P(CA)2: PCA-Based Cell Agglomeration for CFD Simulations with Detailed Kinetic Mechanisms

Abstract

The inclusion of detailed chemical kinetics in multidimensional simulations of reactive flows remains computationally very demanding. Among the techniques used to reduce the cost associated with detailed chemistry, cell agglomeration (CA) has proven particularly effective in simulations based on the operator-splitting approach, where cells with similar thermochemical states are grouped and integrated together during the chemical step. In this work, a new methodology for the automatic selection of clustering variables in CA is proposed based on principal component analysis (PCA). In the proposed P(CA)2 (PCA-based Cell Agglomeration) approach, the clustering is performed in a reduced space defined by the most relevant principal components of the thermochemical state. This removes the arbitrariness associated with the manual selection of temperature and species mass fractions typically used as clustering features in conventional CA algorithms. Moreover, the PCA space is dynamically updated during the simulation, allowing the clustering procedure to adapt to the evolving thermochemical structure of the reacting flow. The P(CA)2 methodology was assessed on an unsteady laminar coflow diffusion flame using kinetic mechanisms of increasing complexity, including a mechanism with 224 species and 5939 reactions. The method was also tested on a temporally evolving turbulent planar jet flame. The results show that P(CA)2 provides accurate solutions while achieving significant computational acceleration, with effective overall speed-ups reaching approximately 70–80% of the asymptotic maximum allowed by the nonchemistry fraction of the computational cost. The proposed approach removes the need for heuristic selection of clustering variables, provides systematic control of the solution accuracy, and can be easily integrated into existing CFD solvers based on operator splitting. These features make P(CA)2 a promising tool for accelerating simulations of reactive flows involving detailed chemical kinetic mechanisms.