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

TL;DR

This paper presents a symbolic method for constructing the chemical Jacobian in QSSA-reduced models, enabling efficient, portable computations on exascale platforms with code generation and optimization strategies.

Contribution

It introduces a symbolic approach combined with code generation for the chemical Jacobian in QSSA models, improving efficiency and portability for high-performance computing.

Findings

Successfully tested on a 3D multipulse ignition problem

Enables portable application across chemical models and GPU architectures

Provides open-source implementation for community use

Abstract

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, stiffness remains, and the resulting model 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 rate, 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 a 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.