A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry

TL;DR

This paper introduces a fourth-order finite-volume algorithm for low Mach number reacting flows with detailed chemistry, utilizing a multi-implicit spectral deferred correction strategy to improve stability and accuracy.

Contribution

The paper develops a new iterative scheme within the MISDC framework that enhances stability, conserves mass and energy, and satisfies the equation of state for complex reacting flows.

Findings

Successfully applied to premixed hydrogen, methane, and dimethyl ether flames.

Achieves higher-order accuracy and stability over previous second-order methods.

Demonstrates effective coupling of advection, diffusion, and reactions in low Mach flows.

Abstract

We present a fourth-order finite-volume algorithm in space and time for low Mach number reacting flow with detailed kinetics and transport. Our temporal integration scheme is based on a multi-implicit spectral deferred correction (MISDC) strategy that iteratively couples advection, diffusion, and reactions evolving subject to a constraint. Our new approach overcomes a stability limitation of our previous second-order method encountered when trying to incorporate higher-order polynomial representations of the solution in time to increase accuracy. We have developed a new iterative scheme that naturally fits within our MISDC framework that allows us to simultaneously conserve mass and energy while satisfying on the equation of state. We analyse the conditions for which the iterative schemes are guaranteed to converge to the fixed point solution. We present numerical examples illustrating the performance of the new method on premixed hydrogen, methane, and dimethyl ether flames.