@phdthesis{Ebenezer2014, author = {Ebenezer, Ngozi}, title = {Adaptive Polynomial Tabulation : a computationally efficient strategy for complex kinetics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-30051}, school = {BTU Cottbus - Senftenberg}, year = {2014}, abstract = {In this work Adaptive Polynomial Tabulation (APT) is presented. It is a new approach to solve the initial value chemical rate equation system. In this approach zeroeth, first and second order polynomials are used in real-time to approximate the solution of the initial value chemical rate equation system. The sizes of the local regions encountered for the different orders of polynomial approximation are calculated in real-time. To improve accuracy the chemical state space is partitioned into hypercubes. During calculations the hypercubes accessed by the reactive mixture are divided into adaptive hypercubes depending on the accuracy of the local solution. Mixture initial conditions are stored in the adaptive hypercubes. Around each stored initial condition two concentric ellipsoids of accuracy (EOA) are defined. These include the ISAT and identical EOAs. The time evolution of mixture initial conditions which encounter an identical and ISAT EOA are approximated by zero and first order polynomials respectively. With a certain number of stored initial conditions within an adaptive hypercube, its second order polynomial coefficients are constructed from the stored initial conditions. The time evolution of additional mixture initial conditions that encounter this adaptive hypercube are approximated with second order polynomials. The APT model is simplified by the replacement of the entire set of species mass fractions with a progress variable based on the enthalpy of formation evaluated at 298 K. APT has 3 degrees of freedom which include the progress variable, total enthalpy and pressure. The APT model was tested with a zero dimensional Stochastic Reactor Model (SRM) for HCCI engine combustion. A skeletal n-heptane/toluene mechanism with 148 chemical species and 1281 reactions was used. In the tests, the HCCI engine simulations using APT were in very good agreement with the model calculations using the ODE solver. The cool flame and main ignition events were accurately captured. The major and minor species were also accurately captured by APT. In SRM-HCCI calculations without cyclic variations, a computational speed up factor greater than 1000 was obtained when APT was used for all the operating points considered without significant loss in accuracy. For the SRM-HCCI engine calculations with cyclic variations, APT demonstrated a computational speed up exceeding 12 without significant loss in accuracy.}, subject = {ISAT; PRISM; APT; SRM; Polynom; Approximation; ISAT; PRISM; APT; SRM}, language = {en} }