I am currently puzzled by the implementation of the Sarkar Compressibility Correction (CC) for the SST model.
I think there are multiple levels of errors:
- LV1 - the conceptual error: the Sarkar CC has been developed for the $k$-$\epsilon$ model, thus its porting to the SST $k$-$\omega$ model should not be as-is, but should be shielded by the $F_1$ function.
- LV2 - the model error: the Sarkar CC as implemented considers both the Pressure-Dilatation (PD) term and the Dilatation-Dissipation (DD) term. The second one is present in the original Sarkar model (although it is implemented incorrectly, as it has the same treatment of the Wilcox CC being multiplied by the Heaviside function centered around $M_{t,0}$). The PD term, instead, is not present in the original formulation, although it can be added to any CC (in principle).
The literature is quite vague on these issues, too, which does not help. Usually, Sarkar is multiplied by $(1-F_1)$ when applied to the SST model in some papers (https://arc.aiaa.org/doi/pdf/10.2514/6.2011-279, https://arc.aiaa.org/doi/pdf/10.2514/6.2009-1329) or straight-up left as-is when coupled with SST in other papers (https://doi.org/10.1177/1687814015620319).
For sure, the first correctness fix would be to change the $\zeta_{FMT}$ function of Sarkar CC to be equal to $M_t^2$ and put the Pressure-Dilatation term behind an SSTParsedOption (compPressDil). I have prepared a branch for it named fixCC.
We can discuss if it needs to be shielded behind the $F_1$ function too, although it is important to notice that (Sarkar+PD)*(1-$F_1$) = Suzen--Hoffmann CC (https://arc.aiaa.org/doi/pdf/10.2514/6.1998-322).
Unfortunately, I cannot find the PR related to these implementations to replicate those test cases. Still, I see that there are a couple of configs under the Testcases/rans/flatplate folder, so I will try them.
Desktop (please complete the following information):
- OS: CentOS Linux release 7.6.1810
- C++ compiler and version: GCC 10.2.0
- MPI implementation and version: 4.1.6
- SU2 Version: v8.5.0
I am currently puzzled by the implementation of the Sarkar Compressibility Correction (CC) for the SST model.
I think there are multiple levels of errors:
The literature is quite vague on these issues, too, which does not help. Usually, Sarkar is multiplied by$(1-F_1)$ when applied to the SST model in some papers (https://arc.aiaa.org/doi/pdf/10.2514/6.2011-279, https://arc.aiaa.org/doi/pdf/10.2514/6.2009-1329) or straight-up left as-is when coupled with SST in other papers (https://doi.org/10.1177/1687814015620319).
For sure, the first correctness fix would be to change the$\zeta_{FMT}$ function of Sarkar CC to be equal to $M_t^2$ and put the Pressure-Dilatation term behind an SSTParsedOption (compPressDil). I have prepared a branch for it named fixCC.
We can discuss if it needs to be shielded behind the$F_1$ function too, although it is important to notice that (Sarkar+PD)*(1-$F_1$) = Suzen--Hoffmann CC (https://arc.aiaa.org/doi/pdf/10.2514/6.1998-322).
Unfortunately, I cannot find the PR related to these implementations to replicate those test cases. Still, I see that there are a couple of configs under the Testcases/rans/flatplate folder, so I will try them.
Desktop (please complete the following information):