[hasini]

I'm reading into the Spalart Allmaras (SA) model to implement it in a solver, in its "standard" form without the trip term (see also the nice summary of the different versions on this NASA page: https://turbmodels.larc.nasa.gov/spalart.html#safv3 ).

What I'm wondering now: Spalart and co-authors have written in the paper "Modications and Clarications for the Implementation of the Spalart-Allmaras Turbulence Model" that the standard form of SA is also valid for compressible flows, even though the density does not appear in there.

Can someone explain me the reasoning behind this statement? Is it because we multiply the solved for nu_tilde with the density as kind of a post-processing to get the turbulent viscosity mu after we solved the transport equation?


Thanks!

[sbaffini]

The reasoning behind it is common to several transport equations, which can either be written as rho Dphi/Dt (where D/Dt is the material derivative) or, by taking into account the mass conservation (Drho/Dt=0), D(rho phi)/Dt.

Basically, this is how equation 9 is built in the paper. For a finite volume code that is the form of the equation that you should prefer (besides some rearrangement of the non conservative term, which is discussed in both the Iaccarino thesis and the original SA references)