Numerical algorithms for three dimensional computational fluid dynamic problems
The target of this work is to contribute to the enhancement of numerical methods for the simulation of complex thermal systems. Frequently, the factor that limits the accuracy of the simulations is the computing power: accurate simulations of complex devices require fine three-dimensional discretiza...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2001 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/6685 |
| Acceso en línea: | http://www.tdx.cat/TDX-0405105-183251 http://hdl.handle.net/10803/6685 https://dx.doi.org/10.5821/dissertation-2117-93996 |
| Access Level: | acceso abierto |
| Palabra clave: | fluid dynamic problems numerical algorithms 2204. Física de fluïds 536 |
| Sumario: | The target of this work is to contribute to the enhancement of numerical methods for the simulation of complex thermal systems. Frequently, the factor that limits the accuracy of the simulations is the computing power: accurate simulations of complex devices require fine three-dimensional discretizations and the solution of large linear equation systems.<br/>Their efficient solution is one of the central aspects of this work. Low-cost parallel computers, for instance, PC clusters, are used to do so. The main bottle-neck of these computers is the notwork, that is too slow compared with their floating-point performance.<br/>Before considering linear solution algorithms, an overview of the mathematical models used and discretization techniques in staggered cartesian and cylindrical meshes is provided. <br/>The governing Navier-Stokes equations are solved using an implicit finite control volume method. Pressure-velocity coupling is solved with segregated approaches such as SIMPLEC.<br/>Different algorithms for the solution of the linear equation systems are reviewed: from incomplete factorizations such as MSIP, Krylov solvers such as BICGSTAB and GMRESR to acceleration techniques such as the Algebraic Multi Grid and the Multi Resolution Analysis with wavelts. Special attention is paid to preconditioned Krylov solvers for their application to parallel CFD problems.<br/>The fundamentals of parallel computing in distributed memory computers as well as implemetation details of these algorithms in combination with the domain decomposition method are given. Two different distributed memory computers, a Cray T3E and a PC cluster are used for several performance measures, including network throughput, performance of algebraic subroutines that affect to the overall efficiency of algorithms, and the solver performance. These measures are addressed to show the capabilities and drawbacks of parallel solvers for several processors and their partitioning configurations for a problem model.<br/>Finally, in order to illustrate the potential of the different techniques presented, a three-dimensional CFD problem is solved using a PC cluster. The numerical results obtained are validated by comparison with other authors. The speedup up to 12 processors is measured. An analysis of the computing time shows that, as expected, most of the computational effort is due to the pressure-correction equation,here solved with BiCGSTAB. The computing time algorithm , for different problem sizes, is compared with Schur-Complement and Multigrid. |
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