Adaptive Interpolation Algorithm Based on a kd-Tree for the Problems of Chemical Kinetics with Interval Parameters

Abstract

The questions of simulating chemical processes with uncertainty in their parameters are considered. A new approach consisting in the construction of a dynamic structured grid based on a kd-tree over the space formed by the interval parameters of a problem is proposed. When the algorithm is executed, a piecewise polynomial function interpolating the dependence of a solution on certain values of interval parameters is built at every step of integrating the initial system of ordinary differential equations. The results of testing the algorithm on the problems of chemical kinetics, including the combustion processes, demonstrate its efficiency and broad range of applications.