## Turbulence and Combustion Group |

This work is focused on the development and application of computationally efficient numerical algorithms for the simulation of reacting flow with detailed chemistry. By taking advantage of unique characteristics of the differential equations which govern combustion chemistry, we have developed methodologies which accelerate reacting flow calculations by comparison with conventional methods.

Recently, we are applying time-splitting methods which separate chemical species transport (i.e., convection and diffusion) from chemical reaction. The pure reaction sub-steps are computed using in situ adaptive tabulation (ISAT) which enhances computational performance by taking advantage of unique characteristics of the underlying system of equations. The schemes have been applied to both one- and two-dimensional premixed laminar flames. As demonstrated below, when the ISAT-based splitting scheme is applied to a one-dimensional methane-air flame using detailed chemical kinetics (i.e., GRIMech3.0), an overall speed-up factor of approximately 7.5 is achieved after the ISAT table has been constructed and populated. This application to unsteady laminar flames is challenging because of the strong coupling between reaction and diffusion and because of the evolving flow. In contrast, in PDF methods the incorporation of ISAT is much simpler and effective and speed-ups of 100-1000 are typical.

To further improve the efficiency of chemistry calculations in parallel computations, recently, the ISAT algorithm has been extended to the multi-processor environment, with the aim of minimizing the wall clock time required for chemistry calculations. Different parallel ISAT strategies are developed by combining the existing serial ISAT algorithm with different distribution strategies. The distribution strategies enable the load redistribution of chemistry calculations among processors using message passing. They are implemented in the software x2f mpi , which is a Fortran 90 library for facilitating many parallel evaluations of a general function. With the parallel ISAT strategies, another speed-up factor of up to 30 is achieved for chemistry calculations in parallel computations.