Hi,

I think Courant number is a basic concept to many people here. In many CFD textbooks, it's defined as C=u*delta_t/delta_x, where u is the local flow velocity. But sometimes for the compressible flow simulations, people often take it as C=(u+a)*delta_t/delta_x, in which a is the local sonic speed. I am very confused about this. Can anyone give an explanation?

Thank you.

The local velocity ( velocity in each cell) equal to the max of eigenvaluse of the jacobien matrix. the eigenvaluse are forms of: (U+adiabatic sound speed),(U-adiabatic sound speed),(U). and automatically choised (U+a) because is the most great.

a=sqrt(gama*P/rou) EMCAS

this brings more confusion! let me ask another question regarding the Courant (CFL ) number which maybe helpful in going through the depth of it. you may have seen in steady computation that CFL number does still exsist. but in definition you see that CFL=Udt/dx . how can it be possible since we are in steasy mode and there might not be any Delta (t) ... time step in the other word.

[immortality]

to new readers,
steady solvers also use a virtual time to reach to steady results,so they have time in their code too.