Content-Type: multipart/alternative; boundary=001a11c3813662471604de92e023 --001a11c3813662471604de92e023 Content-Type: text/plain; charset=ISO-8859-1 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 initially surprising. -- John --001a11c3813662471604de92e023 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable
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 t= he 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= 9;t change the flux Jacobian matrix... it is the same as for the constant-a= rea 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 d= on't recover dF/dx except in the case of an ideal gas. =A0The attached = slides go into additional detail... I'd be grateful if someone could ta= ke a look and point me in the right direction -- this has been driving me c= razy for a couple days now.

Note that one small, but possibly significant, differen= ce 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 gene= ral case... =A0I don't think this has any direct bearing on the quasi-l= inear form, but I found it initially surprising.

--
John
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