The GAMM Committee for Numerical Methods in Fluid Mechanics organizes workshops which should bring together experts of a narrow field of computational fluid dynamics (CFD) to exchange ideas and experiences in order to speed-up the development in this field. In this sense it was suggested that a workshop should treat the solution of CFD problems on vector computers. Thus we organized a workshop with the title "The efficient use of vector computers with emphasis on computational fluid dynamics". The workshop took place at the Computing Centre of the University of Karlsruhe, March 13-15,1985. The participation had been restricted to 22 people of 7 countries. 18 papers have been presented. In the announcement of the workshop we wrote: "Fluid mechanics has actively stimulated the development of superfast vector computers like the CRAY's or CYBER 205. Now these computers on their turn stimulate the development of new algorithms which result in a high degree of vectorization (sca1ar/vectorized execution-time). But with 3-D problems we quickly reach the limit of present vector computers. If we want e.g. to solve a system of 6 partial differential equations (e.g. for u, v, w, p, k, € or for the vectors u, curl u) on a 50x50x50 grid we have 750.000 unknowns and for a 4th order difference method we have circa 60 million nonzero coefficients in the highly sparse matrix. This characterizes the type of problems which we want to discuss in the workshop".

This volume contains papers presented to a EUROMECH-Colloquium held in Munich, September 30 to October 2, 1985. The Colloquium is number 199 in a series of colloquia inaugurated by the European Mechanics Committee. The meeting was jointly organized by the 'Lehrstuhl fur Stromungsmechanik' at the 'Technische Universitat Munchen' and the 'Institut fur Physik der Atmosphare' of the 'Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt' (DFVLR) in Oberpfaffenhofen. 'Direct' and 'large eddy simulation' are terms which denote two closely con nected methods of turbulence research. In a 'direct simulation' (DS), turbu lent motion is simulated by numerically integrating the Navier-Stokes equations in three-dimensional space and as a function of time. Besides ini tial and boundary conditions no physical simplifications are involved. Com puter resources limit the resolution in time and space, though simulations with an order of one million discrete points in space are feasible. The simu lated flow fields can be considered as true realizations of turbulent flow fields and analysed to answer questions on the basic behaviour of turbulence. Direct simulations are valid as long as all the excited scales remain within the band of resolved scales. This means that viscosity must be strong enough to damp out the not resolved scales or the simulation is restricted to a lim ited integration-time interval only. In summary, DS provides a tool to investigate turbulent motions from first principles at least for a finite band of scales.

The aim of the 1989 GAMM Workshop on 3D-Computation of Incompressible Internal Flows was the simulation of a realistic incompressible flow field in an important industrial application. In view of the difficulties involved in formulating such a test case, requiring the availability of an experimental data base, extreme care had to be taken in the selection of the proper one. Professor I. L. Ryhming's proposal, that the flow through a Francis turbine configuration or parts thereof would be feasible as a test case, because of the numerical challenges as well as the possibility to produce an experimental data base by using the experimental facilities of the Hydraulic Machines and Fluid Mechanics Institute (IMHEF) at the Swiss Federal Institute of Technology in Lausanne (EPFL), was accepted by the GAMM Committee in April 1987. A scientific committee, formed under the chairmanship of Professor I. L. Ryhming, met a few times to decide on the Francis turbine configuration, the test case specifications, etc. , whereby the design input came from the water turbine experts. This committee decided to restrict the studies to the three following typical applications for the best operating point of the turbine: • simulation of the 3D flow in a Francis runner in rotation • simulation of the 3D flow in the distributor (stay and guide vane rings) of this turbine • simulation of the 3D flow in an elbow draft tube The simultaneous computation of two or three of these geometries was encouraged.

This volume contains 37 contributions in which the research work is summarized which has been carried out between 1984 and 1990 in the Priority Research Program "Physik abgeloster Stromungen" of the Deutsche Forschungsgemeinschaft (DFG, German Research Society). The aim of the Priority Research Program was the inten sive research of the whole range of phenomena associated with separated flows. Physi cal models as well as prediction methods had to be developed based on detailed experi mental investigations. It was in accordance with the main concept of the research program that scientists working on problems of separated flows in different technical areas of application participated in this program. The following fields have been represented in the program: aerodynamics of wings and bodies, aerodynamics of auto mobiles, turbomachinery, ship hydrodynamics, hydraulics, internal flows, heat exchan gers, bio-fluid-dynamics, aerodynamics of buildings and structures. In order to concentrate on problems common in all those areas the emphasis of the program was on basic research dealing with generic geometric configurations showing the fundamental physical phenomena of separated flows. The engagement and enthusiasm of all participating scientists are highly appreciated. The program was organized such that all researchers met once a year to report on the progress of their work. Special thanks ought to go to Prof. E. A. Muller (Gottingen), Prof. H. Oertel jun. (Braunschweig), Dr. W. Schmidt (Dornier), Dr. H. -W. Stock (Dornier) and Dr. B. Wagner (Dornier), who had the functions of referees on those annual meetings.