An efficient storage scheme for reduced chemical kinetics based on orthogonal polynomials

Simplified chemical kinetic schemes are a crucial prerequisite for the simulation of complex three-dimensional turbulent flows, and various methods for the generation of reduced mechanisms have been developed in the past. The method of intrinsic low-dimensional manifolds (ILDM), e.g., provides a mathematical tool for the automatic simplification of chemical kinetics, but one problem of this method is the fact that the information which comes out of the mechanism reduction procedure has to be stored for subsequent use in reacting-flow calculations. In most cases tabulation procedures are used which store the relevant data (such as reduced reaction rates) in terms of the reaction progress variables, followed by table look-up during the reacting-flow calculations. This can result in huge amounts of storage needed for the multi-dimensional tabulation. In order to overcome this problem a storage scheme is presented which is based on orthogonal polynomials. Instead of the use of small tabulation cells and local mesh refinement, the thermochemical state space is divided into a small number of coarse cells. Within these coarse cells polynomial approximations are used instead of frequently used multi-linear interpolation. This leads to a considerable decrease of needed storage. The hydrogen-oxygen system is considered as an example. Even for this small chemical system, a decrease of the needed storage requirement by a factor of 100 is obtained.