The simulation of fluid flow processes using vector processors
Ierotheou, Constantinos Savvas (1990) The simulation of fluid flow processes using vector processors. PhD thesis, Thames Polytechnic.

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Abstract
In this thesis the potential gains in vectorisation of linear and nonlinear systems of equations are investigated. Previous studies carried out on the suitability of algorithms for vectorisation have been based on the solution of Poisson's equation. In accordance with this, a range of algorithms are explored and compared using a VA1 pipeline processor attached to a MASSCOMP MC5400. Analysis shows that almost full vectorisation is possible leading to speedup factors of up to 90. Based on these results the vectorised conjugate gradient with a Jacobi preconditioner (JCGV) is the best of the algorithms considered.
This work is extended to the development of a twodimensional fluid flow code which is used to solve the NavierStokes equations, SIMPLE is implemented to handle the nonlinear nature of the equations. The first two problems are isothermal flows, viz, the 'moving lid cavity' and the 'sudden expansion in a duct' problem. A study of where the greatest computational effort is expended, and subsequent vectorisation leads to 98% of SIMPLE being modified. This results in speedup factors of 6 for the cavity problem and 29 for the sudden expansion problem. In both problems the JCGV is marginally faster than the vectorised Jacobi with underrelaxation (JURY). However, the JCGV algorithm is not robust and it is necessary to relax carefully the approximation, otherwise high computation times or divergence is likely.
Two further problems are considered each with increasing complexity, these include scalar quantities of temperature and characteristics of ke turbulence. One problem is based on 'turbulent Lshaped flow in a duct' and the other on the 'natural convection in a square cavity'. A consequence of the higher scalar computation gives speedup factors of 5 for the turbulent Lshaped flow and 11 for the natural convection problem. There is little to choose between the JCGV and JURV algorithms, however, the robustness problems with the JCGV algorithm remain.
A multigrid method (ACM) is used to improve the convergence rate of the algorithms, particularly as the size of problem is increased. Although it is more effective in scalar, it also provides worthwhile improvements for the vectorised algorithms with overall factors of 8.5. Convergence difficulties with the JCG algorithm also prevents the combination with the ACM method. Therefore, the vectorised JUR algorithm with the ACM method is not only more efficient and reliable, but also has scope for improvement as the grid is increased.
The potential gains in vectorisation of the SIMPLE family on pipeline architectures have been clearly demonstrated and indicate that such efforts on practical CFD codes should be well rewarded with regard to processor performance.
Item Type:  Thesis (PhD) 

Additional Information:  uk.bl.ethos.254313 
Uncontrolled Keywords:  fluid mechanics, mathematics, algorithms, equations 
Subjects:  Q Science > QA Mathematics 
Pre2014 Departments:  School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis 
Last Modified:  14 Oct 2016 09:21 
URI:  http://gala.gre.ac.uk/id/eprint/8674 
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