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At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

A technique for accelerating iterative convergence in numerical integration, with application in transonic aerodynamics

A technique is described for the efficient numerical solution of nonlinear partial differential equations by rapid iteration. In particular, a special approach is described for applying the Aitken acceleration formula (a simple Pade approximant) for accelerating the iterative convergence. The method finds the most appropriate successive approximations, which are in a most nearly geometric sequence, for use in the Aitken formula. Simple examples are given to illustrate the use of the method. The method is then applied to the mixed elliptic-hyperbolic problem of steady, inviscid, transonic flow over an airfoil in a subsonic free stream.

Martin, E. D.↗
NASA NTRS1976

Light scattering by tenuous particles - A generalization of the Rayleigh-Gans-Rocard approach

We consider scattering by arbitrarily shaped particles that satisfy two conditions: (1) that the polarizability of the particle relative to the ambient medium be small compared to 1 and (2) that the phase shift introduced by the particle be less than 2. We solve the integro-differential equation proposed by Shifrin by using the method of successive iterations and then applying a Fourier transform. For the second iteration, results are presented that accurately describe scattering by a broad class of particles. The phase function and other elements of the scattering matrix are shown to be in excellent agreement with Mie theory for spherical scatterers.

Acquista, C.↗
NASA NTRS1977

Comparison of some optimal control methods for the design of turbine blades

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Desilva, B. M. E.↗
NASA NTRS1980

A vortex-lattice method for the calculation of the nonsteady separated flow over delta wings

An analysis is made of the wake structure and the forces on a delta wing as it undergoes nonsteady motion, wherein the flow separates at the leading edge. Comparisons of these predictions with existing experimental and theoretical data for the nonsteady linear and nonlinear motions indicate good agreement. It was found that the time-dependent, wake-shedding numerical procedure applied here for the wake rollup and the lift force calculation resulted in considerable saving of computer time over methods using the iterative wake rollup procedure. Calculated results for various motions of the delta wing, including the plunging motion, are presented for both the separated and the attached flow cases.

Levin, D.↗
NASA NTRS1980

Surface tension-driven convections

The study of time-dependent flows generated by surface-tension gradients in thin liquid layers is reported. Numerical techniques for dealing with the complete float-zone process were investigated. In particular, finite element methods with fast iterative procedures, using multipoint constraints and nonlinear optimization were examined.

Ostrach, S.↗
NASA NTRS1980

Radiative transfer in dusty nebulae. III - The effects of dust albedo

The effects of an albedo of internal dust, such as ionization structure and temperature of dust grain, were studied by the quasi-diffusion method with an iterative technique for solving the radiative heat transfer equations. It was found that the generalized on-the-spot approximation solution is adequate for most astrophysical applications for a zero albedo; for a nonzero albedo, the Eddington approximation is more accurate. The albedo increases the average energy of the diffuse photons, increasing the ionization level of hydrogen and heavy elements if the Eddington approximation is applied; the dust thermal gradient is reduced so that the infrared spectrum approaches blackbody spectrum with an increasing albedo.

Petrosian, V.↗
NASA NTRS1980

Numerical investigation of the onset of separation of an incompressible viscous flow from objects in ducts

Simulation has been used to investigate the phenomenon of separation of a steady flow of an incompressible viscous fluid from a symmetric object in a duct. Two essentially two-dimensional problems were studied: (1) an elliptical cylinder located between two parallel plates, and (2) a sphere placed on the axis of a cylindrical pipe. The steady-state vorticity transport equation and the second order differential equation relating vorticity and the stream function were iterated using the method of overrelaxation to obtain a solution for each set of initial conditions. The relationship between the Reynolds number corresponding to the onset of separation and the size of the object relative to the duct was found to be linear over a wide range.

Winchester, L. W., Jr.↗
NASA NTRS1983

New discretization and solution techniques for incompressible viscous flow problems

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.

Gunzburger, M. D.↗
NASA NTRS1983

Progress in computational physics

Recent progress in computational methods for time dependent fluid dynamics is presented. The emphasis is on advances applicable to large scale systems with the connection between the numerics and the physics of the code stressed. All aspects of a working code are discussed including such topics as initialization, boundary conditions, grid generation in addition to algorithmic advances. One sometimes uses a time dependent method as an iteration procedure to reach a steady state solution. Work in accelerating the convergence to the steady state is also surveyed.

Turkel, E.↗
NASA NTRS1983

New discretization and solution techniques for incompressible viscous flow problems

This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.

Gunzburger, M. D.↗
NASA NTRS1983

A fast approach to identification using deconvolution

In this paper, we propose a fast approach to impulse response and noise-variance identification for a finite-order, linear, time-invariant, single-input/single-output system, whose input driving noise is white (stationary or nonstationary) and measurement noise is stationary, white and Gaussian. Our algorithm is an iterative block component method that includes two stages, deconvolution and prediction-error identification. Experiences with our method indicate that it works well and saves about an order of magnitude in computation. Analyses and examples are given in this paper to support this claim.

Chi, C.-Y.↗
NASA NTRS1986

Self-adaptive difference method for the effective solution of computationally complex problems of boundary layer theory

An implicit difference procedure for the solution of equations for a chemically reacting hypersonic boundary layer is described. Difference forms of arbitrary error order in the x and y coordinate plane were used to derive estimates for discretization error. Computational complexity and time were minimized by the use of this difference method and the iteration of the nonlinear boundary layer equations was regulated by discretization error. Velocity and temperature profiles are presented for Mach 20.14 and Mach 18.5; variables are velocity profiles, temperature profiles, mass flow factor, Stanton number, and friction drag coefficient; three figures include numeric data.

Schoenauer, W.↗
NASA NTRS1986

Dislocation dynamics during the growth of silicon ribbon

The thermal viscoplastic stresses and the dislocation densities in silicon ribbon are computed for an axially changing thermal profile by using an iterative finite difference method. A material constitutive equation (Haasen-Sumino model) which involves an internal variable (mobile dislocation density) is used. The results are interpreted as showing that there is a maximum width of silicon ribbon that can be grown when viscoplasticity and dislocations are considered. This maximum width limitation does not exist if the material behavior is elastic.

Dillon, O. W., Jr.↗
NASA NTRS1988

A transonic-small-disturbance wing design methodology

An automated transonic design code has been developed which modifies an initial airfoil or wing in order to generate a specified pressure distribution. The design method uses an iterative approach that alternates between a potential-flow analysis and a design algorithm that relates changes in surface pressure to changes in geometry. The analysis code solves an extended small-disturbance potential-flow equation and can model a fuselage, pylons, nacelles, and a winglet in addition to the wing. A two-dimensional option is available for airfoil analysis and design. Several two- and three-dimensional test cases illustrate the capabilities of the design code.

Phillips, Pamela S.↗
NASA NTRS1988

Analysis of a closed-kinematic chain robot manipulator

Presented are the research results from the research grant entitled: Active Control of Robot Manipulators, sponsored by the Goddard Space Flight Center (NASA) under grant number NAG-780. This report considers a class of robot manipulators based on the closed-kinematic chain mechanism (CKCM). This type of robot manipulators mainly consists of two platforms, one is stationary and the other moving, and they are coupled together through a number of in-parallel actuators. Using spatial geometry and homogeneous transformation, a closed-form solution is derived for the inverse kinematic problem of the six-degree-of-freedom manipulator, built to study robotic assembly in space. Iterative Newton Raphson method is employed to solve the forward kinematic problem. Finally, the equations of motion of the above manipulators are obtained by employing the Lagrangian method. Study of the manipulator dynamics is performed using computer simulation whose results show that the robot actuating forces are strongly dependent on the mass and centroid locations of the robot links.

Nguyen, Charles C.↗
NASA NTRS1988

The solution of the Elrod algorithm for a dynamically loaded journal bearing using multigrid techniques

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

Woods, Claudia M.↗
NASA NTRS1988

Unsteady aerodynamics of rotor-stator interaction in a turbine stage

The two-dimensional, compressible, unsteady, thin-layer Navier-Stokes equations have been used to study the turbulent flow field of a turbine rotor/stator configuration in the high pressure oxidizer turbopump of the Space Shuttle main engine. The calculations were performed on a system of patched and overlaid grids. The grid system consists of 'O-' and 'H-' grids, with the inner 'O-'grid enclosing the blade surface for an accurate resolution of the leading and trailing edges, while the outer 'H-'grid makes the treatment of boundary conditions easier. The integration scheme used is an iterative, factored, implicit method with numerical fluxes evaluated by the third-order accurate upwind-biased Osher scheme. Computed results in the form of pressure contours, Mach number contours, time-averaged surface pressure, unsteady pressure amplitude and unsteady velocity vectors are presented. Many flow phenomena, such as wake cutting by rotor airfoils and evolution of unsteady passage vortices, are discussed.

Yang, R.-J.↗
NASA NTRS1989

Treatment of body forces in boundary element design sensitivity analysis

The inclusion of body forces has received a good deal of attention in boundary element research. The consideration of such forces is essential in the desgin of high performance components such as fan and turbine disks in a gas turbine engine. Due to their critical performance requirements, optimal shapes are often desired for these components. The boundary element method (BEM) offers the possibility of being an efficient method for such iterative analysis as shape optimization. The implicit-differentiation of the boundary integral equations is performed to obtain the sensitivity equations. The body forces are accounted for by either the particular integrals for uniform body forces or by a surface integration for non-uniform body forces. The corresponding sensitivity equations for both these cases are presented. The validity of present formulations is established through a close agreement with exact analytical results.

Saigal, Sunil↗