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Overview of multifluid-flow-calculation methods

Description: Two categories of numerical methods which may be useful in multiphase flow research are discussed. The first category includes methods which are specifically intended for accurate computation of discontinuities, such as the method of characteristics, particle-in-cell method, flux-corrected transport, and random choice methods. Methods in this category could be applied to research on rocket exhaust plumes and interior ballistics. The second category includes methods for smooth, subsonic flows, such as fractional step methods, semi-implicit method, and methods which treat convection implicitly. The subsonic flow methods could be of interest for ice flows. (LCL)
Date: January 1, 1981
Creator: Stewart, H.B.
Partner: UNT Libraries Government Documents Department

Chaos, dynamical structure and climate variability

Description: Deterministic chaos in dynamical systems offers a new paradigm for understanding irregular fluctuations. Techniques for identifying deterministic chaos from observed data, without recourse to mathematical models, are being developed. Powerful methods exist for reconstructing multidimensional phase space from an observed time series of a single scalar variable; these methods are invaluable when only a single scalar record of the dynamics is available. However, in some applications multiple concurrent time series may be available for consideration as phase space coordinates. Here the authors propose some basic analytical tools for such multichannel time series data, and illustrate them by applications to a simple synthetic model of chaos, to a low-order model of atmospheric circulation, and to two high-resolution paleoclimate proxy data series. The atmospheric circulation model, originally proposed by Lorenz, has 27 principal unknowns; they establish that the chaotic attractor can be embedded in a subspace of eight dimensions by exhibiting a specific subset of eight unknowns which pass multichannel tests for false nearest neighbors. They also show that one of the principal unknowns in the 27-variable model--the global mean sea surface temperature--is of no discernible usefulness in making short-term forecasts.
Date: September 1, 1995
Creator: Stewart, H.B.
Partner: UNT Libraries Government Documents Department

Dynamical structure in paleoclimate data

Description: Deterministic chaos in dynamical systems offers a new paradigm for understanding irregular fluctuations. The theory of chaotic dynamical systems includes methods which can test whether any given set of time series data, such as paleoclimate proxy data, are consistent with a deterministic interpretation. Paleoclimate data with annual resolution and absolute dating provide multiple channels of concurrent time series; these multiple time series can be treated as potential phase space coordinates to test whether interannual climate variability is deterministic. Dynamical structure tests which take advantage of such multichannel data are proposed and illustrated by application to a simple synthetic model of chaos, and to two paleoclimate proxy data series.
Date: December 1, 1994
Creator: Stewart, H.B.
Partner: UNT Libraries Government Documents Department

Assessment of the IVA3 code for multifield flow simulation. Formal report

Description: This report presents an assessment of the IVA3 computer code for multifield flow simulation, as applied to the premixing phase of a hypothetical steam explosion in a water-cooled power reactor. The first section of this report reviews the derivation of the basic partial differential equations of multifield modeling, with reference to standard practices in the multiphase flow literature. Basic underlying assumptions and approximations are highlighted, and comparison is made between IVA3 and other codes in current use. Although Kolev`s derivation of these equations is outside the mainstream of the multiphase literature, the basic partial differential equations are in fact nearly equivalent to those in other codes. In the second section, the assumptions and approximations required to pass from generic differential equations to a specific working form are detailed. Some modest improvements to the IVA3 model are suggested. In Section 3, the finite difference approximations to the differential equations are described. The discretization strategy is discussed with reference to numerical stability, accuracy, and the role of various physical phenomena - material convection, sonic propagation, viscous stress, and interfacial exchanges - in the choice of discrete approximations. There is also cause for concern about the approximations of time evolution in some heat transfer terms, which might be adversely affecting numerical accuracy. The fourth section documents the numerical solution method used in IVA3. An explanation for erratic behavior sometimes observed in the first outer iteration is suggested, along with possible remedies. Finally, six recommendations for future assessment and improvement of the IVA3 model and code are made.
Date: July 1, 1995
Creator: Stewart, H.B.
Partner: UNT Libraries Government Documents Department

Phase portrait methods for verifying fluid dynamic simulations

Description: As computing resources become more powerful and accessible, engineers more frequently face the difficult and challenging engineering problem of accurately simulating nonlinear dynamic phenomena. Although mathematical models are usually available, in the form of initial value problems for differential equations, the behavior of the solutions of nonlinear models is often poorly understood. A notable example is fluid dynamics: while the Navier-Stokes equations are believed to correctly describe turbulent flow, no exact mathematical solution of these equations in the turbulent regime is known. Differential equations can of course be solved numerically, but how are we to assess numerical solutions of complex phenomena without some understanding of the mathematical problem and its solutions to guide us
Date: January 1, 1989
Creator: Stewart, H.B.
Partner: UNT Libraries Government Documents Department

Forecasting catastrophe by exploiting chaotic dynamics

Description: Our purpose here is to introduce a variation on the theme of short term forecasting from a chaotic time series. We show that for the lowest-dimensional chaotic attractors, it is possible to predict incipient catastrophes, or crises, by examining time series data taken near the catastrophic bifurcation threshold, but always remaining on the safe side of the threshold.
Date: January 1, 1990
Creator: Stewart, H.B. & Lansbury, A.N.
Partner: UNT Libraries Government Documents Department

High-Temperature Gas-Cooled Reactor Critical Experiment and Its Application

Description: Two types of critical experiments were conducted in support of the 40- Mw(e) Peach Bottom HTGR nucleardesign program. The first was the test-lattice experiment, where detailed measurements of reaction rates were examined in a lattice having a cold neutron spectrum characteristic of the HTGR. This program provided a method for checking the resonance integral of thorium, the Doppler coeificient of thorium, the detailed flux distribution in the lattice, and control-rod effectiveness within a cell. The second experiment was designed as a gross test of the calculational procedures and data. A small critical experiment having a clean geometry and a composition similar to that of the HTGR was constructed. This assembly had approximately one-sixth the volume of the HTGR core and was surrounded on all sides by a 2-ft graphite reflector. Owing to the small core size and the large reflector area, this experiment provided a severe test of the calculational methods. Experiments with this facility encompassed reactivity-coefficient measurements, neutron-flux distributions, effectiveness of groups of control rods, and a measurement of the overall temperature coefficient. (N.W.R.)
Date: August 1, 1963
Creator: Bardes, R. G.; Brown, J. R.; Drake, M. K.; Fischer, P. U.; Pound, D. C.; Sampson, J. B. et al.
Partner: UNT Libraries Government Documents Department

Chaotic transients and fractal structures governing coupled swing dynamics

Description: Numerical simulations are used to study coupled swing equations modeling the dynamics of two electric generators connected to an infinite bus by a simple transmission network. In particular, the effect of varying parameters corresponding to the input power supplied to each generator is studied. In addition to stable steady operating conditions, which should correspond to synchronized, normal operation, the coupled swing model has other stable states of large amplitude oscillations which, if realized, would represent non-synchronized motions: the phase space boundary separating their basins of attraction is fractal, corresponding to chaotic transient motions. These fractal structures in phase space and the associated fractal structures in parameter space will be of primary concern to engineers in predicting system behavior.
Date: January 1, 1990
Creator: Ueda, Y.; Enomoto, T. (Kyoto Univ. (Japan)) & Stewart, H.B. (Brookhaven National Lab., Upton, NY (USA))
Partner: UNT Libraries Government Documents Department