On-demand generation of reduced mechanisms based on hierarchically extended intrinsic low-dimensional manifolds in generalized coordinates

A new implementation scheme for reduced mechanisms based on hierarchically generated and extended intrinsic low-dimensional manifolds (ILDMs) created “on-demand” is presented. The algorithm includes the use of ILDMs in generalized coordinates and a new hierarchical concept for the extension of the ILDMs into the domain of slow chemistry. Problems of pre-calculated ILDM tables are overcome by generating ILDM cells on-demand during the flame calculation, yielding an increased efficiency of the table generation and implementation. In view of a future generation of ILDMs with adaptive dimension based on a local online error control, the presented algorithm includes the possibility to increase the ILDM dimension hierarchically after the stationary solution (solution after 10⁴ s) of the first flame calculation with an n_c-dimensional ILDM is reached and to re-calculate the result of this first flame calculation using higher-dimensional manifolds with a subsequent error test. The paper presents the generation of hierarchically extended ILDMs in generalized coordinates as well as the on-demand implementation scheme. A sample free flame calculation for the syngas-air system validates the algorithms.