Solving a no linear equation of the Spalart-Allmaras model

Please read Read before posting: How do I get my question answered? . The code you posted isn’t reproducible.

I would first of all try with a direct solver. Are you sure that you can use cg to solve with the jacobian matrix on the left-hand side? Looking at the expressions you have in fv1, I wouldn’t vouch that J is symmetric positive definite.