Symbolic construction of the chemical Jacobian of quasi-steady state (QSS) chemistries for Exascale computing platforms

The Quasi-Steady State Approximation (QSSA) can be an effective tool for reducing the size and stiffness of chemical mechanisms for implementation in computational reacting flow solvers. However, for many applications, the resulting model still requires implicit methods for efficient time integration. In this paper, we outline an approach to formulating the QSSA reduction that is coupled with a strategy to generate C++ source code to evaluate the net species production rates, and the chemical Jacobian. The code-generation component employs a symbolic approach enabling a simple and effective strategy to analytically compute the chemical Jacobian. For computational tractability, the symbolic approach needs to be paired with common subexpression elimination which can negatively affect memory usage. Several solutions are outlined and successfully tested on a 3D multipulse ignition problem, thus allowing portable application across chemical model sizes and GPU capabilities. The implementation of the proposed method is available at https://github.com/AMReX-Combustion/PelePhysics under an open-source license.

Novelty and Significance

A symbolic method is proposed to write analytical chemical Jacobians. The benefit of the symbolic method is that it is easy to implement and flexible to any elementary reaction type. Its benefit is shown in the context of QSS-reduced chemistries: there, constructing an analytical chemical Jacobian is complex since one must include the effect of traditional elementary reactions and algebraic closure for the QSS species. To the authors’ knowledge, there is no open-source package available to construct analytical Jacobians of QSS-reduced chemistries. We expect this work to facilitate the use of analytical Jacobians in arbitrarily complex chemical mechanisms. The proposed method was integrated into an open-source suite of reacting flow solvers https://github.com/AMReX-Combustion/PelePhysics to facilitate its dissemination.