We present a fourth-order finite-volume algorithm in space and time for lowMach number reacting flow with detailed kinetics and transport. Our temporalintegration scheme is based on a multi-implicit spectral deferred correction(MISDC) strategy that iteratively couples advection, diffusion, and reactionsevolving subject to a constraint. Our new approach overcomes a stabilitylimitation of our previous second-order method encountered when trying toincorporate higher-order polynomial representations of the solution in time toincrease accuracy. We have developed a new iterative scheme that naturally fitswithin our MISDC framework that allows us to simultaneously conserve mass andenergy while satisfying on the equation of state. We analyse the conditions forwhich the iterative schemes are guaranteed to converge to the fixed pointsolution. We present numerical examples illustrating the performance of the newmethod on premixed hydrogen, methane, and dimethyl ether flames.
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