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

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 and allows us to conserve mass and energy while simultaneously satisfying 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.

Keywords:

• low Mach number combustion
• spectral deferred corrections
• fourth-order spatiotemporal discretisations
• flame simulations
• detailed chemistry and kinetics

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work at LBNL was supported by the Applied Mathematics Program of the DOE Office of Advanced Scientific Computing Research under the US Department of Energy [contract DE-AC02-05CH11231]. The submitted manuscript has been authored by a contractor of the US Government under this contract. Accordingly, the US Government retains a non-exclusive royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for US Government purposes.