The GAMM-Commi ttee for Numerical Methods in Fluid Mechanics (GAMM-Fachausschuss für Numerische Methoden in der Strömungsmechanik) has sponsored the organization of a GAMM Workshop dedicated to the numerical simulation of three dimensional incompressible unsteady viscous laminar flows to test Navier-Stokes solvers. The Workshop was held in Paris from June 12th to June 14th, 1991 at the Ecole Nationale Superieure des Arts et Metiers. Two test problems were set up. The first one is the flow in a driven-lid parallelepipedic cavity at Re = 3200 . The second problem is a flow around a prolate spheroid at incidence. These problems are challenging as fully transient solutions are expected to show up. The difficulties for meaningful calculations come from both space and temporal discretizations which have to be sufficiently accurate to resol ve detailed structures like Taylor-Görtler-like vortices and the appropriate time development. Several research teams from academia and industry tackled the tests using different formulations (veloci ty-pressure, vortici ty velocity), different numerical methods (finite differences, finite volumes, finite elements), various solution algorithms (splitting, coupled ...), various solvers (direct, iterative, semi-iterative) with preconditioners or other numerical speed-up procedures. The results show some scatter and achieve different levels of efficiency. The Workshop was attended by about 25 scientists and drove much interaction between the participants. The contributions in these proceedings are presented in alphabetical order according to the first author, first for the cavi ty problem and then for the prolate spheroid problem. No definite conclusions about benchmark solutions can be drawn.

Today understanding turbulence is one of the key issues in tackling flow problems in engineering. Powerful computers and numerical methods are now available for solving flow equations, but the simulation of turbulence effects, which are nearly always important in practice, are still at an early stage of development. Successful simulation of turbulence requires the understanding of the complex physical phenomena involved and suitable models for describing the turbulence momentum, heat and mass transfer. The 89 papers, including 5 invited papers, in this volume present and discuss new developments in the area of turbulence modelling and measurements, with particular emphasis on engineering-related problems. The high standard of the contributions on the developing and testing of turbulent models attests to the world-wide interest this domain is currently attracting from researchers.

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.

The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organizes workshops on subjects concerning the algorithmical treat ment of partial differential equations. The topics are discretization methods like the finite element and finite volume method for various types of applications in structural and fluid mechanics. Particular attention is devoted to advanced solu tion techniques. th The series of such workshops was continued in 1993, January 22-24, with the 9 Kiel-Seminar on the special topic "Adaptive Methods Algorithms, Theory and Applications" at the Christian-Albrechts-University of Kiel. The seminar was attended by 76 scientists from 7 countries and 23 lectures were given. The list of topics contained general lectures on adaptivity, special discretization schemes, error estimators, space-time adaptivity, adaptive solvers, multi-grid me thods, wavelets, and parallelization. Special thanks are due to Michael Heisig, who carefully compiled the contribu tions to this volume. November 1993 Wolfgang Hackbusch Gabriel Wittum v Contents Page A. AUGE, G. LUBE, D. WEISS: Galerkin/Least-Squares-FEM and Ani- tropic Mesh Refinement. 1 P. BASTIAN, G. WmUM : Adaptive Multigrid Methods: The UG Concept. 17 R. BEINERT, D. KRONER: Finite Volume Methods with Local Mesh Alignment in 2-D. 38 T. BONK: A New Algorithm for Multi-Dimensional Adaptive Nume- cal Quadrature. 54 F.A. BORNEMANN: Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux. 69 J. CANU, H. RITZDORF : Adaptive, Block-Structured Multigrid on Local Memory Machines. 84 S. DAHLKE, A. KUNaTH: Biorthogonal Wavelets and Multigrid. 99 B. ERDMANN, R.H.W. HOPPE, R.

Computational Fluid Dynamics research, especially for aeronautics, continues to be a rewarding and industrially relevant field of applied science in which to work. An enthusiastic international community of expert CFD workers continue to push forward the frontiers of knowledge in increasing number. Applications of CFD technology in many other sectors of industry are being successfully tackled. The aerospace industry has made significant investments and enjoys considerable benefits from the application of CFD to its products for the last two decades. This era began with the pioneering work ofMurman and others that took us into the transonic (potential flow) regime for the first time in the early 1970's. We have also seen momentous developments of the digital computer in this period into vector and parallel supercomputing. Very significant advances in all aspects of the methodology have been made to the point where we are on the threshold of calculating solutions for the Reynolds-averaged Navier-Stokes equations for complete aircraft configurations. However, significant problems and challenges remain in the areas of physical modelling, numerics and computing technology. The long term industrial requirements are captured in the U. S. Governments 'Grand Challenge' for 'Aerospace Vehicle Design' for the 1990's: 'Massively parallel computing systems and advanced parallel software technology and algorithms will enable the development and validation of multidisciplinary, coupled methods. These methods will allow the numerical simulation and design optimisation of complete aerospace vehicle systems throughout the flight envelope'.