Hi all,
The scaling is actually with the number of species cubed, due to the LU factorization of the Jacobian matrix, which has a bandwidth proportional to the number of variables at each grid point. AramcoMech 2.0 has 493 species, compared to 53 for GRI 3.0. Not counting the other variables at each grid point, that would suggest about a factor of 800 increase in the computational time. The result you're getting is maybe a little better than that, since not all of the time is spent in the LU factorization, at least for the smaller problem.
There are approaches that would avoid this unfortunate cubic scaling, some of which are discussed in
this Enhancement proposal. As a near term alternative, you could also consider using
Ember, which solves a time-dependent 1D flame using an explicit integrator for the chemistry term, which gives it near-linear scaling in the number of species.
Regards,
Ray