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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

Whitfield, David L.↗
NASA NTRS1988

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

Warming, Robert F.↗
NASA NTRS1976

Incremental analysis of large elastic deformation of a rotating cylinder

The effect of finite deformation upon a rotating, orthotropic cylinder was investigated using a general incremental theory. The incremental equations of motion are developed using the variational principle. The governing equations are derived using the principle of virtual work for a body with initial stress. The governing equations are reduced to those for the title problem and a numerical solution is obtained using finite difference approximations. Since the problem is defined in terms of one independent space coordinate, the finite difference grid can be modified as the incremental deformation occurs without serious numerical difficulties. The nonlinear problem is solved incrementally by totaling a series of linear solutions.

Buchanan, G. R.↗
NASA NTRS1977

TOMCAT - A code for numerical generation of boundary-fitted curvilinear coordinate systems on fields containing any number of arbitrary two-dimensional bodies

A method for automatic generation of boundary-fitted curvilinear coordinate systems, where the transformed coordinates are solutions of an elliptic differential system in the physical plane, and where the coordinate lines are coincident with all boundaries of a general multiply-connected, two-dimensional region containing any number of arbitrarily shaped bodies, and is described along with a suitable computer code for implementing the method. Any partial differential system can be solved on the boundary-fitted coordinate system by appropriate transformations. The transformed equations are approximated by finite differences and solved numerically in the transformed plane. All computations, whether for generating coordinate system or then solving the transformed equations, can be done on a rectangular field with square mesh with no interpolation required on the boundaries. The physical boundaries may even be time-dependent.

Thompson, J. F.↗
NASA NTRS1987

Effect of atmospheric turbulence on the bit error probability of a space to ground near infrared laser communications link using binary pulse position modulation and an avalanche photodiode detector

The effect of atmospheric turbulence on the bit error rate of a space-to-ground near infrared laser communications link is investigated, for a link using binary pulse position modulation and an avalanche photodiode detector. Formulas are presented for the mean and variance of the bit error rate as a function of signal strength. Because these formulas require numerical integration, they are of limited practical use. Approximate formulas are derived which are easy to compute and sufficiently accurate for system feasibility studies, as shown by numerical comparison with the exact formulas. A very simple formula is derived for the bit error rate as a function of signal strength, which requires only the evaluation of an error function. It is shown by numerical calculations that, for realistic values of the system parameters, the increase in the bit error rate due to turbulence does not exceed about thirty percent for signal strengths of four hundred photons per bit or less. The increase in signal strength required to maintain an error rate of one in 10 million is about one or two tenths of a db.

Safren, H. G.↗
NASA NTRS2015

Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies

Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 − q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.

chaos aEuro" galaxies:↗
NASA NTRS1987

On local approximations of the pressure-strain term in turbulence models

The results of numerical simulations of turbulent channel flows were used to examine the validity of the local approximation of the pressure-strain term in the Reynolds stress transport equation. Outside of the viscous sublayer the local approximation compares very well with the exact pressure strain. This agreement is due, at least in part, to the high correlation between the rapid pressure and its Laplacian, which suggests that only the near parts of the flow contribute to the rapid pressure at a point. In the viscous sublayer the distance over which the mean shear can be considered constant is comparable to the length scale in the normal direction of the correlations of velocity gradients, leading to failure of the local approximation.

Bradshaw, P.↗
NASA NTRS1996

Mixing and Transition Control Studied

Considerable progress in understanding nonlinear phenomena in both unbounded and wallbounded shear flow transition has been made through the use of a combination of high- Reynolds-number asymptotic and numerical methods. The objective of this continuing work is to fully understand the nonlinear dynamics so that ultimately (1) an effective means of mixing and transition control can be developed and (2) the source terms in the aeroacoustic noise problem can be modeled more accurately. Two important aspects of the work are that (1) the disturbances evolve from strictly linear instability waves on weakly nonparallel mean flows so that the proper upstream conditions are applied in the nonlinear or wave-interaction streamwise region and (2) the asymptotic formulations lead to parabolic problems so that the question of proper out-flow boundary conditions--still a research issue for direct numerical simulations of convectively unstable shear flows--does not arise. Composite expansion techniques are used to obtain solutions that account for both mean-flow-evolution and nonlinear effects. A previously derived theory for the amplitude evolution of a two-dimensional instability wave in an incompressible mixing layer (which is in quantitative agreement with available experimental data for the first nonlinear saturation stage for a plane-jet shear layer, a circular-jet shear layer, and a mixing layer behind a splitter plate) have been extended to include a wave-interaction stage with a three-dimensional subharmonic. The ultimate wave interaction effects can either give rise to explosive growth or an equilibrium solution, both of which are intimately associated with the nonlinear self-interaction of the three dimensional component. The extended theory is being evaluated numerically. In contrast to the mixing-layer situation, earlier comparisons of theoretical predictions based on asymptotic methods and experiments in wall-bounded shear-flow transition have been somewhat lacking in one aspect or another. The current work strongly suggests that the main weakness is the underlying asymptotic representation of the linear "part" of the problem and not the explicit modeling of the nonlinear/wave-interaction effects. Consequently, the long-wave-length/high-Reynolds-number asymptotic limit for the Blasius boundary-layer stability problem was reexamined, and a new dispersion relationship for the instability waves that is uniformly valid for both the upper- and lower branch regions to the required order of approximation was obtained. A comparison with numerical results, obtained by solving the Orr-Sommerfeld stability problem, shows that the asymptotic formula provides surprisingly good results, even for values of the frequency parameter usually encountered in experimental investigations. This is particularly evident in the dynamically important upper-branch region, where much of the nonlinear interactions in transition experiments are believed to take place. The result is important in that it can be used to greatly improve the accuracy of weakly nonlinear critical-layer-based theories, and a consistent nonlinear theory is currently under evaluation.

Source record↗
NASA NTRS1984

Convergent-tapered annular seals - Analysis and testing for rotordynamic coefficients

A combined analytical-computational method has been developed to calculate the pressure field and dynamic coefficients for tapered high-pressure annular seals. Completely developed turbulent flow is assumed in both the circumferential and axial directions, according to Hirs' (1973) bulk-flow turbulent-lubrication equations. In a numerical experiment with the method, a short bearing approximation is used to derive an analytical expression for the first-order (dynamic) pressure gradient. This expression is integrated numerically to define dynamic coefficients of the seal. Numerical results of the integration are compared with previous results for straight and tapered seals. It is found that direct stiffness and leakage coefficients increase in the present seal, while the remaining coefficients decrease. An optimal taper angle is shown to exist with respect to: (1) the direct stiffness and (2) the ratio of direct stiffness to leakage. On the basis of the optimal taper angle calculations, stiffness increases on the order of 40 to 50 percent are predicted. Experimental results for three taper angles are presented, and are found to be in good agreement with the theoretical predictions.

Childs, D. W.↗
NASA NTRS1993

Three-dimensional magnetotail equilibria by numerical relaxation techniques

Consideration is given to a numerical method to iteratively approach 3D magnetostatic force equilibria, with modeling emphasis on the development of a suitable model of the earth's magnetotail, including a portion of the inner magnetosphere, i.e., on models which violate the 'tail approximation' commonly employed in analytical models. The numerical approach is compared to methods developed for laboratory plasma physics. The method is applied to the magnetotail outside of 10 R(E), using Tsyganenko's (1987) model for the quiet magnetosphere as an initial condition. The changes of the magnetic field necessary to yield an equilibrium configuration and the resulting distribution of the self-consistently derived pressure are discussed. It is shown that a self-consistent magnetotail equilibrium based on a close approximation to Tsyganenko's requires a region 1 type current system, which is not present in the initial configuration.

Hesse, Michael↗
NASA NTRS2016

Optics of Water Microdroplets with Soot Inclusions: Exact Versus Approximate Results

We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.

cloud droplets↗
NASA NTRS1994

Gradient drift eigenmodes in the equatorial electrojet

The problem of kilometer-scale irregularities in the daytime equatorial electrojet is revisited by means of an eigenmode analysis of the gradient drift instability. Realistic physical parameters are used, including the modeled altitude variations of ion and electron collision frequencies and mobilities. The full fourth-order system of two coupled differential equations (each of second order) for the denisty and electrostatic potential perturbations is solved numerically by a relaxation technique. Under some approximations, the fourth-order system can be shown to reduce to a second-order differential equation for the perturbed potential or density. The latter is solved using a shooting technique and provides initial guesses for numerical solutions to the full problem. It is shown that the linear growth rate peaks for kilometer-scale waves, contrary to the findings of recent initial-value studies. This occurs because the equilibrium velocity shear is much more effective as a damping mechanism for short-wavelength modes than it is for the longer, kilometer-scale modes. These results provide a natural qualitative explanation for the observed dominance of kilometer-scale structures in the daytime electrojet spectrum.

Wang, X.-H.↗
NASA NTRS1977

Numerical determination of the fundamental eigenvalue for the Laplace operator on a spherical domain

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (i.e., the membrane eignevalue problem for the vibration equation) on the unit spherical surface are developed. Two types of spherical surface domains are considered: the interior of a spherical triangle, and the exterior of a great circle arc extending for less than pi radians (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is employed. The fundamental eigenvalue is approximated by iteration utilizing the power method and point successive overrelaxation. Some numerical results are given and compared, in certain special cases, with analytical solutions to the eigenvalue problem. The significance of the numerical eigenvalue results is discussed in terms of the singularities in the solution of three-dimensional boundary-value problems near a polyhedral corner of the domain.

Walden, H.↗
NASA NTRS1972

Methods and approximations for the computation of transmission profiles in the v4 band of methane in the atmosphere of Jupiter.

This note discusses the validity of certain band models and scaling approximations for computing transmissions in the v4 band of methane along inhomogeneous paths in the atmosphere of Jupiter. It is shown that Goody's random band model approximates the results of a rigorous numerical line-by-line calculation of the transmission profile of a Jovian model atmosphere.

Taylor, F. W.↗
NASA NTRS1973

The relativistic dynamics of a point charge in the field of a plane electromagnetic wave traveling in the direction of a uniform static magnetic field

The motion of a charged particle in electromagnetic fields of various geometric configurations and arising from a variety of sources is of intrinsic interest in electromagnetic theory. The particular configuration consisting of a plane wave propagating in the presence of a static uniform magnetic field whose direction is parallel to the wave normal is examined. The analysis presented here is treated within the context of classical electromagnetic theory. A numerical solution - at least to the approximate Lorentz-Dirac equation - is obtained.

Mitchell, T. P.↗