Summary
The efficiency with which a fluid flow algorithm can be computed on a supercomputer depends on two factors: economy and performance. In the present context, economy refers to the algorithm’s ability to produce an accurate simulation in the least number of arithmetic calculations. The algorithm’s performance, on the other hand, relates to the number of floating point operations per second (FLOPS) sustainable during the computation. As used in this sense, the two factors are not necessarily compatible; to exhibit maximum performance strictly in terms of FLOPS, an algorithm must usually sacrifice a degree of economy. The attainment of optimal algorithm efficiency requires a careful balance of both performance and economy.
In the present paper, two separate algorithms are compared for their efficiency and accuracy. The two codes differ markedly in their solution procedure. The Pressure Implicit with Splitting of Operators (PISO) [1,2] method has been demonstrated to be an exceptionally economical method to simulate transient, convective heat transfer in two or three dimensions. Our research has indicated that PISO can compute transient convection simulations two orders of magnitude faster than the Semi-Implicit Method for Pressure-Linked Equations, Revised (SIMPLER) method [3]. In order to gain optimal performance on a supercomputer, we have optimized the PISO algorithm for speed-up on a vector processor. The PISO method programmed for this test uses the power law [3] for calculating advection-diffusion at control volume interfaces. For the comparison case, an explicit method using a marker and cell technique (MAC) has been modified with a Bounded Directional Transportive Upwind Differencing Scheme (BDTUD) [4,5] in an attempt to give the advective transport a higher order of accuracy than that obtained using the power law. The MAC/BDTUD has also been vectorized to exploit pipelined architecture.
Driven cavity flow and natural convection in a box are solved to steady state on one processor of the Cray XMP to test each code for its 374 Applications of Supercomputers in Engineering efficiency. The solution accuracy of both codes is determined by comparing each against benchmark results for driven cavity flow.
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© 1991 Computational Mechanics Publications
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Ganesh, S., Schreiber, W.C., Chuan, C.H., Sharif, M.A.R. (1991). A Comparison of Two Algorithms Vectorized to Solve Transient, Convective Heat Transfer on Supercomputers. In: Brebbia, C.A., Peters, A., Howard, D. (eds) Applications of Supercomputers in Engineering II. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3660-0_27
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DOI: https://doi.org/10.1007/978-94-011-3660-0_27
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