The Dynamic Adaptive Chemistry method also takes advantage of the operator-splitting method described above in Operator Splitting Method and Parallel Implementation , by focusing on the local conditions of each cell. This method performs on-the-fly mechanism reduction for each local condition prior to solving the chemistry terms in the transient chemistry integration step of the operator-splitting method. The reduction is dynamically applied cell-by-cell (or cluster-by-cluster if the Dynamic Cell Clustering method is used) at each time step. In this way the dynamic chemistry solution often uses locally valid, smaller mechanisms instead of the full mechanism, causing significant time savings for the overall transient integration.

To ensure validity over a wide range of thermochemical conditions, comprehensive kinetic mechanisms for the combustion of realistic fuels typically include hundreds of species and thousands of elementary reactions. However, much smaller subsets of species and reactions often are adequate to capture the dominant reaction pathways for specific, local conditions over a short time span (typically taken to be the hydrodynamic time step in CFD calculations). To make use of this fact, the dynamic adaptive chemistry (DAC) method reduces the comprehensive detailed mechanism to locally valid smaller mechanisms. This operation is performed on the fly (that is, during the dynamic simulation, at every time step). It is based on a skeletal mechanism-reduction method called Directed-Relation-Graph with Error Propagation (DRGEP) [54] method, which offers very efficient and very accurate reduction.

Given a detailed kinetic mechanism and a specific thermochemical state X( T, p, yk ), where k is the species index ( k =1, , K ) and yk is the mass fraction of species k , the directed relation graphs in the DRGEP method are constructed such that one vertex (species) is connected to all others by directed edges. These edges are weighted by the immediate dependence of one species on another. This dependence is quantified by the normalized contribution of species B to A , defined by

(5–13)

where i is the reaction index ( i =1, …, I ), υ _Ai is the stoichiometric coefficient of species A in the i th reaction, and ω _i is the progress variable of reaction i . r _AB is a measure of the error introduced to the production rate of A due to elimination of all the reactions that contain B . Certain species deemed of primary importance are selected as initial species in the reduced mechanism. Then starting from each of these pre-selected initial species, a breadth-first search (BFS) is performed to identify the species on which the initial species depends to form a subsidiary set. Consequently, the union of the subsidiary sets of all the initial species forms the active species set of the reduced mechanism. Thus the mechanism reduction is equivalent to identifying vertices to which there exist "strong" paths that connect them to a vertex in the initial set.

The strength of the connection between the species being visited and the initial species diminishes as we proceed along a path. This diminution can be used to control the search depth. To quantify the decreasing dependence, an " R -value" is defined at each vertex V with reference to the initial vertex V ₀ :

(5–14)

where Ω is the set of all possible paths leading from V ₀ to V , and Π r _ij is the chain product of the weights of the edges along the given path. Based on this definition, vertex V will be marked as "reachable" if R _V 0(V) is larger than a user-defined threshold value ε _R . Thus, all the reachable vertices starting from V ₀ constitute the subsidiary set of V ₀ , and the union of such sets gives the species that are active in the reduced mechanism. This method has been tested on both diesel and gasoline surrogate fuels in Liang et al. [[48] , [49] ]. The studies proved that {fuel, CO and HO2} is an effective choice for the search-initiating species set, and suggested that ε _R be set in the range of 10 ^-5 to 10 ^-4 . Both the search-initiating species set and the search threshold are provided as user inputs in Ansys Forte (Initial Species and Search Tolerance, respectively).

The DRGEP method extracts a group of active species for the existing local thermochemical conditions. Consequently, a reaction is included in the reduced mechanism only if all the reactants and products are active species (third bodies are not counted as participants). Species not in the active set are treated as inactive, with their mass fractions kept fixed. Given a system that involves m active and n inactive species , where the superscripts " a " and " i " denote active and inactive species, respectively, the formulation can be expressed as

(5–15)

In Equation 5–15 Equation 5-15 , ordinary differential equations are formulated with respect to only active species. When the rate functions are evaluated, however, all the species are considered, thus eliminating the need to include the third-body species in the reduced mechanisms.