70 research outputs found
Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science
Fourth NASA Workshop on Computational Control of Flexible Aerospace Systems, part 2
A collection of papers presented at the Fourth NASA Workshop on Computational Control of Flexible Aerospace Systems is given. The papers address modeling, systems identification, and control of flexible aircraft, spacecraft and robotic systems
Proceedings of the Workshop on Applications of Distributed System Theory to the Control of Large Space Structures
Two general themes in the control of large space structures are addressed: control theory for distributed parameter systems and distributed control for systems requiring spatially-distributed multipoint sensing and actuation. Topics include modeling and control, stabilization, and estimation and identification
[Research activities in applied mathematics, fluid mechanics, and computer science]
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period April 1, 1995 through September 30, 1995
Proceedings of the Workshop on Computational Aspects in the Control of Flexible Systems, part 2
The Control/Structures Integration Program, a survey of available software for control of flexible structures, computational efficiency and capability, modeling and parameter estimation, and control synthesis and optimization software are discussed
Classically Unstable Approximations for Linear Evolution Equations and Applications.
Temporal discretization methods for evolutionary differential equations that factorize the resolvent into a product of easily computable operators have great numerical appeal. For instance, the alternating direction implicit (ADI) method of Peaceman-Rachford for 2-D parabolic problems greatly reduces the simulation time when compared with the Crank-Nicolson scheme. However, just like many other factorized approximation methods that exhibit numerical stability, the ADI method is known to satisfy only the Von Neumann stability condition, a necessary condition that is usually surmised as sufficient in practical cases as pointed out by Lax and Richtmyer. Intensive efforts have been directed to understand the Von Neumann condition, e.g. by John, Lax and Richtmyer, Lax, Lax and Wendroof, and Strang. Their way of investigation is to find conditions under which the Von Neumann condition becomes sufficient for stability. Recently, we found a factorized (FAC) temporal approximation method and a well-posed problem for which the FAC method is unstable but satisfies the Von Neumann stability condition. However, the method still exhibits excellent numerical stability even for large time step sizes. Thus, to better understand the Von Neumann condition, we investigate the relation between stability and convergence in directions not covered by the Lax equivalence theorem which equates the stability with convergence for all initial values under some uniform consistency condition. To do that, we extend the Trotter-Kato theorem and the Chernoff product formula to possibly unstable spatial and temporal approximations and indicate how our results can be used for some unstable factorized approximation methods
1991 Summer Study Program in Geophysical Fluid Dynamics : patterns in fluid flow
The GFD program in 1991 focused on pattern forming processes in physics and geophysics. The pricipallecturer, Stephan
Fauve, discussed a variety of systems, including our old favorite, Rayleigh-Bénard convection, but passing on to exotic
examples such as vertically vibrated granular layers. Fauve's lectures emphasize a unified theoretical viewpoint based on
symmetry arguments. Patterns produced by instabilties can be described by amplitude equations, whose form can be deduced
by symmetry arguments, rather than the asymptotic expansions that have been the staple of past Summer GFD Programs. The
amplitude equations are far simpler than the complete equations of motion, and symetry arguments are easier than
asymptotic expansions. Symmetry arguments also explain why diverse systems are often described by the same amplitude
equation. Even for granular layers, where there is not a universaly accepted continuum description, the appropnate amplitude
equation can often be found using symmetry arguments and then compared with experiment.
Our second speaker, Daniel Rothan, surveyed the state of the art in lattice gas computations. His lectures illustrate the
great utility of these methods in simulating the flow of complex multiphase fluids, particularly at low Reynolds numbers. The
lattice gas simulations reveal a complicated phenomenology much of which awaits analytic exploration.
The fellowship lectures cover broad ground and reflect the interests of the staff members associated with the program. They
range from the formation of sand dunes, though the theory of lattice gases, and on to two dimensional-turbulence and
convection on planetary scales. Readers desiring to quote from these report should seek the permission of the authors (a
partial list of electronic mail addresses is included on page v). As in previous years, these reports are extensively reworked for
publication or appear as chapters in doctoral theses. The task of assembling the volume in 1991 was at first faciltated by our
newly acquired computers, only to be complicated by hurricane Bob which severed electric power to Walsh Cottage in the
final hectic days of the Summer.Funding was provided by the National Science Foundation
through Grant No. OCE 8901012
Recommended from our members
Office of Advanced Scientific Computing Research Applied Mathematics Principal Program Annual PI Meeting Abstracts
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