Chemical kinetics calculation using explicit schemes with geometric adaptive step selection

We show that explicit schemes can be implied even for superstiff problems if one utilizes the geometrically adaptive meshes in which the step is selected basing on the curvature of the integral curve. We propose efficient formulae for the curvature calculation which do not increase the complexity of the explicit schemes. In contrast to commonly accepted algorithms, the proposed technique allows to perform computations and to obtain an asymptotically precise error estimation of the solution simultaneously. This permits to use efficient explicit Runge-Kutta schemes preserving chemical balances for calculation of chemical kinetics problems. As an applied example, we calculate hydrogen-oxygen at a constant temperature. We investigate a set of details of the algorithm and provide practical recommendations of the adjusting parameters selection.