Adaptive polynomial tabulation

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This work introduces a novel method called Adaptive Polynomial Tabulation (APT) for solving initial value chemical rate equation systems. APT employs zeroth, first, and second order polynomials in real-time to approximate solutions. To enhance accuracy, the chemical state space is divided into hypercubes, which are further refined into adaptive hypercubes based on the local solution's precision. Initial conditions of the mixture are stored in these adaptive hypercubes, with each condition surrounded by two concentric ellipsoids of accuracy (EOA): the ISAT and identical EOAs. The time evolution of mixture initial conditions that intersect with these EOAs is approximated using appropriate polynomial orders. When a sufficient number of initial conditions are stored, second order polynomial coefficients are derived from them, allowing for the approximation of additional conditions within the hypercube. Notably, APT simplifies the entire species mass fraction into a single progress variable. The method was validated using the Stochastic Reactor Model (SRM) for HCCI engines, employing a n-heptane/toluene mechanism comprising 148 species and 1281 reactions. Results demonstrated significant computational gains, with factors exceeding 12 and 1000 for multi-cycle calculations, accurately capturing cool flame, blue flame, and main excitation events throughout the tests.