Adaptive Polynomial Tabulation (APT): A computationally economical strategy for the HCCI engine simulation of complex fuels

The solution mapping method Adaptive Polynomial Tabulation (APT) for complex chemistry is presented. The method has the potential of reducing the computational time required for stochastic reactor model simulations of the HCCI combustion process. In this method the solution of the initial value chemical rate equation system is approximated in real-time with zero, first and second order polynomial expressions. These polynomials are algebraic functions of a progress variable, pressure and total enthalpy. The chemical composition space is divided a priori into block-shaped regions (hypercubes) of the same size. Each hypercube may be divided in real-time into adaptive hypercubes of different sizes. During computations, initial conditions are stored in the adaptive hypercubes. Two concentric Ellipsoids of Accuracy (EOA) are drawn around each stored initial condition. The time evolution of additional initial conditions which enter the inner EOA and outer EOA are approximated by zero and first order polynomials respectively. With a certain number of stored initial conditions in the adaptive hypercube, the second order polynomial coefficients are constructed from stored initial condition information. When an initial condition enters this adaptive hypercube, its ODE solution is calculated by evaluating the second order polynomials. The APT model is tested with a zero dimensional Stochastic Reactor Model (SRM) for HCCI engine combustion. A skeletal n-heptane/toluene mechanism with 137 chemical species and 1302 reactions is used. In the tests, the HCCI engine simulations using APT are in very good agreement with the model calculations using the ODE solver. The cool flame and main ignition events are accurately captured. The computational performance of the SRM-HCCI engine model is improved by a factor of 12.