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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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Three-dimensional boundary layer calculation by a characteristic method

A numerical method for solving the three-dimensional boundary layer equations for bodies of arbitrary shape is presented. In laminar flows, the application domain extends from incompressible to hypersonic flows with the assumption of chemical equilibrium. For turbulent boundary layers, the application domain is limited by the validity of the mixing length model used. In order to respect the hyperbolic nature of the equations reduced to first order partial derivative terms, the momentum equations are discretized along the local streamlines using of the osculator tangent plane at each node of the body fitted coordinate system. With this original approach, it is possible to overcome the use of the generalized coordinates, and therefore, it is not necessary to impose an extra hypothesis about the regularity of the mesh in which the boundary conditions are given. By doing so, it is possible to limit, and sometimes to suppress, the pre-treatment of the data coming from an inviscid calculation. Although the proposed scheme is only semi-implicit, the method remains numerically very efficient.

Houdeville, R.↗
NASA NTRS1989

A stable numerical solution method in-plane loading of nonlinear viscoelastic laminated orthotropic materials

In response to the tremendous growth in the development of advanced materials, such as fiber-reinforced plastic (FRP) composite materials, a new numerical method is developed to analyze and predict the time-dependent properties of these materials. Basic concepts in viscoelasticity, laminated composites, and previous viscoelastic numerical methods are presented. A stable numerical method, called the nonlinear differential equation method (NDEM), is developed to calculate the in-plane stresses and strains over any time period for a general laminate constructed from nonlinear viscoelastic orthotropic plies. The method is implemented in an in-plane stress analysis computer program, called VCAP, to demonstrate its usefulness and to verify its accuracy. A number of actual experimental test results performed on Kevlar/epoxy composite laminates are compared to predictions calculated from the numerical method.

Gramoll, K. C.↗
NASA NTRS1986

Improved Numerical Evaluation Method for Elliptic Integrals

Two modifications to Bartky's method for numerical evaluation of complete elliptic integrals increase rate of convergence and eliminate loss of accuracy due to roundoff errors. Other integrals (nonelliptic) evaluated by manipulating integrand into form F(R)/R required for evaluation by this method. Improved method used to map upper half of complex plane conformally onto interior or exterior of round-nosed wedges of various angles.

Rossow, V. J.↗
NASA NTRS1975

The use of back corrections in multistep methods of numerical integration

Generalized multistep methods for the numerical solution of nonlinear systems of ordinary differential equations are introduced which allow the correction of previously computed values of the solution at internal points of the grid. These methods are shown to possess enhanced numerical stability. Preliminary numerical results indicate that for some satellite orbit problems these methods also possess greater overall efficiency. A uniformly converging theory of error propagation is presented which is valid for nonasymptotic values of the step size. Experimental results are seen to conform with theory.

Beaudet, P.↗
NASA NTRS1984

Design sensitivity analysis with Applicon IFAD using the adjoint variable method

A numerical method is presented to implement structural design sensitivity analysis using the versatility and convenience of existing finite element structural analysis program and the theoretical foundation in structural design sensitivity analysis. Conventional design variables, such as thickness and cross-sectional areas, are considered. Structural performance functionals considered include compliance, displacement, and stress. It is shown that calculations can be carried out outside existing finite element codes, using postprocessing data only. That is, design sensitivity analysis software does not have to be imbedded in an existing finite element code. The finite element structural analysis program used in the implementation presented is IFAD. Feasibility of the method is shown through analysis of several problems, including built-up structures. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy associated with selection of a finite difference perturbation.

Frederick, Marjorie C.↗
DOE OSTI2024

Efficient general method for numerically modeling laser pulse propagation, overlap, and lifetime effects in amplifiers

An efficient numerical time-dependent general method is developed to address incoherent pulse overlap and lifetime effects in laser amplifiers. The alternating propagation-population laser energetics method (APPLE) has been validated against a semi-discrete coupled rate equation numerical method (SDRE) and analytic formalisms in bounding cases. APPLE is based on decoupled rates applied to a time-dependent framework where both space-time-dependent populations and pulse energetics are consistently updated in each time step. A significant advantage of APPLE lies in its conceptual simplicity, ease of implementation, and relatively small computational cost. SDRE tracks the populations through coupled rates and uses the method of lines to discretize the hyperbolic partial differential transport equations allowing for use of ordinary differential equation solvers. With reasonably sized mesh, we report both energetic and power pulse shape relative differences on the order of one percent between the models over a large range of initial conditions.

47 OTHER INSTRUMENTATION↗
NASA NTRS1974

Development of inverse inviscid transonic solution methods

A numerical method suitable for the analysis and/or design of supercritical transonic airfoils is reported. In order to achieve accuracy, the method utilizes the full inviscid potential flow equations; and in order to remain simple it solves the problem in a stretched Cartesian grid system. The resulting computer program has several advantages over others of its type -- its use in either the direct analysis mode in which the airfoil shape is prescribed and the flow field and surface pressures are determined, or in the inverse mode in which the surface pressures are given and the airfoil shape and flow field are computed. Other advantages of the program include its use in a design program, the rotated finite difference scheme and its determination of the airfoil shape simultaneously with the flow field relaxation solution.

Carlson, L. A.↗
NASA NTRS1973

The development of accurate and efficient methods of numerical quadrature

Some new methods for performing numerical quadrature of an integrable function over a finite interval are described. Each method provides a sequence of approximations of increasing order to the value of the integral. Each approximation makes use of all previously computed values of the integrand. The points at which new values of the integrand are computed are selected in such a way that the order of the approximation is maximized. The methods are compared with the quadrature methods of Clenshaw and Curtis, Gauss, Patterson, and Romberg using several examples.

Feagin, T.↗
NASA NTRS1991

A Fourier collocation time domain method for numerically solving Maxwell's equations

A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.

Shebalin, John V.↗
NASA NTRS1988

Numerical solution methods for viscoelastic orthotropic materials

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Gramoll, K. C.↗
NASA NTRS2014

Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation

This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.

CFD↗