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| Author | : S. N. Tiwari |
| Publisher | : |
| Total Pages | : 8 |
| Release | : 1984 |
| Genre | : Navier-Stokes equations |
| ISBN | : |
| Author | : James M. Ortega |
| Publisher | : SIAM |
| Total Pages | : 100 |
| Release | : 1985-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611971774 |
This volume reviews, in the context of partial differential equations, algorithm development that has been specifically aimed at computers that exhibit some form of parallelism. Emphasis is on the solution of PDEs because these are typically the problems that generate high computational demands. The authors discuss architectural features of these computers insomuch as they influence algorithm performance, and provide insight into algorithm characteristics that allow effective use of hardware.
| Author | : Alexander Victor |
| Publisher | : |
| Total Pages | : |
| Release | : 2017 |
| Genre | : |
| ISBN | : |
One of the most important applications of finite difference lies in the field of computational fluid dynamics (CFD). In particular, the solution to the Navier-Stokes equation grants us insight into the behavior of many physical systems. The 2-D and 3-D incompressible Navier-Stokes equation has been studied extensively due to its analogous nature to many practical applications, and several numerical schemes have been developed to provide solutions dedicated to different environmental conditions (such as different Reynolds numbers). This research also covers the assignment of boundary conditions, starting with the simple case of driven cavity flow problem. In addition, several parts of the equations are given implicitly, which requires efficient ways of solving large systems of equations.We also considered numerical solution methods for the incompressible Navier-Stokes equations discretized on staggered grids in general coordinates. Numerical experiments are carried out on a vector computer. Robustness and efficiency of these methods are studied. It appears that good methods result from suitable combinations of multigrid methods.Numerically solving the incompressible Navier-Stokes equations is known to be time-consuming and expensive; hence this research presents some MATLAB codes for obtaining numerical solution of the Navier-Stokes equations for incompressible flow through flow cavities, using method of lines, in three-dimensional space (3-D). The code treats the laminar flow over a two-dimensional backward-facing step, and the results of the computations over the backward-facing step are in excellent agreement with experimental results.
| Author | : James M. Ortega |
| Publisher | : SIAM |
| Total Pages | : 99 |
| Release | : 1985-09-01 |
| Genre | : Mathematics |
| ISBN | : 0898710553 |
Mathematics of Computing -- Parallelism.
| Author | : Willi Schönauer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 281 |
| Release | : 2013-11-11 |
| Genre | : Science |
| ISBN | : 3663139123 |
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".
| Author | : J. S. Shang |
| Publisher | : |
| Total Pages | : 11 |
| Release | : 1979 |
| Genre | : |
| ISBN | : |
A three-dimensional, time dependent Navier-Stokes code using MacCormack's explicit scheme has been vectorized for the CRAY-1 computer. Computations were performed for a turbulent, transonic, normal shock wave boundary layer interaction in a wind tunnel diffuser. The vectorized three-dimensional Navier-Stokes code on the CRAY-1 computer achieved a speed of 128 times that of the original scalar code processed by a CYBER 74 computer. The vectorized version of the code outperform the scalar code on the CRAY computer by a factor of 8.13. A comparison between the experimental data and the numerical simulation is also made. (Author).
| Author | : |
| Publisher | : |
| Total Pages | : 72 |
| Release | : 1993 |
| Genre | : |
| ISBN | : |
| Author | : James C. Robinson |
| Publisher | : Cambridge University Press |
| Total Pages | : 487 |
| Release | : 2016-09-07 |
| Genre | : Mathematics |
| ISBN | : 1316715124 |
A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier–Stokes equations, this book provides self-contained proofs of some of the most significant results in the area, many of which can only be found in research papers. Highlights include the existence of global-in-time Leray–Hopf weak solutions and the local existence of strong solutions; the conditional local regularity results of Serrin and others; and the partial regularity results of Caffarelli, Kohn, and Nirenberg. Appendices provide background material and proofs of some 'standard results' that are hard to find in the literature. A substantial number of exercises are included, with full solutions given at the end of the book. As the only introductory text on the topic to treat all of the mainstream results in detail, this book is an ideal text for a graduate course of one or two semesters. It is also a useful resource for anyone working in mathematical fluid dynamics.
| Author | : Wolfgang Gentzsch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 255 |
| Release | : 2013-03-08 |
| Genre | : Science |
| ISBN | : 3322878619 |
The scope of the present book is to offer the most efficient tools for the vectorization of serial computer programs. Here, by vectorization we understand the adaptation of computer programs to the special architecture of modern available vector computers to exploit fully their potential, which will often result in remarkable performance improvements. The book is written primarily for users working in the various fields of computational physics, for scientists as well as for programmers running their jobs on a vector computer. The text may, however, also be of value to those who are interested in numerical algorithms. Although the examples discussed in chapter 9 have been taken from Computational Fluid Dynamics, the numerical methods are well-known, and are applied in many fields of Computational Physics. The book is divided into four parts. After a short introduction which outlines the limits of conventional serial computers in contrast to the possibilities offered by the new vector machines, the second part is addressed to the discussion of some main features of existing computer architectures. We restrict ourselves to the vector computers CRAY-1S and CDC-CYBER 205, although, in the meantime, many vector and parallel computers and array processors are available such as DENELCOR's Heterogeneous Element Processor (HEP), ICL's Distributed Array Processor (DAP), SPERRY UNIVAC's Array Processing System (APS), STAR TECHNOLOGIES ST-l00, FLOATING POINT SYSTEMS' Array Processor (FPS), FUJITSU's FACOM VP-l00 and VP-200, HITACHI's Integrated Array Processor (lAP), HITACHI's S 810/10 and S 810/20 and others.
| Author | : James W. Thomas |
| Publisher | : |
| Total Pages | : 13 |
| Release | : 1982 |
| Genre | : |
| ISBN | : |
A three-dimensional version of the Beam-Warming scheme for solving the compressible Navier-Stokes equations was implemented on the Cray-1 computer. The scheme is implicit and second-order accurate. The code is totally vectorized, allows for complicated geometries and includes a thin layer turbulence model. Timings and comparisons are given. A preliminary discussion of the full viscous model is included. (Author).
