these simulation numerique et modelisation de l'ecoulement autour ...

ARTIFICIAL VISCOSITY MODELS
As a consequence, the only action of this model is to put a lot of 2 nd order AV everywhere in the field.
Moreover, this AV is applied on all transport variables (momentum, energy and species).
This option produces highly non-physical results as it adds a lot of viscosity everywhere. It often leads
to stationnary results which look very similar to RANS computations. It must never be used to produce
LES results. This option can be used for example to initialise a computation, but even in this case, the
“Jameson” model should be preferred.
A.4.2
“Jameson” model
A “Jameson” sensor based on pressure is used in this case.
ζ JAM = ζ J Ω j
(P )
(A.24)
The amount of 2 nd order AV that is applied is directly proportional to this sensor. The amount of 4 th
order AV also depends on the sensor. Actually, the input parametersmu4 is replaced by :
smu4 ′ = max(0, smu4 − ζ JAM smu2)
(A.25)
This formulation allows to put 4 th order AV only where the sensor is small (as well as the amount of 2 nd
order AV). On the other hand, if the sensor is large, it is no use to put 4 th order AV, because the 2 nd order
AV operates fully and overcomes most of the problems.
Both operators are applied on all variables (momentum, energy and species).
This model was originally proposed by Jameson and Turkel Jameson et al. (1981). It is very well
suited for “aerodynamics” configurations, with shocks and without combustion, solved with a RANS
solver. However it appears that for reacting LES, this model is much too dissipative and must only be
used during transient phases. It allows to stabilise a computation when non-physical processes of high
amplitudes happen (at the initialisation phase for example). However, for LES simulations we recommend
the use of the “Colin” model.
A.4.3
“Colin” model
Three sensors are used here in conjunction. The first one is based on total energy, the second one is
based on species densities, and the last one is the maximum of the two previous.
ζE COL = ζΩ C j
(ρE), ζY COL = max
k=1,neqs ζC Ω j
(ρ k ) and ζmax
COL
= max(ζE
COL , ζY COL ) (A.26)
The way these operators are combined and applied is a little bit tricky.
Let’s begin by the AV on the species. As for the Jameson model, we build a modified coefficient for the
4 th order operator, but this time it is based on the maximum sensor ζ COL
max :
smu4 ′ = max(0, smu4 − ζ COL
max smu2) (A.27)
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