  The two-regime method (TRM) has been recently developed for optimizing
stochastic reaction-diffusion simulations. It is a multiscale (hybrid)
algorithm which uses stochastic reaction-diffusion models with different levels
of detail in different parts of the computational domain. The coupling
condition on the interface between different modelling regimes of the TRM was
previously derived for one-dimensional models. In this paper, the TRM is
generalized to higher dimensional reaction-diffusion systems. Coupling Brownian
dynamics models with compartment-based models on regular (square)
two-dimensional lattices is studied in detail. In this case, the interface
between different modelling regimes contain either flat parts or right-angled
corners. Both cases are studied in the paper. For flat interfaces, it is shown
that the one-dimensional theory can be used along the line perpendicular to the
TRM interface. In the direction tangential to the interface, two choices of the
TRM parameters are presented. Their applicability depends on the compartment
size and the time step used in the molecular-based regime. The two-dimensional
generalization of the TRM is also discussed in the case of corners.
