Dual timestepping methods for detailed combustion chemistry

In this work, we develop and study several dual time integration methods for the solution of stiff, explosive differential equations governing combustion chemistry. Dual time integration is an implicit method wherein the sub-iteration process of each timestep is performed as a steady-state integration process, rather than the commonly used Newton–Raphson method. This allows stabilisation when nonlinear ignition events are contained within a timestep, providing considerable freedom in the choice of resolved phenomena. Timesteps may be chosen so as to resolve relatively long process timescales accurately rather than fast chemical timescales, something not possible with the common Newton's method. We illustrate this method using several backward difference formula methods and demonstrate the efficacy of our method in resolving low-frequency solutions of continuous flow stirred-tank reactors with periodic ignition–extinction events. We are able to step over ignition–extinction events with our stable, adaptive dual time method, and we study numerical convergence and error scaling on process timescales.