Butterfly-Effect for Massively Separated Flows

Abstract

Purpose

During a routine benchmarking and scalability study of CFD codes for typical large-scale wind engineering runs, it was observed that the resulting loads for buildings varied considerably with the number of parallel processors employed. The differences remained very small at the beginning of a typical run, and then grew progressively to a state of total dissimilitude. A “butterfly-effect” for such flows was suspected and later confirmed. The paper aims to discuss these issues.

Design/methodology/approach

A series of numerical experiments was conducted for massively separated flows. The same geometry – a cube in front of an umbrella – was used to obtain the flowfields using different grids, different numbers of domains/processors, slightly different inflow conditions and different codes.

Findings

In all of these cases the differences remained very small at the beginning of a typical run, they then grew progressively to a state of total dissimilitude. While the mean and maximum loads remained similar, the actual (deterministic) instantiations were completely different. The authors therefore suspect that for flows of this kind a “butterfly effect” is present, whereby even very small (roundoff) errors can have a pronounced effect on the actual deterministic instantiation of a flowfield.

Research limitations/implications

This implies that for flows of this kind the CFD runs have to be carried out to much larger times than formerly expected (and done) in order to obtain statistically relevant ensembles.

Practical implications

For practical calculations this implies running to much larger times in order to reach statistically relevant ensembles, with the associated much higher CPU time requirements.

Originality/value

This is the first time such a finding has been reported in the numerical wind engineering context.