@mastersthesis {105,
title = {Large Eddy Simulation with the unstructured collocated arrangement},
volume = {PhD Thesis, The University of Manchester},
year = {2006},
school = {University of Manchester},
address = {Manchester},
abstract = {Several industrial applications of CFD, such as thermal fatigue, aero-acoustic
noise or fluid-structure interaction need to capture the unsteady behaviour of an
incompressible flow. Large Eddy Simulation is the only reasonable approach in
CFD to obtain a time-dependent solution, as well demonstrated on academic cases.
However, performing LES on fully unstructured finite-volume grids, as required for
complex industrial geometries, as well as to locally adapt the grid resolution to the
large spatial variations of turbulent scales, remains challenging. The main purpose
of the present work is to deal with the collocated arrangement implemented in the
in-house {\textasciiacute}Electricit{\textasciiacute}e De France (EDF) code Code Saturne and to show whether
reasonable LES computations are feasible with this discretization.
Several numerical issues such as numerical dissipation are first analyzed in a
discrete sense. It is found that the Rhie and Chow interpolation, widely used in all
the collocated approaches, introduces a numerical dissipation which drains energy
equally at all the wave-numbers. Removing this interpolation on regular Cartesian
grids allows, with a second order Crank-Nicolson scheme and sub-iterations on the
predictor-corrector algorithm for pressure/velocity coupling, to strictly conserve
kinetic energy. Nevertheless, the interpolation is maintained as it has a stabilizing
effect on skewed grids and as it avoids odd-even decoupling phenomenon. It is also
found that a {\textquoteright}symmetrical{\textquoteright} formulation allows to strictly conserve kinetic energy for
the convection term. The use of this formulation alters the second order precision
of the code. Thus, a second order approach for the convection term is kept with
implicit gradient reconstruction for non-orthogonal grids. Finally, sub-iterations
on the predictor-corrector algorithm for pressure/velocity coupling are retained as
this allows to reduce time splitting errors.
A particular attention is then paid to the Decaying Isotropic Turbulence in
order to identify the implicit filter induced by the discretization and to find the
appropriate Smagorinsky constant. It is found that the implicit filter induced by
the numerical discretization with a Smagorinsky model resembles to a Gaussian
filter with a filter-width equal to 2h where h is the grid-spacing in a regular mesh.
The value of the Smagorinsky constant is between 0.16 and 0.18 what corresponds
to consensual values found in the literature for highly accurate discretizations.
The explicit filter employed for the dynamic model is a smoothing operator that
involves all the neighbours of a cell which share a node with it. The filter-width
of this explicit filter is equal, on uniform meshes, to 3h. The averaging of the
Smagorinsky constant is done for its numerator and denominator separately. It
is also shown that local averaging gives reasonable results with the DIT which
is encouraging for industrial simulations in which no homogeneous direction is
available.
The last two academic cases to be tested are the standard and the oscillating
channel flows. After usual tests on structured Cartesian meshes, the ability of nonconforming
meshes to adapt the resolution large eddy scale variations at the wall is
pointed out. The global over-estimation of the mean velocity often observed with Cartesian meshes is cured by introducing local refinements in the near-wall region
using the capabilities of a collocated approach to naturally handle non-conforming
meshes. This solution is very promising to run industrial cases at moderate to high
Reynolds numbers without artificial wall functions. To conclude the channel flow
simulations, a distributed non-conforming mesh is created following the behaviour
of the Kolmogorov scales in each direction in order to obtain a very fine mesh compatible
with a Direct Numerical Simulation resolution but with a lower number of
computational cells than in the conforming cases. The results are very satisfactory
compared to previous DNS calculations on structured grids. This capability can
be exploited to run DNS calculations at higher Reynolds numbers with much less
nodes than in the structured case.
Finally, The potential of LES to predict complex vortical separation is reported
using a 3D axi-symmetric bump considered very challenging by the CFD
community as all Reynolds Averaged Navier-Stokes attempts totally failed. The
calculations give satisfactory quantitative results. The main physical structures
observed in the experiment are captured. The quantitative results are globally
satisfactory except for the wall-normal component of the velocity which is far from
the experimental results and for the Reynolds stresses which are overestimated.},
url = {http://cfd.mace.manchester.ac.uk/coffee/papers/phdSofian.pdf},
author = {Sofiane Benhamadouche}
}