Towards an efficient multiscale modeling of low-dimensional reactive systems: study of numerical closure procedures

We study a numerical closure approach for systems of chemically reacting systems [corrected] on lattices with low-dimensional support, for which a mean-field approximation is insufficiently accurate because of lateral interaction on the lattice. We introduce a hierarchy of macroscopic state variables, taking particle clusters into account, whose time evolution is obtained via microscopic (kinetic Monte Carlo) simulation. The macroscopic state variables are chosen such that they can be [corrected] straightforwardly conserved during reconstruction of a microscopic configuration (the so-called lifting step). We present and compare the effects of different alternatives to initialize the remaining degrees of freedom. We illustrate the strong interplay between the number of macroscopic state variables and the specifics of the lifting and that, for a given lifting operator, accuracy of the macroscopic dynamics does not necessarily improve monotonically when adding macroscopic state variables.