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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 415 records · Page 23
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NASA NTRS1993

A least-squares finite element method for 3D incompressible Navier-Stokes equations

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.

Jiang, Bo-Nan↗
NASA NTRS1975

Relaxation methods in fluid mechanics

The present work considers the iterative solution of a coupled set of difference equations and examines methods that carry successive approximates to a state that is invariant with further iteration and independent of the initial guess. Methods are studied with regard to their efficiency and economy of computer resources. The basic principles of classical relaxation are set forth, with attention confined to linear elliptic equations. This discussion involves the evaluation of the spectral radius that is the magnitude of the eigenvalue with largest modulus. The subject of relaxation is then related to the study of ordinary differential equations and hyperbolic partial differential equations. Problems that occur when linearly dependent eigenvectors appear in the relaxation matrix are discussed, leading to multiply connected eigenvalues in the Jordan canonical form. Finally, a brief survey of relaxation methods used in aerodynamics is given.

Lomax, H.↗
NASA NTRS1985

Stable boundary conditions and difference schemes for Navier-Stokes equations

The Navier-Stokes equations can be viewed as an incompletely elliptic perturbation of the Euler equations. By using the entropy function for the Euler equations as a measure of energy for the Navier-Stokes equations, it was possible to obtain nonlinear energy estimates for the mixed initial boundary value problem. These estimates are used to derive boundary conditions which guarantee L2 boundedness even when the Reynolds number tends to infinity. Finally, a new difference scheme for modelling the Navier-Stokes equations in multidimensions for which it is possible to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation was proposed.

Dutt, P.↗
NASA NTRS1993

Study of supersonic intersection flowfield at modified wing-body junctions

The problem of supersonic flow control using fillets and sweep for a wing-body junction has been investigated numerically using a three-dimensional Navier-Stokes code, which employs the MacCormack's time-split finite volume technique. An elliptic grid generation technique with direct control over spacing has been developed for constructing the grid at a filleted wing-body junction. The computed results for pressure distribution, particle paths, and limiting streamlines on the flat plate and fin surface for a swept fin show a decrease in the peak pressure on the fin leading edge and in the extent of the separated flow region. Moreover, the results for filleted juncture clearly show that the flow streamline patterns lose much of their vortical character with proper filleting. It has been demonstrated that fillets with a radius of three-and-one-half times the fin leading-edge diameter are required to weaken the vorticity in the horseshoe vortex by a factor of three for the Mach number and Reynolds number considered in the present study.

Lakshmanan, B.↗
NASA NTRS1990

Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming

The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Shi, Yun. Y.↗
NASA NTRS1974

Vibration analysis of a completely free elliptical plate

The Ritz method is applied to the variation analysis of a completely free elliptical plate as an efficient alternative to a procedure using a truncated series of regular and modified Mathieu functions. It is shown that a solution as accurate as desired can be obtained with the Ritz method in solving thin plate vibration problems with difficult geometries.

Beres, D. P.↗
NASA NTRS1985

Multigrid solutions to quasi-elliptic schemes

Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate then corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.

Brandt, A.↗
NASA NTRS1985

Multigrid solutions to quasi-elliptic schemes

Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate than corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.

Brandt, A.↗
NASA NTRS1992

Aerobraking Magellan

While the Magellan spacecraft is currently in an elliptical orbit around Venus, its orbit may be circularized by means of an aerobraking maneuver during which a minor amount of aerodynamic drag is applied to 1000-2000 orbits. An evaluation is presently undertaken of the thermal-control and operational problems arising from such a maneuver, in virtue of its not having been considered among the design requirements of the spacecraft. Attention is given to atmospheric erosion and contamination problems to which the spacecraft surfaces could be exposed.

Lyons, Daniel T.↗
NASA NTRS1999

Solving Upwind-Biased Discretizations: Defect-Correction Iterations

This paper considers defect-correction solvers for a second order upwind-biased discretization of the 2D convection equation. The following important features are reported: (1) The asymptotic convergence rate is about 0.5 per defect-correction iteration. (2) If the operators involved in defect-correction iterations have different approximation order, then the initial convergence rates may be very slow. The number of iterations required to get into the asymptotic convergence regime might grow on fine grids as a negative power of h. In the case of a second order target operator and a first order driver operator, this number of iterations is roughly proportional to h-1/3. (3) If both the operators have the second approximation order, the defect-correction solver demonstrates the asymptotic convergence rate after three iterations at most. The same three iterations are required to converge algebraic error below the truncation error level. A novel comprehensive half-space Fourier mode analysis (which, by the way, can take into account the influence of discretized outflow boundary conditions as well) for the defect-correction method is developed. This analysis explains many phenomena observed in solving non-elliptic equations and provides a close prediction of the actual solution behavior. It predicts the convergence rate for each iteration and the asymptotic convergence rate. As a result of this analysis, a new very efficient adaptive multigrid algorithm solving the discrete problem to within a given accuracy is proposed. Numerical simulations confirm the accuracy of the analysis and the efficiency of the proposed algorithm. The results of the numerical tests are reported.

Diskin, Boris↗
NASA NTRS1973

Long-term motion in a restricted problem of rotational motion

A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the long-term effects of gravity-gradient torque and orbital evolution on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is constrained to precess and spin with constant rates. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite to second order in n/omega sub 0, where n is the orbital mean motion of the center of mass and omega sub 0 is a reference value of the magnitude of the satellite's rotational angular velocity. The differential equations derivable from the transformed Hamiltonian are integrable, and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed, and a comparison of theoretical results with observations is made.

Cochran, J. E.↗
NASA NTRS1977

Simplified clustering of nonorthogonal grids generated by elliptic partial differential equations

A simple clustering transformation is combined with the Thompson, Thames, and Mastin (TTM) method of generating computational grids to produce controlled mesh spacings. For various practical grids, the resulting hybrid scheme is easier to apply than the inhomogeneous clustering terms included in the TTM method for this purpose. The technique is illustrated in application to airfoil problems, and listings of a FORTRAN computer code for this usage are included.

Sorenson, R. L.↗
NASA NTRS1979

A viscous flow analysis for the tip vortex generation process

A three dimensional, forward-marching, viscous flow analysis is applied to the tip vortex generation problem. The equations include a streamwise momentum equation, a streamwise vorticity equation, a continuity equation, and a secondary flow stream function equation. The numerical method used combines a consistently split linearized scheme for parabolic equations with a scalar iterative ADI scheme for elliptic equations. The analysis is used to identify the source of the tip vortex generation process, as well as to obtain detailed flow results for a rectangular planform wing immersed in a high Reynolds number free stream at 6 degree incidence.

Shamroth, S. J.↗
NASA NTRS1988

Boundary element method for 3-D cracks in a plate

Fundamental solutions which automatically satisfy boundary conditions at the interfaces of an elastic plate perfectly bonded to two elastic halfspaces are implemented in a three-dimensional BEM for crack problems. The BEM features a new integration scheme for highly singular kernels. The capability is achieved through a part analytic and part numerical integration procedure, such that the analytic part of the integration is similar for all slip/opening variations. Part-through elliptic cracks in an elastic plate with traction-free surfaces are analyzed and the SIF values along the crack front are found to compare favorably with the numerical SIF results of Raju and Newman (1979).

Fares, N.↗
NASA NTRS1991

Traction free finite elements with the assumed stress hybrid model

An effective approach in the finite element analysis of the stress field at the traction free boundary of a solid continuum was studied. Conventional displacement and assumed stress finite elements were used in the determination of stress concentrations around circular and elliptical holes. Specialized hybrid elements were then developed to improve the satisfaction of prescribed traction boundary conditions. Results of the stress analysis indicated that finite elements which exactly satisfy the free stress boundary conditions are the most accurate and efficient in such problems. A general approach for hybrid finite elements which incorporate traction free boundaries of arbitrary geometry was formulated.

Kafie, Kurosh↗
NASA NTRS1974

A finite difference method for the solution of the transonic flow around harmonically oscillating wings

A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.

Ehlers, E. F.↗
NASA NTRS1981

Shock-free configurations in two-and three-dimensional transonic flow

Efforts to replace Sobieczky's complicated analog computations of solutions to the hodograph equations by a fast elliptic solver in order to generate shock-free airfoil designs more effectively are described. The indirect design of airfoil and wing shapes that are free from shock waves even though the local flow velocity exceeds the speed of sound is described. The problem of finding an airfoil in two dimensional, irrotational flow that has a prescribed pressure distribution is as addressed. Sobieczky's suggestion to use a fictitious gas for finding shock-free airfoils directly in the physical plane was the basis for a more efficient procedure for achieving the same end.

Seebass, A. R.↗
NASA NTRS1981

Line-spring model for surface cracks in a Reissner plate

In this paper the line-spring model developed by Rice and Levy for a surface crack in elastic plates is reconsidered. The problem is formulated by using Reissner's plate bending theory. For the plane strain problem of a strip containing an edge crack and subjected to tension and bending new expressions for stress intensity factors are used which are valid up to a depth-to-thickness ratio of 0.8. The stress intensity factors for a semi-elliptic and a rectangular crack are calculated. Considering the simplicity of the technique and the severity of the underlying assumptions, the results compare rather well with the existing finite element solutions.

Delale, F.↗