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The sensor used in the 2 nd order operator is also the maximum sensor ζ COL
max .
2 nd and 4 th order operators are then applied on each species.
For energy we also build the modified coefficient based on ζ COL
max
A.4 The 4 models implemented in AVBP
smu4 ′ = max(0, smu4 − ζ COL
max smu2) (A.28)
and we apply the 2 nd order AV with the same sensor.
The subtilty comes when dealing with momentum. The 4 th order operator is not applied
smu4 ′ = 0
(A.29)
and the 2 nd order operator uses the energy sensor ζ COL
E
instead of the maximum sensor ζ COL
max .
This model is particularly dedicated to LES of reactive flows. The lack of 4 th order AV on momentum
allows to keep many small scale structures, while damping the wiggles on energy and species.
A.4.4
“SLK” model
This is an improvement of the “Colin” model. We have noticed that applying no 4 th order AV at all on
momentum can yet lead to non-negligible wiggles in some cases (often depending on the quality of the
mesh) and this had to be avoided. This new “SLK” model is very similar to the “Colin” model, except
that instead of setting the modified 4 th order coefficient to zero for momentum equation, it is set to 10 %
of the value used for the other equations. This gives :
ζE SLK = ζΩ C j
(ρE), ζY SLK = max
k=1,neqs ζC Ω j
(ρ k ) and ζmax
SLK
= max(ζE
SLK , ζY SLK ) (A.30)
smu4 ′ Y,E = max(0, smu4 − ζmax SLK smu2) and smu4 ′ U = 1 max(0, smu4 − ζSLK max smu2)
10
(A.31)
This model is very well suited for computations on poor quality meshes that exhibit velocity wiggles
with the standard “Colin” model.
201