Confusion of the Courant number definition

bearcat

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.