Analytical Jacobian for Cantera

[mbkumar]

Abstract

I am working on implementing analytical Jacobian for Cantera to replace the finite difference Jacobian computed internally by SUNDIALS.

Motivation

Jacobian matrix can be computed analytically for chemical kinetics. Analytical Jacobian improves the accuracy when compared to the finite difference Jacobian computed with forward difference scheme especially for stiff kinetics. With a good implementation, it can also reduce the computational expense when compared to the finite difference Jacobian.

Description

To obtain the analytical Jacobian, derivatives of the production rates w.r.t. species mass fractions and state variables are computed. Based on the governing equations of a reactor model, derivatives corresponding to the Jacobian can be computed from the computed derivatives of the production rates. An API for the end user to enable/disable analytical Jacobian is added.

Alternatives

Analytical Jacobian can also be obtained by using auto-differentiation packages. Such packages introduce additional dependencies and the fundamental classes of Cantera need to rewritten to account for auto-differentiation. Instead, the current implementation adds additional member variables and methods to the existing classes to compute the required derivatives without touching existing methods.

References

https://github.com/mbkumar/cantera/tree/derivative

[12Chao]

Hi @mbkumar, I think this feature is very helpful, I was wondering is this improvement still in progress?

[mbkumar]

I coded most of the stuff, but I am not working on cantera anymore because I changed jobs. Only few functions are left for implementing the analytical Jacobian. If anyone can take the mantle, I'd be happy to assist. Bharat Medasani Engineer Princeton Plasma Physics Lab (PPPL)

…

On Thu, Aug 5, 2021 at 2:34 PM Chao Xu ***@***.***> wrote: Hi @mbkumar <https://github.com/mbkumar>, I think this feature is very helpful, I was wondering is this improvement still in progress? — You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub <#19 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AA62VEF5NDA4ZEZNLVWOM5TT3LKTRANCNFSM4KD6SB2Q> .

[ischoegl]

I am currently looking at implementing this in the core - there have already been quite a few changes in reaction rate evaluators in 2.6 already, so previous work won't map cleanly. Also, I have not looked at temperature derivatives beyond Arrhenius. The new PR Cantera/cantera#1081 should get species derivatives; there also is some overlap with Cantera/cantera#1010, so hopefully this will be available in 2.6.

@mbkumar ... once I get to temperature derivatives, it may be great if I could recycle your code if you don't mind (and would certainly give credit).

[mbkumar]

@ischoegl
Feel free to use the code in anyway you see fit.

[ischoegl]

Closed via Cantera/cantera#1089.