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23 produkter
23 produkter
EUROPT — A European Initiative on Optimum Design Methods in Aerodynamics
Proceedings of the Brite/Euram Project Workshop “Optimum Design in Areodynamics”, Barcelona, 1992
Häftad, Engelska, 2012
1 068 kr
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This volume entitled "EUROPT - A European Initiative on Optimum Design in Aerodynamics" contains the results of the contributors during a workshop which took place in Barcelona in June 1992. This workshop was organized in the framp work of the Brite/Euram Aeronautics project "Optimum Design in Aerodynamics" (AERO-89-0026). The project brought together nine European partners from Acade my and Industry with big experience in numerical optimization techniques applif'd to automated optimum design. The manuscript is directed to the optimization field and its goal is to provide the reader with useful numerical optimization techniques for optimum design in aerody namIcs. The field of numerical optimization techniques has been growing since the early 50's. But only recently, with the recent advent of powerful computers. it has yielded real-life applications that demonstrate industrial potential for design purposes. Nowadays, optimization is at the stage where those scientists and engineers who have worked in the field are to be paid to apply numerical optimization to automated design of real problems, namely aerodynamic shapes in Aerospace Engineering. For the above reasons, it was evident that a Workshop on numerical optimization techniques for the validation of optimum design methods would be of interest to most of the partners involved in the AERO-S9-0026 project in order to compare in terms of accuracy and efficiency several optimization soft wares performed on the same selected flow problems.
Del 60 - Notes on Numerical Fluid Mechanics
New Results in Numerical and Experimental Fluid Mechanics
Contributions to the 10th AG STAB/DGLR Symposium Braunschweig, Germany 1996
Häftad, Engelska, 2012
1 068 kr
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This volume contains the papers of the 10th AG STAB (German Aerospace Aerodynamics Association). In this association all those scientists and engineers from universities, research-establishments and industry are involved, who are doing research and project work in numerical and experimental fluid mechanics and aerodynamics for aerospace and other applications. Many of the contributions are giving first results from the "Luftfahrtforschungsprogramm der Bundesregierung (German Aeronautical Research Program) 1995-1998". Some of the papers report on work sponsored by the Deutsche Forschungsgemeinschaft, DFG, which also was presented at the symposium. The volume gives a broad overview over the ongoing work in this field in Germany.
Portable Parallelization of Industrial Aerodynamic Applications (POPINDA)
Results of a BMBF Project
Häftad, Engelska, 2012
1 068 kr
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This book contains the main results of the German project POPINDA. It surveys the state of the art of industrial aerodynamic design simulations on parallel systems. POPINDA is an acronym for Portable Parallelization of Industrial Aerodynamic Applications. This project started in late 1993. The research and development work invested in POPINDA corresponds to about 12 scientists working full-time for the three and a half years of the project. POPINDA was funded by the German Federal Ministry for Education, Science, Research and Technology (BMBF). The central goals of POPINDA were to unify and parallelize the block-structured aerodynamic flow codes of the German aircraft industry and to develop new algorithmic approaches to improve the efficiency and robustness of these programs. The philosophy behind these goals is that challenging and important numerical appli cations such as the prediction of the 3D viscous flow around full aircraft in aerodynamic design can only be carried out successfully if the benefits of modern fast numerical solvers and parallel high performance computers are combined. This combination is a "conditio sine qua non" if more complex applications such as aerodynamic design optimization or fluid structure interaction problems have to be solved. When being solved in a standard industrial aerodynamic design process, such more complex applications even require a substantial further reduction of computing times. Parallel and vector computers on the one side and innovative numerical algorithms such as multigrid on the other have enabled impressive improvements in scientific computing in the last 15 years.
Del 51 - Notes on Numerical Fluid Mechanics
Numerical Treatment of Coupled Systems
Proceedings of the Eleventh GAMM-Seminar, Kiel, January 20–22, 1995
Häftad, Engelska, 2012
1 068 kr
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The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organizes seminars and workshops on subjects concerning the algorithmic treatment of partial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various type of applications in structural and fluid mechanics. Particular attention is devoted to the advanced solution methods. The series of such seminars was continued in 1995, January 20-22, with the 11th Kiel-Seminar on the special topic Numerical Treatment of Coupled Systems at the Christian-Albrechts-University of Kiel. The seminar was attended by 100 scientist from 9 countries. 23 lectures were given, including two survey lectures. Different kinds of couplings are considered in this volume. The coupling of different components may occur in the physical model. On the other hand, a coupling of subsystems can be generated by the numerical solution technique. General examples of the latter kind are the domain decomposition (see p. 128) or subspace decomposition (p. 117). The local defect correction method couples different discretizations of the same problem in order to improve the results, although the basic linear system to be solved remains unchanged (p. 47). In general, the aim of the numerical coupling is to make use of (efficient) subsystem solvers (p. 1). The combination of different discretization techniques is mentioned on page 59.
Del 59 - Notes on Numerical Fluid Mechanics
Modeling and Computation in Environmental Sciences
Proceedings of the First GAMM-Seminar at ICA Stuttgart, October 12–13, 1995
Häftad, Engelska, 2012
1 068 kr
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This volume contains 20 contributions to the 1st GAMM-Seminar at ICA Stuttgart, which was held in Stuttgart, October 12 - 13, 1995. In the field of environmental sciences, numerical procedures for the simulation of ecological problems are growing increasingly topical. The solution of typical problems in environmental research is closely connected with numerical supercomputing. The main subject of the seminar was the modeling and numerical simulation of ground water and soil water. Further topics were multi-scale modeling, special discretization schemes, adaptivity, multi-grid methods, heterogenity, parameter identification, homogenization, density driven groundwater flow, and coupling of transport and chemistry.
Computation of Three-Dimensional Complex Flows
Proceedings of the IMACS-COST Conference on Computational Fluid Dynamics Lausanne, September 13–15, 1995
Häftad, Engelska, 2012
1 068 kr
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The IMACS-COST conference on "Computational Fluid Dynamics, Three-Dimensional Complex Flows" was held in Lausanne, Switzerland, September 13 - 15, 1995. The scien tific sponsors of the conference were • IMACS: International Association for Mathematics and Computers in Simulation, • COST: European Cooperation in the field of Scientific and Technical Research, • ERCOFTAC: European Research Community on Flow, Turbulence and Combus tion. The scientific interests of the IMACS and ERCOFTAC associations are closely related to computational fluid dynamics whereas the European Union programme COST covers a wider range of scientific subjects. The COST' Action F1' launched in 1992 by Professor I. L. Ryhming deals with "Complex three-dimensional viscous flows: prediction, modelling, manipulation and control". It has several subtopics among which numerical methods and modelling issues are the main areas of research and development. The meeting gathered together eighty-seven scientists, engineers and researchers from sev enteen countries: Belgium, Finland, France, Germany, Greece, Hong Kong, Israel, Italy, Japan, the Netherlands, Norway, Russia, Spain, Sweden, Switzerland, United Kingdom, United States of America. All major numerical approximation methods were discussed: finite differences, finite volumes, finite elements, spectral methods. The topics covered by the sixty communications spanned the full spectrum of computational fluid dynam ics: direct numerical simulation, large-eddy simulation, turbulence modelling, free surface flows, non Newtonian fluids, thermal convection, etc.
Del 48 - Notes on Numerical Fluid Mechanics
Flow Simulation with High-Performance Computers II
DFG Priority Research Programme Results 1993–1995
Häftad, Engelska, 2012
538 kr
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Der Band enthalt den Abschlussbericht des DFG-Schwerpunktprogramms "Flusssimulation mit Hochstleistungsrechnern". Es fuhrt die Arbeiten fort, die schon als Band 38 in der Reihe "Notes on Numerical Fluid Mechanics" erschienen sind.Work is reported, which was sponsored by the Deutsche Forschungsgemeinschaft from 1993 to 1995. Scientists from numerical mathematics, fluid mechanics, aerodynamics, and turbomachinery present their work on flow simulation with massively parallel systems, on the direct and large-eddy simulation of turbulence, and on mathematical foundations, general solution techniques and applications. Results are reported from benchmark computations of laminar flow around a cylinder, in which seventeen groups participated.
Del 5 - Notes on Numerical Fluid Mechanics
Computation and Comparison of Efficient Turbulence Models for Aeronautics — European Research Project ETMA
Häftad, Engelska, 2012
538 kr
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The computation of complex turbulent flows by statistical modelling has already a long history. The most popular two-equation models today were introduced in the early sev enties. However these models have been generally tested in rather academic cases. The develope ment of computers has led to more and more acurate numerical methods. The interactions betwe~n numerical and modelling techniques are generally not well mastered. Moreover, computation of real life cases, including 3D effects, complex geometries and pressure gra dients based on two-equation models with low-Reynolds treatment at the proximity of walls are not really of common use. A large number of models has been proposed; this is perhaps the sign that none of them is really satisfactory, and then the assessment of their generality is not an easy task: it requires a lot of understanding of the physics and a lot of work for testing the large number of relevant cases in order to assess their limits of validity which is a condition for an improved confidence in engineering applications. This is probably why workshops and working groups are frequent and the ETMA consor tium has choosen to build a state of the art in theoretical and numerical statistical turbu lence modelling for real life computations by taking some marks with respect to previous workshops such as the Stanford meetings (1980,1981); some problems are kept or updated by new experiments, some problems are discarded, some new problems are introduced; the focus is kept on flows with 2D geometries.
Boundary Elements: Implementation and Analysis of Advanced Algorithms
Proceedings of the Twelfth GAMM-Seminar Kiel, January 19–21, 1996
Häftad, Engelska, 2012
1 068 kr
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The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organizes seminars and workshops on subjects concerning the algorithmic treatment of partial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various type of applications in struc tural and fluid mechanics. Particular attention is devoted to advanced solution method". The latest seminar in this series was the 12th Kiel-Seminar which took place on January 19-21, 1996 at Christian-Albrechts-University of Kiel and focussed on the topic Boundary Elements: Implementation and Analysis of Advanced Algorithms. The seminar was attended by 65 scientists from 10 countries. 23 lectures were given, including two survey lectures. In the last years, a remarkable progress in the numerical treatment of boundary de ment methods (BEM) has been obtained in Germany. This is, in particular, a res~I1t of a Schwerpunktverfahren supported by the DFG. Many aspects of the BEM are not ouly analysed but also implemented. Therefore, these proceedings present a number of papers on implementational aspects besides the analysis of advanced techniques.
Del 65 - Notes on Numerical Fluid Mechanics
Recent Development of Aerodynamic Design Methodologies
Inverse Design and Optimization
Häftad, Engelska, 2013
538 kr
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Computational Fluid Dynamics (CFD) has made remarkable progress in the last two decades and is becoming an important, if not inevitable, analytical tool for both fundamental and practical fluid dynamics research. The analysis of flow fields is important in the sense that it improves the researcher's understanding of the flow features. CFD analysis also indirectly helps the design of new aircraft and/or spacecraft. However, design methodologies are the real need for the development of aircraft or spacecraft. They directly contribute to the design process and can significantly shorten the design cycle. Although quite a few publications have been written on this subject, most of the methods proposed were not used in practice in the past due to an immature research level and restrictions due to the inadequate computing capabilities. With the progress of high-speed computers, the time has come for such methods to be used practically. There is strong evidence of a growing interest in the development and use of aerodynamic inverse design and optimization techniques. This is true, not only for aerospace industries, but also for any industries requiring fluid dynamic design. This clearly shows the matured engineering need for optimum aerodynamic shape design methodologies. Therefore, it seems timely to publish a book in which eminent researchers in this area can elaborate on their research efforts and discuss it in conjunction with other efforts.
Del 61 - Notes on Numerical Fluid Mechanics
Optimum Aerodynamic Design & Parallel Navier-Stokes Computations ECARP — European Computational Aerodynamics Research Project
Häftad, Engelska, 2012
1 068 kr
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This volume entitled "European Computational Aerodynamics Research Project (ECARP)" contains the contributions of partners presented in two work shops focused on the following areas: Task 3 on Optimum Design and Task 4.2 on Navier Stokes Flow algorithms on Massively Parallel Processors. ECARP has been supported by the European Union (EU) through the Indus trial and Materials Technology Programme, Area 3 Aeronautics, with the Third Research Framework Programme (1990-1994). Part A of this volume is focused on computational constrained optimization as a follow up of the EU research project" Optimum Design in Aerodynamics" , (AERO-S9-0026) dealing with more viscous flow based real applications. It pro vides the reader with a set of optimization tools and referenced data useful in modern aerodynamic design. Task 3 of the project entitled "Optimum Design" brought together 13 Euro pean partners from the academic and industrial aeronautic oriented community showing state of the art expertise in traditional automated optimization software on current computer technology to improve the capability to optimize aircraft shapes.
Del 56 - Notes on Numerical Fluid Mechanics
EUROSHOCK - Drag Reduction by Passive Shock Control
Results of the Project EUROSHOCK, AER2-CT92-0049 Supported by the European Union, 1993 – 1995
Häftad, Engelska, 2012
538 kr
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It has been recognized by the European Union (EU) that the survival of the Aeronautical Industries of Europe in the highly competitive World Aviation Market is strongly dependent on such factors as time-to-market of a new or derivative aircraft and on its manufacturing costs but also on the achievement of a competitive technological advantage by which an increased market share can be gained. Cooperative research is therefore continuously encouraged and co-financed by the European Union in order to strengthen the scientific and technological base of the Aeronautical Industries thus facilitating the future design and manufacture of civil air craft products and providing the technological edge needed for survival. Targets of research within Area 3, Aeronautics, of the Industrial and Materials Technology Programme (1991 - 1993) have been identified to be aircraft efficiency, cost effectiveness and environmental im pact. Concerning aircraft efficiency - relevant to the present research - a reduction in aircraft drag of 10010, a reduction in aircraft fuel consumption of 30010 and a reduction in airframe, en gine and system weight of 20% are envisaged. Meeting these objectives has, of course, also a strong positive impact on the environment. In order to further technology, the philosophy is to avoid spreading the available resources too thinly and rather concentrate on the feasibility demonstration of a limited number of tech nologies of high economic and industrial impact.
Del 48 - Notes on Numerical Fluid Mechanics
Numerical Solutions of the Euler Equations for Steady Flow Problems
Häftad, Engelska, 1992
538 kr
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The last decade has seen a dramatic increase of our abilities to solve numerically the governing equations of fluid mechanics. In design aerodynamics the classical potential-flow methods have been complemented by higher modelling-level methods. Euler solvers, and for special purposes, already Navier-Stokes solvers are in use. The authors of this book have been working on the solution of the Euler equations for quite some time. While the first two of us have worked mainly on algorithmic problems, the third has been concerned off and on with modelling and application problems of Euler methods. When we started to write this book we decided to put our own work at the center of it. This was done because we thought, and we leave this to the reader to decide, that our work has attained over the years enough substance in order to justify a book. The problem which we soon faced, was that the field still is moving at a fast pace, for instance because hyper sonic computation problems became more and more important.
Adaptive Methods — Algorithms, Theory and Applications
Proceedings of the Ninth GAMM-Seminar Kiel, January 22–24, 1993
Häftad, Engelska, 1994
538 kr
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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.
Del 4 - Notes on Numerical Fluid Mechanics
Numerical Simulation in Science and Engineering
Proceedings of the FORTWIHR Symposium on High Performance Scientific Computing, München, June 17–18, 1993
Häftad, Tyska, 1994
553 kr
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This volume contains 14 papers, presented at the Symposium on High Performance Scientific Computing organized by FORTWIHR, the Bavarian consortium for HPSC, and held on June 17-18, 1993 in Munich, Germany. The numerical simulation, for example, the mathematical calculation of technical processes in advance, has gained immensely in significance for numerous key areas of the economy. It is now possible to understand and master entire technical processes before going into production by means of numerical simulation on the computer. The papers of this volume give a survey on recent research efforts and industrial applications of numerical simulation in the areas of fluid mechanics, dynamic systems in aerospace, melting processes and crystal growth, and semin-conductor and electric circuit technology.
Fast Solvers for Flow Problems
Proceedings of the Tenth GAMM-Seminar Kiel, January 14–16, 1994
Häftad, Tyska, 1995
553 kr
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This volume contains 23 contributions to the 10th GAMM-Seminar, which was held in Kiel on the 14-16 of January 1994. The central topics are advanced numerical techniques for solving flow problems. The Navier-Stokes equations are discussed with respect to anisotropically refined meshes, in combination with non-equilibrium chemistry and with respect to implicit time-discretizations and parallel solvers. Furthermore, robust multi-grid methods are described for this problem. Five papers are devoted to parallel algorithms, and a further one to domain decomposition techniques. The very important aspect of adaptive strategies is considered in several contributions, including a discussion of appropriate error estimators. Other subjects are the FEM-BEM coupling, convection-dominated systems, unstructured grid techniques and complex geometries in 3-D.
Del 3 - Notes on Numerical Fluid Mechanics
Numerical Methods for the Computation of Inviscid Transonic Flows with Shock Waves
A GAMM Workshop
Häftad, Tyska, 1981
553 kr
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Del 6 - Notes on Numerical Fluid Mechanics
Numerical Methods in Laminar Flame Propagation
A GAMM-Workshop
Häftad, Tyska, 1982
553 kr
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Del 21 - Notes on Numerical Fluid Mechanics
Panel Methods in Fluid Mechanics with Emphasis on Aerodynamics
Proceedings of the Third GAMM-Seminar Kiel, January 16 to 18, 1987
Häftad, Tyska, 1988
702 kr
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Del 40 - Notes on Numerical Fluid Mechanics
Physics of Separated Flows — Numerical, Experimental, and Theoretical Aspects
DFG Priority Research Programme 1984–1990
Häftad, Engelska, 1993
538 kr
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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.
Del 15 - Notes on Numerical Fluid Mechanics
Direct and Large Eddy Simulation of Turbulence
Proceedings of the EUROMECH Colloquium No. 199, München, FRG, September 30 to October 2, 1985
Häftad, Engelska, 1986
1 068 kr
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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.
Del 48 - Notes on Numerical Fluid Mechanics
Numerical Simulation of 3-D Incompressible Unsteady Viscous Laminar Flows
A GAMM-Workshop
Häftad, Engelska, 1992
537 kr
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The GAMM-Commi ttee for Numerical Methods in Fluid Mechanics (GAMM-Fachausschuss fur Numerische Methoden in der Stromungsmechanik) 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-Gortler-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.
Del 72 - Notes on Numerical Fluid Mechanics
New Results in Numerical and Experimental Fluid Mechanics II
Contributions to the 11th AG STAB/DGLR Symposium Berlin, Germany 1998
Häftad, Engelska, 2013
537 kr
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This volume contains the papers of the 11th Symposium of the AG STAB (German Aerospace Aerodynamics Association). In this association those scientists and engineers from universities, research-establishments and industry are involved, who are doing research and project work in numerical and experimental fluid mechanics and aerodynamics for aerospace and other applications. Many of the contributions are giving results from the "Luftfahrtforschungsprogramm der Bundesregierung (German Aeronautical Research Programme). Some of the papers report on work sponsored by the Deutsche Forschungsgemeinschaft, DFG, which also was presented at the symposium. The volume gives a broad overview over the ongoing work in this field in Germany.