SEARCH · Search NASA
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Inviscid flux Jacobian matrices and their properties used in numerical solutions of conservation laws are extended to general, equilibrium gas laws. Exact and approximate generalizations of the Roe average are presented. Results are given for one-dimensional flow, and then extended to three-dimensional flow with time-varying grids.
Restricted three-body calculations of high-inclination low-impact-parameter encounters between a disk galaxy and its companion are used to demonstrate that the shell-like ripples noted in a number of disk galaxies are also collisional artifacts. It is suggested that some of the ripples may be the results of internal oscillations following such encounters. It is assumed that the target is an early-type disk with a sufficiently low gas fraction that recent star formation does not dominate the appearance of the disturbed disk.
Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.
This paper treats the accurate and efficient calculation of thermodynamic properties of arbitrary gas mixtures for equilibrium flow computations. New improvements in the Stupochenko-Jaffe model for the calculation of thermodynamic properties of diatomic molecules are presented. A unified formulation of equilibrium calculations for gas mixtures in terms of irreversible entropy is given. Using a highly accurate thermo-chemical data base, a new, efficient and vectorizable search algorithm is used to construct piecewise interpolation procedures with generate accurate thermodynamic variable and their derivatives required by modern computational algorithms. Results are presented for equilibrium air, and compared with those given by the Srinivasan program.
Dynamical friction is incorporated in the numerical modeling of colliding ring galaxies. It is shown that dynamical friction may lead to the capture of an initially unbound companion into a damped oscillatory orbit before ultimately merging with the target disk. In the late stages of its motion the companion may be virtually merged with the main galaxy while rings are still propagating in the disk. This raises the possibility that there exist (at least) two classes of ring galaxies: a class of ring galaxies with separate detached companions in which dynamical friction is too weak to have captured the collider, and a second class with no apparent companion in which the latter has either merged with the target galaxy or has disrupted. These two classes could possibly be identified with O-type and P-type ring galaxies of Few and Madore (1986).
Modern numerical techniques employing properties of flux Jacobian matrices are extended to general, nonequilibrium flows. Generalizations of the Beam-Warming scheme, Steger-Warming and van Leer Flux-vector splittings, and Roe's approximate Riemann solver are presented for 3-D, time-varying grids. The analysis is based on a thermodynamic model that includes the most general thermal and chemical nonequilibrium flow of an arbitrary gas. Various special cases are also discussed.
Improved formulation includes generalized Roe average and extension to three dimensions. Flux Jacobian matrices derived for use in numerical solutions of conservation-law differential equations of inviscid flows of ideal gases extended to real gases. Real-gas formulation of these matrices retains simplifying assumptions of thermodynamic and chemical equilibrium, but adds effects of vibrational excitation, dissociation, and ionization of gas molecules via general equation of state.
Various methods of calculating the internal energy of diatomic molecules are studied. An accurate and efficient method for computing the eigenvalues of the vibrational Schroedinger equation for an arbitrary potential is developed. The method is based on a finite-element discretization using the cubic Lobatto element. A combination of spectrum slicing and the Laguerre algorithm is used to solve for the eigenvalues. A simple method to compute the quasi-bound states is presented. For N2 molecules, all vibrational-rotational states of eleven available electronic potentials are computed, and summed to obtain the exact internal energy function with temperature. The total computation required 314 seconds of CPU-time on NASA's Cray 2 computer. Various approximate models are discussed and compared with the exact numerical simulation. It is shown that the splitting of the macroscopic internal energy into separate electronic, rotational, and vibrational energies is not justified at high temperatures.
Interacting galaxies show a variety of exotic morphologies besides the well-known rings, spirals, and bars. It is proposed that many of these can be identified with nonlinear, caustic structures that are known from singularity theory to be generic in collisionless dynamics. A simple kinematical model for stellar orbits is used to study the development of caustic waveforms in galaxy disks following impulsive, nonaxially symmetric (collisional) disturbances. It appears that all of the caustics known from singularity theory to be generic in two dimensions develop as transient forms in at least some moderately off-center collisions. The more complex, higher-order caustics appear most prominently in the more off-center and larger amplitude disturbances. It is further suggested that the highly nonlinear caustic waves may play an important role in interaction-induced star formation.
Numerical, restricted three-body and analytic calculations are used to study the formation and propagation of cylindrically symmetric stellar ring waves in galaxy disks. It is shown that such waves can evolve in a variety of ways, depending on the amplitude of the perturbation and the potential of the target galaxy. Rings can thicken as they propagate outward, remain at a nearly constant width, or be pinched off at large radii. Multiple, closely spaced rings can result from a low-amplitude collision, while an outer ring can appear well-separated from overlapping inner rings or an apparent lens structure in halo-dominated potentials. All the single-encounter rings consist of paired fold caustics. The simple, impulsive, kinematic oscillation equations appear to provide a remarkably accurate model of the numerical simulations. Simple analytic approximations to these equations permit very good estimates of oscillation periods and amplitudes, the evolution of ring widths, and ring birth and propagation characteristics.
Generalizations of the two flux-vector splittings and the Roe average to an arbitrary equilibrium gas are presently shown to introduce one degree of freedom in each case. The forms developed are those believed to be the simplest capable of satisfying basic physical principles while being valid for the most general flow conditions and gas laws, entailing only minor modifications of the perfect gas formulas. The flux-vector splittings represent a simpler problem, since they involve a single thermodynamic state for each split-flux term; only the pressure and the sound speed need to be evaluated, in place of the individual pressure derivatives.
The azimuthally averaged neutral hydrogen (HI) distribution, and the total gas density distribution derived from HI and CO observations (N sub H2 = 2.8 x 10(exp 20) I sub CO) as a function of radius in several nearby, early-type disks are examined.
Multi-color surface photometry (BVri) is presented for the tidal features in a sample of interacting galaxies. Large color variations are found between the morphological components and within the individual components. The blue colors in the primary and the tidal features are most dramatic in B-V, and not in V-i, indicating that star formation instead of metallicity or age dominates the colors. Color variations between components is larger in systems shortly after interaction begins and diminishes to a very low level in systems which are merged. Photometric models for interacting systems are presented which suggest that a weak burst of star formation in the tidal features could cause the observed color distributions. Dynamical models indicate that compression occurs during the development of tidal features causing an increase in the local density by a factor of between 1.5 and 5. Assuming this density increase can be related to the star formation rate by a Schmidt law, the density increases observed in the dynamical models may be responsible for the variations in color seen in some of the interacting systems. Limitations of the dynamical models are also discussed.
The author lists a few reasons for studying collisions with relatively low mass companions, specifically those that are less than about one third of the mass of the target galaxy. The primary effect of such collisions on a target galaxy with a 'cold' disk component is the generation of waves in the disk. The focus here is on the purely stellar waves in such disks. The example of a ring galaxy case is examined.
A series of one and two dimensional hydrodynamic simulations of a ring wave in interstellar gas disks was completed. These calculations included nonlinear source terms to model the effects of interstellar interactions and star formation, as well as the spatial-temporal gas flow. Toomre's kinematical model was merged with the Arnold, Shandarin, and Zeldovich 'pancake' theory of caustics in galaxy formation. The resulting theory can describe almost all the structure in restricted three-body simulations of single-pass collisions, even with multi-component potentials. Off-center galactic collisions were studied to understand the dynamics involved. Multi-color optical and near-infrared observations of faint tidal features were performed in about two dozen interacting galaxies selected from the Arp atlas. This sample provided evidence for ongoing star formation in tidal structures, and even enhancements of star formation in some cases. The task of assembling the data for gas-rich, late-type galaxies, was undertaken to see if a more coherent picture of the gas distribution would emerge from the more complete data. Analytic solutions of the equations with subsonic flows to balance gas consumption for expulsion form a galactic fountain were also derived.
Hydrodynamic constraints or driving forces that determine steady disk gas radial distributions are discussed, and observed gas distributions in late-type disks and correlations with disk rotation curves are analyzed. Evidence for quasi-steady states with radial gas flow is examined, and gas consumption rates and stellar density profiles are discussed, as are models of steady states with radial flows and more extreme 'driven' disks. The results indicate that the radial structure of a gas-rich disk can be simply and consistently accounted for as an azimuthally averaged hydrodynamic steady state in a fixed gravitational potential.
The time-dependent, three-dimensional incompressible Navier-Stokes equations are presently solved in generalized coordinate systems by means of a fractional-step method whose primitive variable formulation uses as dependent variables, in place of the Cartesian components of the velocity: (1) pressure (defined at the center of the computational cell), and (2) volume fluxes across the faces of the cells. The momentum equations are solved by means of an approximate factorization method. A novel 'ZEBRA' scheme incorporating four-color ordering efficiently solves the Poisson equation. Illustrative two- and three-dimensional laminar flow test cases are computed and evaluated relative to extant numerical and experimental results, and good agreement is obtained.
The present method of addressing the resonance problems that emerge in such MHD phenomena as the resonant absorption of waves at the Alfven resonance point avoids solving the fourth-order differential equation of dissipative MHD by recourse to connection formulae across the dissipation layer. In the second part of this investigation, the absorption of solar 5-min oscillations by sunspots is interpreted as the resonant absorption of sounds by a magnetic cylinder. The absorption coefficient is interpreted (1) analytically, under certain simplifying assumptions, and numerically, under more general conditions. The observed absorption coefficient magnitude is explained over suitable parameter ranges.