Low-cost Jacobian-free mapping for dynamic cell clustering in multi-regime reactive flows

Dynamic Cell Clustering (DCC), also referred as Cell Agglomeration, is an optimisation technique used to reduce the cost of finite-rate chemistry in reactive flows. It consists of three steps: (i) grouping of elements with similar composition into clusters, (ii) computation of a single element per cluster and (iii) mapping of the computed elements to the remaining elements of the cluster through interpolation and extrapolation. The size of the clusters results from a compromise between cost reduction and desired accuracy. A new Jacobian-free mapping method (JFM) combined to Principal Component Analysis (PCA) is introduced in order to provide the accuracy of a higher-order mapping without the overhead of a Jacobian evaluation. The increased accuracy is obtained by creating a connectivity map between adjacent clusters. Along the cluster connections, composition and source term gradients are known enabling an approximation of the Jacobian. The JFM methodology is validated on a hydrogen–air triple flame, a multi-regime flame which covers a wide region in the species/temperature phase space. It is shown that for realistic clustering conditions the JFM method shows a similar accuracy to the explicit Jacobian. Compared to other mapping methods, an error reduction of up to 74% is observed while the cell agglomeration overhead remains less than 1% of the initial cost.