Computational Fluid Structure Interaction - Computational Hemodynamics: Theory, Modelling and Applications - page 109

whereby large turbulent structures, in the form of eddies/vortices are resolved di-
rectly (i.e. no modelling) while smaller eddies are modelled. Large scale turbulence
depends strongly on the flow and boundary conditions, thus is flow-dependent and
is difficult to model. On the other hand small scale turbulence is nearly homogenous
and isotropic, making it independent of the flow and easier to model. LES is a time-
dependent and 3D model which uses the mesh size as the filtering scale. This places
a high demand on computational resources, since the mesh and time step sizes need
to be fine enough to resolve down to the smallest turbulence scales, which becomes
increasingly severe in near-wall regions where the scales are much smaller than
those in the bulk flow region. LES is an advanced approach to RANS-based models
which can handle transitional flows. It has the ability to represent coherent turbulent
structures, and large scale turbulence, while modelling the small-scale effects.
The most complete approach is DNS (Direct Numerical Solution) which in fact
is not a modelling approach at all. Rather it directly solves the governing equations
without any modelling by using sufficiently fine mesh and time steps to capture all
scales of turbulence. This places an enormous demand on computational resources.
For example a typical flow domain having a cross-sectional area of 0.1 m by 0.1 m
with a high Reynolds number turbulent flow might contain eddies as small as 10 or
100 μ m in size. This means that to resolve the flow at all length scales, a compu-
tational mesh of 10 9 to 10 12 grid points are needed. Furthermore, the fastest events
that can take place have a frequency of the order of 10 kHz, which would require a
time step of about 100 μ s. At this stage and even in the near future, DNS of turbulent
flows at high Reynolds numbers are not feasible. Only low to moderate Reynolds
numbers under very simple geometries can be handled with the fastest computers
today. This means that for practical engineering applications, DNS is an unrealistic
and inefficient approach since the smallest scales of turbulence may not be nec-
essary. Figure 5.14 shows a comparison of the different modelling approaches in
terms of how much of the flow is modelled or resolved, and the required computa-
tional demand for each approach.
Fig. 5.14 Comparison of turbulence models and the amount of flow physics that is resolved or
modelled