6.9 Reynolds-averaged simulation
The computational cost of DNS and, to a lesser extent, LES is too great for most practical CFD, as discussed in Sec. 6.8 . Instead, a Reynolds-averaged simulation (RAS) provides a much more aﬀordable method to calculate turbulence.
It solves equations for “averaged” ﬁeld variables to avoid resolving small ﬂuctuations. Rather than consider an average over a time interval, we imagine the same ﬂow repeated several times under nominally the same initial conditions (2 examples below).
Solutions vary due of diﬀerences in initial conditions and the chaotic nature of turbulence. The ensemble average calculates the mean solution for multiple realisations of the same ﬂow.
Each ﬁeld, e.g. , is decomposed into the averaged ﬁeld and ﬁeld of random ﬂuctuations , according to
The terms for mean quantities in Eq. (6.13 ) are the same as in Eq. (6.12 ). The diﬀerence is that Eq. (6.13 ) includes the additional term containing ﬂuctuations .
The argument of this divergence derivative is a tensor known as the Reynolds stress11