Efficient time stepping for reactive turbulent simulations with stiff chemistry

TL;DR

This paper introduces a combined operator splitting and semi-implicit integration approach to improve efficiency and stability in simulating turbulent reacting flows with detailed chemistry, enabling larger time steps and accurate predictions.

Contribution

The paper presents a novel combination of a steady-state preserving operator splitting method with a Rosenbrock-Krylov semi-implicit scheme for reactive turbulent flow simulations.

Findings

Stable and accurate ignition/extinction predictions near critical conditions.

Reduced computational cost through improved stability and efficiency.

Effective large-scale parallel simulation capability.

Abstract

A combination of a steady-state preserving operator splitting method and a semi-implicit integration scheme is proposed for efficient time stepping in simulations of unsteady reacting flows, such as turbulent flames, using detailed chemical kinetic mechanisms. The operator splitting is based on the Simpler balanced splitting method, which is constructed with improved stability properties and reduced computational cost. The method is shown to be capable of stable and accurate prediction of ignition and extinction for reaction-diffusion systems near critical conditions. The ROK4E scheme is designed for semi-implicit integration of spatially independent chemically reacting systems. Being a Rosenbrock-Krylov method, ROK4E utilizes the low-rank approximation of the Jacobian to reduce the cost for integrating the system of ODEs that have relative few stiff components. The efficiency of the scheme is further improved via the careful choice of coefficients to require three right-hand-side evaluations over four stages. Combing these two methods, efficient calculation is achieved for large-scale parallel simulations of turbulent flames.