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1986 | Book

Introduction to the Workshop: Some Bottlenecks and Deficiencies of Existing Vector Computers and Their Consequences for the Development of General PDE Software Read chapter Read first chapter

The Efficient Use of Vector Computers with Emphasis on Computational Fluid Dynamics

A GAMM-Workshop

Editors: Prof. Dr. Willi Schönauer, Dr. Wolfgang Gentzsch

Publisher: Vieweg+Teubner Verlag

Book Series : Notes on Numerical Fluid Mechanics and Multidisciplinary Design

Included in: Professional Book Archive

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About this book

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".

Table of Contents

Frontmatter
Introduction to the Workshop: Some Bottlenecks and Deficiencies of Existing Vector Computers and Their Consequences for the Development of General PDE Software
Summary
In the first part of this introductory paper a review of the different types of vector computer programs and algorithms is presented. Then the hardware of the presently most relevant vector computers together with their bottlenecks will be discussed as well as the trends in development. The weakest point of the existing vector computers is the compiler, this problem is closely related to the lacking vector statements of Fortran 77. Therefore some proposals of Fortran 8X will be presented. In the second part of this paper the authors report about some experiences which have been obtained in the development of “black-box software” for PDE’s. There will be given a pragmatic definition of a “data flow algorithm”, and the separation of data selection and processing will be demonstrated for the evaluation of difference formulae. Then the i/o bottleneck is discussed for the iterative solution of large linear systems in diagonal storing. There will be presented our view of portability of software for different vector computers. The numerical example for ILU-preconditioning demonstrates how vecto-risation might invert experiences gained on general purpose computers. Finally some examples demonstrate the application of the Fidisol program package on different vector computers.
W. Schönauer, E. Schnepf
Development of Efficient Algorithms for the Solutions of Full Potential and Euler Equations on Vector Computers
Summary
For the efficient use of vector computers, three problems in the area of computational aerodynamics are dealt with. These are: 3-D full potential equation, body-fitted grid generation for wing-body configurations and 3-D Euler equations. Special features of each of these problems are emphasized. Various techniques to overcome the bottlenecks appearing therein are described.
R. K. Jain, N. Kroll, R. Radespiel
Implementation of 3D Explicit Euler Codes on a CRAY-1S Vector Computer
Abstract
The recent arrival at ONERA of a CRAY-1S vector computer, has raised the problem of adapting codes and of determining the most efficient choices in their features in order to fully exploit the vectorizing capabilities of the computer.
M. Borrel, J. L. Montagne, M. Neron, J. P. Veuillot, A. M. Vuillot
Breaking the I/O Bottleneck with the CRAY Solid-State Storage Device
Summary
The use of the CRAY Solid-state Storage Device as a secondary memory device for large-scale problems in computational fluid dynamics is reported. The high data transfer rate and low access time of the SSD essentially eliminates the I/O-wait penalty. Hardware details, user impact (minimal, the SSD is used like a conventional disk drive), several examples of its use, and the relative performance of I/O types are discussed.
Kent P. Misegades
Simulating 3D Euler Flows on a CYBER 205 Vector Computer
Summary
A computational method for solving the 3D Euler equations is studied. The method is based upon an upwind flux-difference splitting scheme by Osher, exhibiting an implicit mechanism for numerical viscosity, in connection with an explicit time-marching finite-volume technique. The computer program is developed to run efficiently on both a scalar computer and the CYBER 205 vector computer. Demands made by the necessity of vectorizability of the code, on algorithm, data-structuring, and the code itself, are. discussed. Also, the large data sets involved in 3D calculations, appear to impose severe claims on central-memory size, I/O devices and line connections.
The method is tested for a transonic and supersonic quasi-two-dimensional channel flow. The Euler model is found to give an accurate simulation of aerodynamic phenomena in the channel.
P. J. Koppenol
Vector Algorithm for Large-Memory CYBER 205 Simulations of Euler Flows
Summary
The paper reviews a finite-volume method for the large-scale numerical simulation of fluid flow and discusses the vector coding and execution of the procedure on the CYBER 205. With the proper structure given to the data by the grid transformation each coordinate direction can be differenced throughout the entire grid in one vector operation. Boundary conditions must be interleaved which tends to inhibit the concurrency of the overall scheme, but a stragey of no data motion together with only inner-loop vectorization is judged to be the best compromise. The computed example of transonic vortex flow separating from the sharp leading edge of a delta wing demonstrates the processing performance of the procedure. Vectors over 40, 000 elements long are obtained, and a rate of over 125 megaflops, sustained over the entire computation, is achieved when the entire data set is resident in real memory. Attemps to use secondary memory, either explicitly or with virtual management, greatly degrades the performance.
Arthur Rizzi, J. P. Therre
Effective Programming of Finte Element Methods for Computational Fluid Dynamics on Supercomputers
Summary
The effective programming of Finite Element Methods for CFD on vector-machines is discussed. It is shown, that for unstructured grids the performance observed on this class of machine depends heavily of the availability of hardware Gather/Scatter. Timings obtained for a 3-D Euler code are presented for the CYBER-205, CRAY-XMP11 and CRAY-XMP48.
R. Löhner, K. Morgan, O. C. Zienkiewicz
Performance Evaluation of Explicit Shallow-Water Equations Solvers on the CYBER 205
Summary
The performance of an explicit method and an ADI method for the shallow-water equations is compared on a CYBER 205. Furthermore, a stabilization technique is discussed, which stabilizes the explicit method in such a way that any desired time step is possible without the development of instabilities.
Comparing the codes for two test models, we found that the explicit methods are attractive on the CYBER 205. Finally, some proposals are made for the handling of irregular geometries.
F. W. Wubs
Methods for Optimisation and Acceleration of an Explicit Navier-Stokes Code with Application to Shock/Boundary-Layer Interaction
Summary
The two parts of this paper discuss techniques for improving the programming efficiency of explicit algorithms on the CRAY-1 vector computer at the Fortran and Assembler levels respectively. The high degree of modularity was essential for both simplifying the application of the techniques of vectorisation and for calculating the maximal execution speed of the algorithm and achieving this speed using assembly language.
At the Fortran level increasing vector lengths by reducing the dimension of arrays achieved a performance improvement of between 10 % and 50 %, the module coded in assembly language a-chieved a further improvement of 37 %. The FORTRAN coded program attained an average speed of 60 MFLOPS.
E. Katzer, M. Dowling
On Vectorizaton of a 2.D. Navier-Stokes Solver
Summary
This paper is devoted to the implementation of several vectorization techniques for the resolution of 2 D Navier-Stokes problem. The original version of the code was running on classical scalar computers and the main part of this work is the adaptation of the algorithms used for vectorization. In the first part, the equations to be solved are presented; the numerical methods (higher order finite differences)and the algorithms are presented in the second part. The adaptation for vectorization is also detailed. In the third part, the results concerning the speed-up got by the vectorization and by the optimization of the different versions of the codes are presented; endly, some comparisons between a scalar versus a vectorial computer are done.
Y. Lecointe, J. Piquet
On the Efficient Use of Large Data Bases in the Numerical Solution of the Navier-Stokes Equations on a CRAY Computer
Summary
For the numerical integration of the Navier-Stokes equations with the explicit-implicit MacCormack algorithm the efficient use of a CRAY-1S computer is described, if the main memory is too small to handle the tackled problem. The plane concept is used for the transfer of data. Within each plane of data the code is nearly completely vectorized. To be really efficient dedicated input/output devices are needed. Parallel input/output streams are used to speed up the transfer rates. The set up of the code allows to handle large problems, provided sufficient memory is available in core, and if dedicated input/output devices are employed. The code is not well suited for efficient use on a CYBER vector computer because the vector strings are comparatively short.
W. Kordulla
N3S : A 3D Finite Element Code for Fluid Mechanics; Emphasis to Vectorization and Sparse Matrix Problems
Abstract
N3S is a three-dimensional incompressible Navier-Stokes finite element code developped at EDF for the study of industrial flows*). The treatment of complex geometries, the number of nodes (up to 50000) led us to decompose the problem at different levels (geometry, algorithm and numeric). The use of the splitting up technique allows a specific and efficient treatment to be applied to each part of the Navier-Stokes equations:
  • method of characteristics for the advection terms,
  • conjugate gradient method for the diffusion-continuity part.
Ph. Hemmerich, J. Goussebaile, J. P. Gregoire, P. Lasbleiz, ELECTRICITE de FRANCE
Multitasking the Code ARC3D
Abstract
The CFD code ARC3D has been run on a CRAY X-MP/48 computer at the CRAY Research, Inc. headquarters in Mendota Heights, Minnesota. The CRAY multitasking system was invoked in order to utilize all four processors and sharply reduce the wall clock rim time. This paper discusses the techniques used to modify the code for this run and analyzes the achieved speedup.
John T. Barton, Christopher C. Hsiung
The Efficient Use of the CRAY X-MP Multiprocessor Vector Computer in Computational Fluid Dynamics
Summary
For many problems in computational fluid dynamics the elapsed times for simulations are too large to make the routine use of the technique in research and development pragmatic, even with a vector computer such as the CRAY-1. With the CRAY X-MP series of supercomputers the elapsed time for such jobs may be reduced by more than a factor of seven. In this paper we discuss the factors important to the efficient exploitation of the novel features of these machines.
A. K. Dave
Development of an Atmospheric Mesoscale Model on a CRAY — Experiences with Vectorization and Input/Output
Summary
Some concepts and experiences are discussed from the present development of a three-dimensional model for atmospheric flows in the mesoscale (typical lengthscale L ≤ 250 km) on the CRAY-1/S computer of the DFVLR. After an introduction to the range of physical problems and adequate numerical schemes to tackle them two more technical aspects are dealt with. First, an integration algorithm, which minimizes input/output operations, is introduced together with figures that show the capabilities of different software and hardware components for input/output. Then, the emphasis goes to the pressure solution as an important subtask, the vectorization capabilities of existing software and gains due to its restructuration. Calculations involving the entire code (dealing with the Taylor-Green vortex in a 64×36×64 grid) and a discussion of the technical aspects’ impact on three dimensional Navier-Stokes codes conclude the paper.
Hans Volkert, Ulrich Schumann
Techniques for Speeding up Climate Models on the CYBER 205
Summary
A number of different methods are described of reducing the elapsed time taken to run a climate model on a Cyber 205 computer whilst improving the understanding of the meteorological processes and the relationship between the model and the real atmosphere.
Mavis K Hinds
Experience with the Vectorisation of Some Fluid Flow Prediction Codes on the Harwell CRAY-1
Summary
This paper describes the experience obtained at Harwell on the exploitation of the CRAY-1 for the prediction of fluid flows. The topics covered include the use of direct methods and iterative methods for the solution of linear systems of equations, and some other relevant issues such as the use of library kernels and efficient input/output.
I. P. Jones
Summary of the Workshop
Abstract
During the Workshop two main subjects have been discussed comprehensively: Vectorization and numerical algorithms. Vectorization means adaptation of computer programs and numerical algorithms to the special architecture of vector computers in order to exploit fully their potential, which then often results in remarkable performance improvements.
Wolfgang Gentzsch
Backmatter
Metadata
Title
The Efficient Use of Vector Computers with Emphasis on Computational Fluid Dynamics
Editors
Prof. Dr. Willi Schönauer
Dr. Wolfgang Gentzsch
Copyright Year
1986
Publisher
Vieweg+Teubner Verlag
Electronic ISBN
978-3-663-13912-6
Print ISBN
978-3-528-08086-0
DOI
https://doi.org/10.1007/978-3-663-13912-6