Carleman-Taylor Linearization of Reactiong Flows for Quantum Computing

This study proposes a novel method to integrate quantum computing into reactive flow analysis, addressing the nonlinear challenges of Arrhenius reaction rates. While reacting flow systems involve nonlinear equations, quantum computers excel at solving linear systems. To bridge this gap, Carleman linearization is applied to convert nonlinear dynamics into linear form, making them compatible with quantum algorithms. Additionally, Taylor series expansions approximate the exponential temperature dependence of reaction rates. The method is validated through ignition simulations of reacting H₂/air and CH₄/air mixtures. The study explores how the truncation order in Carleman linearization and the fitting order in Taylor expansion affect accuracy and computational cost. Results show that higher-order approximations increase accuracy but may cause numerical stiffness, especially in systems with high activation energy such as CH₄/air. This work demonstrates a trade-off between precision and computational feasibility and lays the groundwork for applying quantum computing to combustion modeling.