Hi all,

I have a weird, maybe stupid, question about the jacobian.

if g = u*dudx + v*dudy (convective termes in NS equations)

i.e. dgdu = d(u*dudx + v*dudy)du

so how am I supposed to derive for example dudx with respect to u?

I know how to do it in Finite Elements but right now I'm applying it in Finite Differences.

Thanks in advance

I'm not sure your math is correct. The typical approach to the convective terms is to write them in a conservative form, so that

g = 0.5*d(u**2)/dx + 0.5*d(v**2)/dy

to use your example. Then the flux terms are defined as

g1 = 0.5*u**2 , g2 = 0.5*v**2

and the Jacobian is defined as the derivatives of the flux terms with respect to the variables (u,v). Not sure if this helps.

Do you mean

g = 0.5*d(u**2)/dx + 0.5*d(u*v)/dy (change is second term)?

My bad - that's what I get for not getting my glasses. Thanks.