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Effects of finite size on the critical behavior of fluid films

Description: This thesis presents the results of refractive index studies performed on films of a critical mixture of 2,6-lutidine+water near the lower critical point. The films ranged in thickness from 0.46 ..mu..m to approx. 300 ..mu..m and were confined between the highly reflecting surfaces of a pair of optical flats in an interferometer. Above the critical temperatures of these films, in the two-phase region, ..delta..n was measured, the difference between the refractive indexes of the two phases. Since to a close approximation ..delta..n is proportional to the order parameter, measurements of ..delta..n as a function of temperature map out the coexistence curves of the films.
Date: January 1, 1978
Creator: Scheibner, B A
Partner: UNT Libraries Government Documents Department

Adaptive mesh refinement for 1-dimensional gas dynamics

Description: We consider the solution of the one-dimensional equation of gas-dynamics. Accurate numerical solutions are difficult to obtain on a given spatial mesh because of the existence of physical regions where components of the exact solution are either discontinuous or have large gradient changes. Numerical methods treat these phenomena in a variety of ways. In this paper, the method of adaptive mesh refinement is used. A thorough description of this method for general hyperbolic systems is given elsewhere and only properties of the method pertinent to the system are elaborated.
Date: January 1, 1982
Creator: Hedstrom, G.; Rodrigue, G.; Berger, M. & Oliger, J.
Partner: UNT Libraries Government Documents Department

The relaxation of the second moments in rapid shear flows of smooth disks

Description: This paper compares the results of numerical simulations for two- dimensional, rapid, homogeneous shear flows of identical, smooth, inelastic disks with the predictions of Jenkins and Richman (JFM 192, 313-328 (1988)) for the relaxation of the second moments of the velocity distribution function following a homogeneous, but anisotropic disturbance of their steady values. For nearly elastic disks, the time-history of the relaxation is in excellent agreement with the theory in both its dense and dilute limits. However, deviations are observed in the case of inelastic particles. 2 refs., 8 figs.
Date: January 1, 1991
Creator: Louge, M.Y. (Cornell Univ., Ithaca, NY (United States). Sibley School of Mechanical and Aerospace Engineering); Jenkins, J.T. (Cornell Univ., Ithaca, NY (United States). Dept. of Theoretical and Applied Mechanics) & Hopkins, M.A. (Army Cold Regions Research and Engineering Lab., Hanover, NH (United States))
Partner: UNT Libraries Government Documents Department

Production of optically thin free-standing oil films from the edge of a rotating disc

Description: A method is described for forming thin free-standing oil films which are spun from the edge of a sharp-edged rotating disc. The films can be made thin enough to show strong optical interference colors when viewed in white light. The thinnest films have areal densities down to about 10 to 20 ..mu..gm/cm/sup 2/. A stable roughly triangular film with an area of about 10 cm/sup 2/ and fairly uniform thickness can be readily produced. Much larger films having either greater thickness or less stability are also possible. Films have been produced both in air and in vacuum.
Date: January 1, 1980
Creator: Cramer, J.G.; Burch, D.F.; Rodenberg, R. & Cramer, P.B.
Partner: UNT Libraries Government Documents Department

Hybrid simulations

Description: The philosophy and numerical implementation of hybrid algorithms are reviewed. In the hybrid approximation, a plasma is described by a set of discrete equations, equivalent to a Vlasov-fluid system. The dynamics of one or more species are modeled using moment equations, while the remaining species are treated as a large number of individual macro-particles. In this paper the hybrid method will be compared to fluid and particle-in-cell algorithms, and the strengths and weaknesses of the various methods will be discussed. A specific limit of the hybrid model, that of macro-particle ions and massless, charge-neutralizing fluid electrons, will be analyzed in detail with particular emphasis on multi-dimensional codes.
Date: January 1, 1987
Creator: Quest, K.B.
Partner: UNT Libraries Government Documents Department

Equation of state of strongly coupled plasma mixtures

Description: Thermodynamic properties of strongly coupled (high density) plasmas of mixtures of light elements have been obtained by Monte Carlo simulations. For an assumed uniform charge background the equation of state of ionic mixtures is a simple extension of the one-component plasma EOS. More realistic electron screening effects are treated in linear response theory and with an appropriate electron dielectric function. Results have been obtained for the ionic pair distribution functions, and for the electric microfield distribution.
Date: February 3, 1984
Creator: DeWitt, H.E.
Partner: UNT Libraries Government Documents Department

Transition of fractal dimension in a latticed dynamical system

Description: We study a recursion relation that manifests two distinct routes to turbulence, both of which reproduce commonly observed phenomena: the Feigenbaum route, with period-doubling frequencies; and a much more general route with noncommensurate frequencies and frequency entrainment, and locking. Intermittency and large-scale aperiodic spatial patterns are reproduced in this new route. In the oscillatory instability regime the fracal dimension saturates at D/sub F/ approx. = 2.6 with imbedding dimensions while in the turbulent regime D/sub F/ saturates at 6.0. 19 refs., 3 figs.
Date: March 1, 1986
Creator: Duong-van, M.
Partner: UNT Libraries Government Documents Department

New approach to multiphase equilibria: application to high-pressure physics problems

Description: A multiphase, multicomponent equation-of-state (EOS) model based on first principles of statistical mechanics is described. The model has been used to study fluid-fluid phase separations in binary (H/sub 2/-He, Ar-Ne, Xe-He, and N/sub 2/-H/sub 2/O) and ternary or more complex systems involving species with C, H, N, and O atoms. Results of these calculations and a brief description of a new theory which can simultaneously describe both solid and fluid EOS properties are given. 26 refs., 4 figs.
Date: June 1, 1985
Creator: Ree, F.H.
Partner: UNT Libraries Government Documents Department

Flow and plasticity via nonequilibrium molecular dynamics

Description: The viscous flow of fluids and the plastic flow of solids, such as metals, are interesting from both the practical and the theoretical points of view. Atomistic molecular dynamics simulations provide a way of visualizing and understanding these flows in a detailed microscopic way. Simulations are necessarily carried out at relatively high rates of strain. For this reason they are ideally suited to the study of nonlinear flow phenomena: normal stresses induced by shear deformation, stress rotation, and the coupling of stress with heat flow, for instance. The simulations require appropriate boundary conditions, forces, and equations of motion. Newtonian mechanics is relatively inefficient for this simulation task. A modification, Nonequilibrium Molecular Dynamics, has been developed to simulate nonequilibrium flows. By now, many high-strain-rate rheological studies of flowing (viscous) fluids and (plastic) solids have been carried out. Here I describe the new methods used in the simulations and some results obtained in this way. A three-body shear-flow exercise is appended to make these ideas more concrete.
Date: June 11, 1984
Creator: Hoover, W.G.
Partner: UNT Libraries Government Documents Department

Acoustic damping for explicit calculations of fluid flow at low Mach number

Description: A method is proposed for damping the sound waves in explicit calculations of fluid flow at low Mach number, where sound waves are usually not of interest but may distract attention from other flow features. The method is based on the introduction of an artificial pressure q of the form q = - q/sub 0/rhoc/sup 2/..delta..t(del x u - del x u/sub 0/), where q/sub 0/ is a coefficient of order unity, rho is the density, c is the sound speed, ..delta..t is the time step, and u/sub 0/ is the velocity field that would obtain at zero Mach number. When del x u/sub 0/ is zero, the method becomes equivalent to the use of an artificial bulk viscosity q/sub 0/rhoc/sup 2/..delta..t. However, del x u/sub 0/ can be substantially different from zero in problems with heat or mass sources (e.g., combustion), and its inclusion is then essential to obtain the correct pressure field. The method is well suited for use in conjunction with explicit numerical schemes that employ acoustic subcycling or artificial reduction of the sound speed for improved efficiency at low Mach number. The beneficial effects of the method are illustrated by means of calculations with an acoustic subcycling computer program. 9 refs., 1 fig.
Date: January 1, 1986
Creator: Ramshaw, J.D.; O'Rourke, P.J. & Amsden, A.A.
Partner: UNT Libraries Government Documents Department

Hybrid simulation codes with application to shocks and upstream waves

Description: Hybrid codes in which part of the plasma is represented as particles and the rest as fluid are discussed. In the past few years such codes with particle ions and massless, fluid electrons have been applied to space plasmas, especially to collisionless shocks. All of these simulation codes are one-dimensional and similar in structure, except for how the field equation are solved. We describe in detail the various approaches that are used (resistive Ohm's law, predictor-corrector, Hamiltonian) and compare results from the various codes with examples taken from collisionless shocks and low frequency wave phenomena upstream of shocks.
Date: February 3, 1985
Creator: Winske, D.
Partner: UNT Libraries Government Documents Department

PIC (Particle-in-Cell) and its progeny

Description: The Particle-in-Cell (PIC) method was developed to solve numerically for the strongly contorting dynamics of several materials in two or three space dimensions. Related numerical techniques with Lagrangian marker particles are also discussed in this brief survey. An extensive bibliography lists many of the earlier publications describing these techniques.
Date: January 1, 1987
Creator: Harlow, F.H.
Partner: UNT Libraries Government Documents Department

Particle code simulations with injected particles

Description: As problems we are interested in become more complex, we often find our simulations stretching the limits of available computer resources. For example, an interesting problem is simulation of dissipation processes in sub-critical collisionless shocks. To simulate this system our simulation box must contain the shock and its upstream and downstream regions over the entire length of a run. If the shock moves with any appreciable speed the box must then be considerably larger than the shock thickness making it hard to resolve the shock front itself with a reasonable number of grid points. A solution to this problem is to run the simulation in the frame of reference of the shock. Particles are injected upstream of the shock and leave the simulation box downstream. With the shock stationary in the simulation box, we only need to contain enough of the up and downstream regions for the fields, etc., to settle down and separate the shock from the box boundaries. In this tutorial we consider some basic algorithms used in a practical particle injection code, such as the two dimensional WAVE code used at Los Alamos. We will try to present these ideas in a simple format general enough to be easily included in any particle code. Topics covered are: smoothly injecting particles, generating the distribution functions, time dependent injection density, and boundary conditions on fields and particles.
Date: January 1, 1985
Creator: Aldrich, C.H.
Partner: UNT Libraries Government Documents Department

Front tracking and two dimensional Riemann problems: a conference report

Description: A substantial improvement in resolution has been achieved for the computation of jump discontinuities in gas dynamics using the method of front tracking. The essential feature of this method is that a lower dimensional grid is fitted to and follows the discontinuous waves. At the intersection points of these discontinuities, two-dimensional Riemann problems occur. In this paper we study such two-dimensional Riemann problems from both numerical and theoretical points of view. Specifically included is a numerical solution for the Mach reflection, a general classification scheme for two-dimensional elementary waves, and a discussion of problems and conjectures in this area.
Date: January 1, 1984
Creator: Glimm, J.; Klingenberg, C.; McBryan, O.; Plohr, B.; Sharp, D. & Yaniv, S.
Partner: UNT Libraries Government Documents Department

Computational method for free surface hydrodynamics

Description: There are numerous flow phenomena in pressure vessel and piping systems that involve the dynamics of free fluid surfaces. For example, fluid interfaces must be considered during the draining or filling of tanks, in the formation and collapse of vapor bubbles, and in seismically shaken vessels that are partially filled. To aid in the analysis of these types of flow phenomena, a new technique has been developed for the computation of complicated free-surface motions. This technique is based on the concept of a local average volume of fluid (VOF) and is embodied in a computer program for two-dimensional, transient fluid flow called SOLA-VOF. The basic approach used in the VOF technique is briefly described, and compared to other free-surface methods. Specific capabilities of the SOLA-VOF program are illustrated by generic examples of bubble growth and collapse, flows of immiscible fluid mixtures, and the confinement of spilled liquids.
Date: January 1, 1980
Creator: Hirt, C.W. & Nichols, B.D.
Partner: UNT Libraries Government Documents Department

Fractional volume of fluid method for free boundary dynamics

Description: The volume of fluid (VOF) technique is presented as a simple and efficient means for numerically treating free boundaries embedded in a calculational mesh of Eulerian or Arbitrary-Lagrangian-Eulerian cells. It is particularly useful because it uses a minimum of stored information, treats intersecting free boundaries automatically, and can be readily extended to three-dimensional calculations.
Date: January 1, 1980
Creator: Nichols, B.D.; Hirt, C.W. & Hotchkiss, R.S.
Partner: UNT Libraries Government Documents Department

Complex temporal and spatial patterns in nonequilibrium systems

Description: Dynamical systems methods are being developed and used to characterize the formation and evolution of temporal and spatial patterns in systems maintained far from equilibrium. In particular, experiments and analyses are considering electrodeposition of fractal metallic clusters, pattern formation in reaction-diffusion systems, and the primary instabilities of some fluid flows. Novel reactors have been developed to search for chemical patterns (spatial variations in the chemical composition), and sustained patterns have been found in several different one- and two-dimensional geometries. Bifurcations in these patterns are studied by varying control parameters, e.g., the concentrations of the feed chemicals or the temperature. The observed two-dimensional chemical patterns range from the stationary patterns, similar to those predicted by Turing in 1952 but not observed until 1990, to chemical turbulence, which is characterized by large numbers of defects and a rapid decay of spatial correlations. These provide general insights into the formation of spatiotemporal patterns in nonequilibrium systems.
Date: September 1, 1991
Creator: Swinney, H. L.
Partner: UNT Libraries Government Documents Department

Analytical and numerical analysis of finite amplitude Rayleigh-Taylor instability

Description: We summarize the results obtained in the last year. These include a simple model of bubble competition in Rayleigh-Taylor unstable flows which gives results which are in good agreement with experiment. In addition the model has been compared with two dimensional numerical simulations of inviscid Rayleigh-Taylor instability using the cloud-in-cell method. These simulations can now be run into the late time regime and can track the competition of as many as ten bubbles. The improvement in performance over previous applications of the cloud-in-cell approach is due to the application of finite difference techniques designed to handle shock-like structures in the vorticity of the interface which occur at late times. We propose to extend the research carried thus far to Rayleigh-Taylor problems in three dimensional and convergent geometries as well as to two-fluid instabilities in which interface roll-up is observed. Finally we present a budget for the fiscal year 1987-1988. 6 refs.
Date: September 18, 1987
Creator: Meiron, D.I. & Saffman, P.G.
Partner: UNT Libraries Government Documents Department

Hydrodynamic effects in evaporating droplets

Description: The vaporization of a spherically symmetric liquid droplet homogeneously heated by a high-intensity laser pulse is investigated on the basis of a hydrodynamic description of the system composed of the vapor and ambient gas. In the limit of convective vaporization, the boundary conditions at the fluid-gas interface are formulated by using the notion of a Knudsen layer across which translational equilibrium is established. Numerical solutions to the hydrodynamic equations exhibit the existence of two shock waves propagating in opposite directions with respect to the contact discontinuity that separates the ambient gas and vapor. 17 refs., 6 figs.
Date: September 25, 1986
Creator: Armstrong, R.L. & Zardecki, A.
Partner: UNT Libraries Government Documents Department

Further studies on equal-order interpolation for Navier-Stokes

Description: The simplest quadrilateral element available for the incompressible Navier-Stokes equations is the mixed interpolation 4-node element with bilinear velocity and (piecewise) constant pressure - denoted herein by 4/1. The next simplest is the 4/4 element, in which (continuous) bilinear approximation is also employed for pressure - i.e., the simplest case of equal-order interpolation. The 4/4 element had been more or less rejected early-on, following the pioneering work of Hood and Taylor who first discovered that equal-order interpolation generated spurious pressures. The 4/1 element, on the other hand, has been very popular, even though it sometimes generates one spurious pressure mode (vs many for the 4/4 element) which is usually filterable. But the 4/1 element generates a poor approximation to (Del P) when distorted elements are employed (via the bilinear isoparametric technique), which often leads to large errors in velocity; e.g. this element generated wrong answers for vortex shedding on the same mesh for which a higher order element (9/4) performed well. Although the 4/4 element generates ostensibly useless pressures, the pressure gradient and the velocity field might be much more accurate than those from the 4/1 element, especially when distorted meshes are employed. Based on these observations, we have successfully tested the 4/4 element on two problems, reported herein, for which the 4/1 element failed. The 4/4 element is no panacea, however; the multiple (and generally unknown) spurious pressure modes (pure and impure) associated with equal-order interpolation leads to a generally delicate solution procedure. After summarizing our experience in this regard, we will present a viable technique for recovering a useful pressure field from the otherwise polluted pressures.
Date: October 1, 1983
Creator: Gresho, P.M.; Lee, R.L. & Sani, R.L.
Partner: UNT Libraries Government Documents Department

Drop separation by numerical solution of the Navier--Stokes equation

Description: A numerical model of separating drop behavior was constructed and tested by simulation, on a general-purpose digital computer, of a hypothetical two-immiscible-phase system. The model uses the Marker-and-Cell (MAC) method to solve the unsteady-state Navier--Stokes (momentum balance) equation with incompressible flow. Input to the model consists of fluid parameters (density, viscosity, interfacial tension), initial conditions( interface profile and velocities), and forcing functions. Simulation results consist of time-varying velocity and pressure fields, and all transformations of the interface profile. The simulation was seen to exhibit many of the features known to accompany separations observed in the laboratory, including characteristic profiles and flow patterns. The simulatio incorporates a one-parameter model of the interface, with the parameter being the equilibrium interfacial tension. Dynamic interfacial tension and interface viscosity are omitted. At each computational time frame the curvature of the interface is computed by numerically fitting a set of cubic splines to the coordinates of the particles which compose the interface. This curvature is used to compute the pressure drop across the phase boundary, and comprises the boundary condition for teh calculation of pressures within the drop. 62 references, 28 figures, 3 tables.
Date: January 1, 1978
Creator: Fitzgibbons, D.A.
Partner: UNT Libraries Government Documents Department