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This volume covers the proceedings ofthe ICASE/LaRC workshop on
"Finite Element Theory and Application" held during July 28-30,
1986. The purpose of this workshop was to provide an update on the
status of finite element theory, to assess the impactoftbis theory
on practice, and to suggest directions for Cuture research. There
were thirteen participants in the workshop. Some of them were
leading mathematicians working on the finite element theory, and
the rest expert practitioners in the areas of fluid dynamics and
structural analysis. The first six articles in this volume provide
a brief review of the theoretical and computational aspects of
finite element methods (FEM). The remaining seven articles deal
with a variety of applications highlighting the type of results
that are possible, and indicating areas which deserve future
research. The first article is by Temam. lt provides an
introduction and overview of the general finite element methods for
the nonspecialist. lt also illustrates the power of finite element
methods with two specific applications-the free surface
flowjstructure interaction problern and the compressible Euler solu
tion to the flow past a finite aspect ratio flat plate at
incidence. The second article by Brezzi is againan introduction and
overview ofmixed finite element methods. lt includes a brief
discussion of special techniques for solving the discrete problem,
as weil as some applications to certain basic problems in
elasticity and hydrodynamics."
The Institute for Computer Applications in Science and Engineer ing
(ICASE) and NASA Langley Research Center (LaRC) brought together on
October 2-4, 1989 experts in the various areas of com bustion with
a view to expose them to some combustion problems of technological
interest to LaRC and possibly foster interaction with the academic
community in these research areas. The top ics chosen for this
purpose were flame structure, flame stability, flame
holding/extinction, chemical kinetics, turbulence-kinetics in
teraction, transition to detonation, and reacting free shear
layers. The lead paper set the stage by discussing the status and
issues of supersonic combustion relevant to scramjet engine. Then
the ex perts were called upon i) to review the current status of
knowledge in the aforementioned ;:I. reas, ii) to focus on how this
knowledge can be extended and applied to high-speed combustion, and
iii) to suggest future directions of research in these areas. Each
topic was then dealt with in a position paper followed by formal
discussion papers and a general discussion involving the
participants. The position papers discussed the state-of-the-art
with an emphasis on key issues that needed to be resolved in the
near future. The discussion papers crit ically examined these
issues and filled in any lacunae therein. The edited versions of
the general discussions in the form of questions from the audience
and answers from the speakers are included wher ever possible to
give the reader the flavor of the lively interactions that took
place.
Turbulence is the lIDst natural nDde of fluid lIDtion, and has been
the subject of scientific study for all Dst a century. During this
period, various ideas and techniques have evolved to nDdel
turbulence. Following Saffman, these theoretical approaches can be
broadly divided into four overlapping categories -- (1) analytical
lIDdelling, (2) physical lIDdelling, (3)
phenomenologicalllDdelling, and (4) nurerical lIDdelling. With the
purpose of stmtnarizing our =ent understanding of these theoretical
approaches to turbulence, recognized leaders (fluid dynamicists,
mathematicians and physicists) in the field were invited to
participate in a formal workshop during October 10-12, 1984,
sponsored by The Institute for CooIputer Applications in Science
and Engineering and NASA Langley Research Center. Kraiciman,
McCcxnb, Pouquet and Spiegel represented the category of analytical
nDdelling, while Landahl and Saffman represented physical
lIDdelling. The contributions of Latmder and Spalding were in the
category of phenanenological lIDdelling, and those of Ferziger and
Reynolds in the area of nurericalllDdelling. Aref, Cholet, Lumley,
Moin, Pope and Temam served on the panel discussions. With the care
and cooperation of the participants, the workshop achieved its
purpose, and we believe that its proceedings published in this
vol\. llre has lasting scientific value. The tone of the workshop
was set by two introductory talks by Bushnell and ChaImm. Buslmell
presented the engineering viewpoint while Chapman reviewed from a
historical perspective developments in the study of turbulence. The
remaining talks dealt with specific aspects of the theoretical
approaches to fluid turbulence.
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