## Preprint 58 Published

Preprint 58, "A predictor-corrector algorithm for the coupling of stiff ODEs to a particle population balance", has been published on the CoMo Group website.

In this paper a novel predictor-corrector algorithm is presented for the solution of coupled gas-phase–particulate systems. The emphasis of this work is the study of soot formation, but the concepts can be applied to other systems. This algorithm couples a stiff ODE solver to a Monte Carlo population balance solver. Such coupling has been achieved previously for similar systems using a Strang operator splitting algorithm, however, that algorithm demonstrated several numerical issues which resulted in a high computational cost to acquire adequate precision. In particular a source-sink instability was identified whereby a large-magnitude source term present in the ODE system was competing with a similarly sized sink term in the population balance. This instability required that the splitting-step size was very small in order to keep numerical error sufficiently low. A predictor-corrector algorithm has been formulated to negate this instability. An additional efficiency is gained with this algorithm as a principal computational cost of the Strang splitting algorithm is removed: the requirement to re-initialise the ODE solver every splitting-step. The numerical convergence of the new algorithm is demonstrated and its efficiency is compared to that of the Strang splitting algorithm. Substantial computation time savings are demonstrated, which allow a fixed error in three studied system functionals to be achieved with an order-of-magnitude reduction in computation time.

The Figure shows the Computation Time—Error Space diagram for gas-phase pyrene concentration (A4). The lines show approximately the lowest achievable error for a given computation time.