system (HES) is proposed to solve for the electron fluids in quasi-neutral plasmas. The HES approach avoids treatments of cross-diffusion terms which cause numerical instabilities in conventional approaches using an elliptic equation (EE). A test calculation reveals that the HES approach can robustly solve problems of strong magnetic confinement by using an upwind method. The computation time of the HES approach is compared with that of the EE approach in terms of the size of the problem and the strength of magnetic confinement. The results indicate that the HES approach can be used to solve problems in a simple structured mesh without increasing computational time compared to the EE approach and that it features fast convergence in conditions of strong magnetic confinement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1977

Supercritical cascade design

The use of the method of complex extension to achieve better aerodynamic designs for supercritical cascades applicable to transonic turbomachinery is discussed. The method permits the computation of analytical solutions to elliptic, hyperbolic or mixed second-order partial equations in two dimensions. Boundary value problems formulated to develop an airfoil shape having a prescribed speed distribution for subsonic flow and a nearby speed distribution in the transonic case are also considered. Computing times necessary to run the blade design program are described as acceptably short.

Korn, D. G.↗
NASA NTRS1983

State and model error estimation for elliptic systems: Applications to large antenna static shape determination

This paper outlines the application of various estimation approaches to the problem of static shape determination for large antenna systems. The problem consists of estimating the shape of an antenna surface from measurements of its static deflection. The estimation schemes are based on any one of the modeling options of a single PDE for early insight and understanding, coarse-resolution multiple-PDE models for parametric studies and fine-resolution piecewise-continuum models for detailed design. For any one of these three models, estimator design can be developed using an infinite-dimensional approach, where the necessary finite-element truncation and approximation is conducted after the analytical design has taken place, or it can be based on a finite-dimensional approach, where the model is truncated before the estimation problem is formulated. One of the main objectives of the paper is to develop both approaches while simultaneously investigating their differences and similarities. Simulation results of an application of the finite-dimensional approach to a large parabolic reflector are presented.

Rodriguez, G.↗
NASA NTRS1993

An adaptive grid with directional control

An adaptive grid generator for adaptive node movement is here derived by combining a variational formulation of Winslow's (1981) variable-diffusion method with a directional control functional. By applying harmonic-function theory, it becomes possible to define conditions under which there exist unique solutions of the resulting elliptic equations. The results obtained for the grid generator's application to the complex problem posed by the fluid instability-driven magnetic field reconnection demonstrate one-tenth the computational cost of either a Eulerian grid or an adaptive grid without directional control.

Brackbill, J. U.↗
NASA NTRS1996

Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

Cai, Xiao-Chuan↗
NASA NTRS2004

On the Transition from Two-Dimensional to Three-Dimensional MHD Turbulence

We report a theoretical investigation of the robustness of two-dimensional inviscid MHD flows at low magnetic Reynolds numbers with respect to three-dimensional perturbations. We analyze three model problems, namely flow in the interior of a triaxial ellipsoid, an unbounded vortex with elliptical streamlines, and a vortex sheet parallel to the magnetic field. We demonstrate that motion perpendicular to the magnetic field with elliptical streamlines becomes unstable with respect to the elliptical instability once the velocity has reached a critical magnitude whose value tends to zero as the eccentricity of the streamlines becomes large. Furthermore, vortex sheets parallel to the magnetic field, which are unstable for any velocity and any magnetic field, are found to emit eddies with vorticity perpendicular to the magnetic field and with an aspect ratio proportional to N(sup 1/2). The results suggest that purely two-dimensional motion without Joule energy dissipation is a singular type of flow which does not represent the asymptotic behaviour of three-dimensional MHD turbulence in the limit of infinitely strong magnetic fields.

Thess, A.↗
DOE OSTI2015

Smoothed aggregation adaptive spectral element-based algebraic multigrid

SAAMGE provides parallel methods for building multilevel hierarchies and solvers that can be used for elliptic equations with highly heterogeneous coefficients. Additionally, hierarchy adaptation is implemented allowing solving multiple problems with close coefficients without rebuilding the hierarchy.

Source record↗
DOE OSTI2024

Asymptotic quasisymmetric high-beta three-dimensional magnetohydrodynamic equilibria near axisymmetry

Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal magnetohydrodynamic (MHD) equilibrium and stability of high-beta plasma in a large-aspect-ratio stellarator. In particular, we show that the lowest-order description of a near-axisymmetric equilibrium vastly simplifies the problem of three-dimensional quasisymmetric MHD equilibria, which can be reduced to a standard elliptic Grad–Shafranov equation for the flux function. We show that any large-aspect-ratio tokamak, deformed periodically in the vertical direction, is a stellarator with approximate volumetric QS. We discuss exact analytical solutions and numerical benchmarks. Finally, we discuss the ideal ballooning and interchange stability of some of our equilibrium configurations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Modeling Simulation and Optimization of a Pressure Relief Feature in a Hermetically Sealed Volume Exposed to Abnormal Thermal Environments

This project investigates the behavior of a venting feature on a hermetically sealed volume under abnormal thermal environments. A pressure profile is used to simulate internal pressure build up due to thermal decomposition of foam caused by temperatures approaching 800K. For the purposes of his scoping study a small can composed of 304L stainless steel is used to emulate the problem at hand and simplify the model. The venting feature can be described as an elliptical thinned area with X-like scoring marks on the circumferential surface of the can where the highest stresses are located without the feature. The feature variables include elliptical size, depth, and quantity to optimize the venting feature geometry to vent at a desired pressure range. Cubit, SIERRA: Solid Mechanics, and Ensight modeling programs are used to simulate and analyze several iterations of this feature to determine the most optimal geometry. The model indicates through the simulations that the feature does in fact vent in a predictable manner and can be used in a variety of pressure vessel applications where uncontrolled over pressurizations are undesirable. Future work includes model validation tests, looking at different geometries, and using a more accurate failure criterion.

42 ENGINEERING↗
NASA NTRS1976

On the computational cost of approximating and recognizing noise-perturbed straight lines and quadratic arcs in the plane

Recognition of underlying straight lines and quadratic arcs in line drawings, and approximation of very noisy data by such line/curve segments, is addressed as a subproblem of the more general problem of optimum recognition of complicated line/curve drawings. Some specific algorithms are presented with extensions and interpretations for more complicated applications, and a data generation model is developed for the problem. Data are generated as a perturbation of a single underlying straight line or an elliptic or hyperbolic arc. Recursive estimation techniques, minimization of central processing unit time, decision making with controlled error probabilities, and modeling and recognition of pictures consisting of noisy curves are dealt with. Applications envisaged include: picture data compression, contour line representation in maps, intelligent data searches, and ballistic missile decoy tracking.

Cooper, D. B.↗
NASA NTRS1985

The role of service areas in the optimization of FSS orbital and frequency assignments

A relationship is derived, on a single-entry interference basis, for the minimum allowable spacing between two satellites as a function of electrical parameters and service-area geometries. For circular beams, universal curves relate the topocentric satellite spacing angle to the service-area separation angle measured at the satellite. The corresponding geocentric spacing depends only weakly on the mean longitude of the two satellites, and this is true also for alliptical antenna beams. As a consequence, if frequency channels are preassigned, the orbital assignment synthesis of a satellite system can be formulated as a mixed-integer programming (MIP) problem or approximated by a linear programming (LP) problem, with the interference protection requirements enforced by constraints while some linear function is optimized. Possible objective-function choices are discussed and explicit formulations are presented for the choice of the sum of the absolute deviations of the orbital locations from some prescribed ideal location set. A test problem is posed consisting of six service areas, each served by one satellite, all using elliptical antenna beams and the same frequency channels. Numerical results are given for the three ideal location prescriptions for both the MIP and LP formulations. The resulting scenarios also satisfy reasonable aggregate interference protection requirements.

Levis, C. A.↗
NASA NTRS1988

Consistent boundary conditions for Reduced Navier-Stokes (RNS) scheme applied to 3-dimensional internal viscous flows

A consistent and efficient set of boundary conditions is developed for the multi-sweep space-marching pressure-elliptic Reduced Navier-Stokes (RNS) scheme as applied for 3-D internal viscous flow problems. No-slip boundary conditions are directly imposed on the solid walls. There is no iteration procedure required in the cross plane to ensure mass conservation across each marching plane. The finite difference equations forming the coefficient matrix are ordered such that the surface normal velocity is specified on all the solid walls; unlike external flows, a pressure boundary condition in the cross plane is not required. Since continuity is directly satisfied at all points in the flow domain, the first order momentum equations can be solved directly for the pressure without the need for a Poisson pressure correction equation. The procedure developed herein can also be applied with periodic boundary conditions. The analysis is given for general compressible flows. Incompressible flow solutions are obtained, for straight and curved ducts of square cross section, to validate the procedure. These solutions are used to demonstrate the applicability of the RNS scheme, with the improved boundary conditions for internal flows with strong interaction, as would be encountered in ducts and turbomachinery geometries.

Reddy, D. R.↗
NASA NTRS1996

MGLab: An Interactive Multigrid Environment

MGLab is a set of Matlab functions that defines an interactive environment for experimenting with multigrid algorithms. The package solves two-dimensional elliptic partial differential equations discretized using either finite differences or finite volumes, depending on the problem. Built-in problems include the Poisson equation, the Helmholtz equation, a convection-diffusion problem, and a discontinuous coefficient problem. A number of parameters controlling the multigrid V-cycle can be set using a point-and-click mechanism. The menu-based user interface also allows a choice of several Krylov subspace methods, including CG, GMRES(k), and Bi-CGSTAB, which can be used either as stand-alone solvers or as multigrid acceleration schemes. The package exploits Matlab's visualization and sparse matrix features and has been structured to be easily extensible.

Bordner, James↗
NASA NTRS1959

An Analysis of the Corridor and Guidance Requirements for Supercircular Entry into Planetary Atmospheres

The analysis of super-circular entry is developed around a new dimensionless parameter which combines certain conditions at the conic perigee altitude with certain characteristics of the vehicle; this parameter conveniently determines either deceleration-limited or heating limited corridor widths for elliptic, parabolic, or hyperbolic approach trajectories. Illustrative calculations of corridor widths and the associated guidance problems are presented for Venus, Earth, Mars, Jupiter, and Titan. Generalized curves are presented for application to various entry conditions.

Chapman, Dean R.↗