I am trying to implement a chemical solver in an implicit approximate factorization code. I need a chemical source term Jacobian. A derivation has been done for this in my group in the past, however the derivation assumed that the fluxes are written as such:

Q= [rho_1,rho_2,...,rho_n-1,rho,rho*u,...]

where rho_1 is the density of species 1, etc.

The code I am using now writes the fluxes in this way:

Q= [rho_1,rho_2,...,rho_n,rho*u,...]

Would anyone know how to "convert" -so to speak- the Jacobian for the first type of flux definition to a Jacobian for the second type of flux definition?

Thanks very much in advance for your replies

--Giovanni

Assuming Q1 is the old Q vector and Q2 is the new Q vector and W is the sorce term vector, you then already have d_W/d_Q1 and you want to compute d_W/d_Q2

d_W/d_Q2 = d_W/d_Q1 * d_Q1/d_Q2

you have to compute the transformation matrix d_Q1/d_Q2 and post multiply the existing jacobian with it. THat should be all.

Regards, Srinivasan