Stochastic algorithms for the analysis of numerical flame simulations

Recent progress in simulation methodologies and high-performance parallel computers have made it is possible to perform detailed simulations of multidimensional reacting flow phenomena using comprehensive kinetics mechanisms. As simulations become larger and more complex, it becomes increasingly difficult to extract useful information from the numerical solution, particularly regarding the interactions of the chemical reaction and diffusion processes. In this paper we present a new diagnostic tool for analysis of numerical simulations of reacting flow. Our approach is based on recasting an Eulerian flow solution in a Lagrangian frame. Unlike a conventional Lagrangian viewpoint that follows the evolution of a volume of the fluid, we instead follow specific chemical elements, e.g. carbon, nitrogen, etc., as they move through the system. From this perspective an “atom” is part of some molecule of a species that is transported through the domain by advection and diffusion. Reactions cause the atom to shift from one chemical host species to another and the subsequent transport of the atom is given by the movement of the new species. We represent these processes using a stochastic particle formulation that treats advection deterministically and models diffusion and chemistry as stochastic processes. In this paper, we discuss the numerical issues in detail and demonstrate that an ensemble of stochastic trajectories can accurately capture key features of the continuum solution. The capabilities of this diagnostic are then demonstrated by applications to study the modulation of carbon chemistry during a vortex–flame interaction, and the role of cyano chemistry in NOx production for a steady diffusion flame.