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NASA NTRS1986

Implicit hybrid schemes for the flux-difference split, three-dimensional Navier-Stokes equations

Implicit hybrid algorithms employing symmetric planar Gauss-Seidel (SPGS) relaxation and either block-tridiagonally structured coefficient matrices (AF-SPGS) or block-triangular coefficient matrices (LU-SPGS) are derived to solve the flux-difference-split Navier-Stokes equations for three-dimensional incompressible flow in an upwind scheme. The physical basis of the approach is discussed, and results for problems involving vortex flow around a thin delta wing at Reynolds numbers 900,000 and 10,000 are presented graphically. It is found that AF-SPGS converges faster on vector computers which depend on long vector lengths to achieve optimum performance, whereas LU-SPGS is preferable on sequentially operating machines and vector computers using shorter vector lengths.

Hartwich, P.-M.↗

NASA NTRS1987

Artificial dissipation and central difference schemes for the Euler and Navier-Stokes equations

An artificial dissipation model, including boundary treatment, that is employed in many central difference schemes for solving the Euler and Navier-Stokes equations is discussed. Modifications of this model such as the eigenvalue scaling suggested by upwind differencing are examined. Multistage time stepping schemes with and without a multigrid method are used to investigate the effects of changes in the dissipation model on accuracy and convergence. Improved accuracy for inviscid and viscous airfoil flow is obtained with the modified eigenvalue scaling. Slower convergence rates are experienced with the multigrid method using such scaling. The rate of convergence is improved by applying a dissipation scaling function that depends on mesh cell aspect ratio.

Swanson, R. C.↗

NASA NTRS1987

Calculating rotordynamic coefficients of seals by finite-difference techniques

For modelling the turbulent flow in a seal the Navier-Stokes equations in connection with a turbulence (kappa-epsilon) model are solved by a finite-difference method. A motion of the shaft round the centered position is assumed. After calculating the corresponding flow field and the pressure distribution, the rotor-dynamic coefficients of the seal can be determined. These coefficients are compared with results obtained by using the bulk flow theory of Childs and with experimental results.

Dietzen, F. J.↗

NASA NTRS1986

Higher-order flux difference splitting schemes for the Euler equations using upstream interpolations

A class of explicit two time-level, 2p + 1 space-point, (2p 1)-th order, upwind-biased flux difference splitting schemes are proposed for the numerical advection based on Lagrange's interpolation, and the method is an accord with the physical domain of dependence. A normalized Jacobian coefficient matrix is introduced to convert the schemes to hyperbolic systems of conservation laws, and approaches to make the higher-order schemes total variation stable are discussed. Accuracy and stability of the present schemes are examined, and implicit total variation diminishing schemes are developed for steady-state calculations.Application to gasdynamic problems for both steady and unsteady flows covering a wide range of Mach numbers is considered, and results for a blast wave passing a cylinder, and head-on collision of two blast waves over a circular arc, are presented. The flow patterns were found to be symmetric, and good resolution of flow structures was obtained.

Yang, J. Y.↗

NASA NTRS1986

Inorganic and protein crystal growth - Similarities and differences

Transport and interface kinetic concepts for the design and control of inorganic crystal growth experiments are reviewed, and their applications and limitations in protein crystal growth are considered. It is suggested that the interfacial concentration gradients are steeper for faster crystallization, and that the interfacial concentration distributions for the protein and the precipitant can differ significantly. Results show that uniformity in crystal composition and steady-state conditions in growth kinetics are favored by larger sample size, since surface-tension gradients drive strong in microgravity experiments and in small samples on earth.

Rosenberger, F.↗

NASA NTRS1986

How different a modern SST would be

The characteristics of a proposed SST are described. The proposed aircraft is to have two engines and an arrow-wing design, a passenger capacity of 250, and attain speeds of Mach 2.7. The low fineness ratio, low-aspect ratio wing planform, different engine nacelles location, and improved lift-to-drag ratio of the aircraft contribute to attaining an economical supersonic cruise. The proposed structural design and materials for the aircraft are examined; the material and design are to be applicable to high Mach and high temperature. Changes in the SST propulsion system, the nozzle designs, and landing and takeoff procedures to improve the operation of the aircraft are discussed.

Driver, C.↗

NASA NTRS1986

Numerical aspects of different Kalman filter implementations

A theoretical analysis is made of the error propagation due to numerical roundoff for four different Kalman filter implementations: the conventional Kalman filter, the square root covariance filter, the square root information filter, and the Chandrasekhar square root filter. An experimental analysis is performed to validate the new insights gained by the theoretical analysis.

Verhaegen, M.↗

NASA NTRS1986

A review of current finite difference rotor flow methods

Rotary-wing computational fluid dynamics is reaching a point where many three-dimensional, unsteady, finite-difference codes are becoming available. This paper gives a brief review of five such codes, which treat the small disturbance, conservative and nonconservative full-potential, and Euler flow models. A discussion of the methods of applying these codes to the rotor environment (including wake and trim considerations) is followed by a comparison with various available data. These data include tests of advancing lifting and nonlifting, and hovering model rotors with significant supercritical flow regions. The codes are also compared for computational efficiency.

Caradonna, F. X.↗

NASA NTRS1985

Finite difference methods for the solution of unsteady potential flows

A brief review is presented of various problems which are confronted in the development of an unsteady finite difference potential code. This review is conducted mainly in the context of what is done for a typical small disturbance and full potential methods. The issues discussed include choice of equation, linearization and conservation, differencing schemes, and algorithm development. A number of applications including unsteady three-dimensional rotor calculation, are demonstrated.

Caradonna, F. X.↗

NASA NTRS1986

CONDIF - A modified central-difference scheme with unconditional stability and very low numerical diffusion

This paper describes a method, called CONDIF, which retains the essential nature of the central difference scheme (CDS) but eliminates the over- and under-shoots. It modifies the CDS by introducing a controlled amount of numerical diffusion based on local gradients. The results obtained for a number of test problems show that the CONDIF is significantly more accurate than the hybrid scheme when the Peclet number is very high and the flow is at large angles to the grid. In the worst case, it yields results similar to those of the hybrid scheme. Though the CONDIF is unconditionally stable, under some conditions the rate of convergence deteriorates as the grid Peclet number is increased. Efforts are currently underway to develop a faster converging variation of CONDIF.

Runchal, Akshai K.↗

NASA NTRS1986

Some insights into the stability of difference approximations for hyperbolic initial-boundary-value problems

This paper states a conjecture which relates Lax-Richmyer stability to the algebraic test of the stability theory of Gustafsson, Kreiss, and Sundstrom (1972), developed for difference approximations to initial boundary value problems where the matrix size J increases linearly with n as n goes to infinity. This corresponds to mesh refinement in both space and time for t = n x delta t = constant.

Warming, Robert F.↗

NASA NTRS1986

Solution of nonlinear finite difference ocean models by optimization methods with sensitivity and observational strategy analysis

The paper studies with finite difference nonlinear circulation models the uncertainties in interesting flow properties, such as western boundary current transport, potential and kinetic energy, owing to the uncertainty in the driving surface boundary condition. The procedure is based upon nonlinear optimization methods. The same calculations permit quantitative study of the importance of new information as a function of type, region of measurement and accuracy, providing a method to study various observing strategies. Uncertainty in a model parameter, the bottom friction coefficient, is studied in conjunction with uncertain measurements. The model is free to adjust the bottom friction coefficient such that an objective function is minimized while fitting a set of data to within prescribed bounds. The relative importance of the accuracy of the knowledge about the friction coefficient with respect to various kinds of observations is then quantified, and the possible range of the friction coefficients is calculated.

Schroeter, Jens↗

NASA NTRS1987

Artificial dissipation and central difference schemes for the Euler and Navier-Stokes equations

An artificial dissipation model, including boundary treatment, that is employed in many central difference schemes for solving the Euler and Navier-Stokes equations is discussed. Modifications of this model such as the eigenvalue scaling suggested by upwind differencing are examined.Multistage time stepping schemes with and without a multigrid method are used to investigate the effects of changes in the dissipation model on accuracy and convergence. Improved accuracy for inviscid and viscous airfoil flows is obtained with the modified eigenvalue scaling. Slower convergence rates are experienced with the multigrid method using such scaling. The rate of convergence is improved by applying a dissipation scaling function that depends on mesh cell aspect ratio.

Swanson, R. C.↗

NASA NTRS1987

On the validity of the modified equation approach to the stability analysis of finite-difference methods

The validity of the modified equation stability analysis introduced by Warming and Hyett was investigated. It is shown that the procedure used in the derivation of the modified equation is flawed and generally leads to invalid results. Moreover, the interpretation of the modified equation as the exact partial differential equation solved by a finite-difference method generally cannot be justified even if spatial periodicity is assumed. For a two-level scheme, due to a series of mathematical quirks, the connection between the modified equation approach and the von Neuman method established by Warming and Hyett turns out to be correct despite its questionable original derivation. However, this connection is only partially valid for a scheme involving more than two time levels. In the von Neumann analysis, the complex error multiplication factor associated with a wave number generally has (L-1) roots for an L-level scheme. It is shown that the modified equation provides information about only one of these roots.

Chang, Sin-Chung↗

NASA NTRS1987

Finite difference solution for a generalized Reynolds equation with homogeneous two-phase flow

An attempt is made to relate elements of two-phase flow and kinetic theory to the modified generalized Reynolds equation and to the energy equation, in order to arrive at a unified model simulating the pressure and flows in journal bearings, hydrostatic journal bearings, or squeeze film dampers when a two-phase situation occurs due to sudden fluid depressurization and heat generation. The numerical examples presented furnish a test of the algorithm for constant properties, and give insight into the effect of the shaft fluid heat transfer coefficient on the temperature profiles. The different level of pressures achievable for a given angular velocity depends on whether the bearing is thermal or nonisothermal; upwind differencing is noted to be essential for the derivation of a realistic profile.

Braun, M. J.↗

NASA NTRS1987

Hemispheric differences in the morphology of the high latitude ionosphere measured at about 500 km

Ambient electron density measurements made by the radio frequency capacitance probe on Ariel 4 have been analyzed in order to study the structures present at about 500 km altitude at latitudes poleward of + or - 50 deg Lambda during the 1971 Northern Hemisphere winter (December solstice) and the 1972 Southern Hemisphere winter (June solstice); data obtained on 94 days centered on each solstice have been used. The general morphology of, and the extreme densities within, the midlatitude electron density trough, the polar cap depletions, and the electron density enhancements associated with the cusp-auroral zone were determined statistically. Analyses of data acquired during quiet magnetic conditions show that the Northern and Southern Hemisphere winter ionospheres were significantly different; in particular, the Southern Hemisphere densities were lower than those in the Northern Hemisphere. The maximum electron densities observed in the Northern Hemisphere occurred in a magnetic-local-time range symmetrical about the 02-14 MLT meridian, whereas in the Southern Hemisphere the maxima were symmetrical with respect to the midnight-noon magnetic meridian.

Tulunay, Y. K.↗

NASA NTRS1987

Global excitation of wave phenomena in a dissipative multiconstituent medium. III - Response characteristics for different sources in the earth's thermosphere

A linear trasnfer function model of the earth's thermosphere which includes the electric field momentum source is used to study the differences in the response characteristics for Joule heating and momentum coupling in the thermosphere. It is found that, for Joule/particle heating, the temperature and density perturbations contain a relatively large trapped component which has the property of a low-pass filter, with slow decay after the source is turned off. The decay time is sensitive to the altitude of energy deposition and is significantly reduced as the source peak moves from 125 to 150 km. For electric field momentum coupling, the trapped components in the temperature and density perturbations are relatively small. In the curl field of the velocity, however, the trapped component dominates, but compared with the temperature and density its decay time is much shorter. Outside the source region the form of excitation is of secondary importance for the generation of the various propagating gravity wave modes.

Mayr, H. G.↗

NASA NTRS1987

The finite-difference time-domain (FD-TD) method for electromagnetic scattering and interaction problems

The formulation and recent applications of the finite-difference time-domain (FD-TD) method for the numerical modeling of electromagnetic scattering and interaction problems are considered. It is shown that improvements in FD-TD modeling concepts and software implementation often make it a preferable choice for structures which cannot be easily treated by conventional integral equations and asymptotic approaches. Recent FD-TD modeling validations in research areas including coupling to wires and wire bundles in free space and cavities, scattering from surfaces in relativistic motion, inverse scattering, and radiation condition theory, are reviewed. Finally, the advantages and disadvantages of FD-TD, and guidelines concerning when FD-TD should and should not be used in high-frequency electromagnetic modeling problems, are summarized.

Taflove, A.↗