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On maximum achievable speeds for field solvers

Rainald Löhner (Center for Computational Fluid Dynamics, George Mason University, Fairfax, Virginia, USA)
Joseph D. Baum (Advanced Technology Group, SAIC, McLean, Virginia, USA)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 26 August 2014




Prompted by the empirical evidence that achievable flow solver speeds for large problems are limited by what appears to be a time of the order of O(0.1) sec/timestep regardless of the number of cores used, the purpose of this paper is to identify why this phenomenon occurs.


A series of timing studies, as well as in-depth analysis of memory and inter-processors transfer requirements were carried out for a typical field solver. The results were analyzed and compared to the expected performance.


The analysis shows that at present flow speeds per core are already limited by the achievable transfer rate to RAM. For smaller domains/larger number of processors, the limiting speed of CFD solvers is given by the MPI communication network.

Research limitations/implications

This implies that at present, there is a “limiting useful size” for domains, and that there is a lower limit for the time it takes to update a flowfield.

Practical implications

For practical calculations this implies that the time required for running large-scale problems will not decrease markedly once these applications migrate to machines with hundreds of thousands of cores.


This is the first time such a finding has been reported in this context.



Löhner, R. and D. Baum, J. (2014), "On maximum achievable speeds for field solvers", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 No. 7, pp. 1537-1544.



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