Scaling and efficiency of PRISM in adaptive simulations of turbulent premixed flames
The dominant computational cost in modeling turbulent combustion phenomena numerically with high fidelity chemical mechanisms is the time required to solve the ordinary differential equations associated with chemical kinetics. One approach to reducing that computational cost is to develop an inexpensive surrogate model that accurately represents evolution of chemical kinetics. One such approach, PRISM, develops a polynomial representation of the chemistry evolution in a local region of chemical composition space. This representation is then stored for later use. As the computation proceeds, the chemistry evolution for other points within the same region are computed by evaluating these polynomials instead of calling an ordinary differential equation solver. If initial data for advancing the chemistry is encountered that is not in any region for which a polynomial is defined, the methodology dynamically samples that region and constructs a new representation for that region. The utility of this approach is determined by the size of the regions over which the representation provides a good approximation to the kinetics and the number of these regions that are necessary to model the subset of composition space that is active during a simulation. In this paper, we assess the PRISM methodology in the context of a turbulent premixed flame in two dimensions. We consider a range of turbulent intensities ranging from weak turbulence that has little effect on the flame to strong turbulence that tears pockets of burning fluid from the main flame. For each case, we explore a range of sizes for the local regions and determine the scaling behavior as a function of region size and turbulent intensity.