From: John Peterson <jwpeterson@gm...> - 2013-06-07 16:25:25
So this is off-topic, but I know that we have a number of CFD experts
floating around on the lists...
Has anyone worked with the 1D variable-area Euler equations before?
I'd like to develop an SUPG formulation based on the typical quasi-linear
form, in particular for general (non-ideal gas) equations of state.
As far as I can tell, the variable-area aspect doesn't change the flux
Jacobian matrix... it is the same as for the constant-area equations.
But I must be making a very basic (and stupid!) math mistake somewhere:
when I multiply (what I believe to be) the flux Jacobian matrix by the
derivative of the conserved variables, I don't recover dF/dx except in the
case of an ideal gas. The attached slides go into additional detail... I'd
be grateful if someone could take a look and point me in the right
direction -- this has been driving me crazy for a couple days now.
Note that one small, but possibly significant, difference between the ideal
gas EOS and a general EOS is that the flux vector F is not necessarily a
"homogeneous function of degree 1" in the general case... I don't think
this has any direct bearing on the quasi-linear form, but I found it