  The convergent reaction-diffusion master equation (CRDME) was recently
developed to provide a lattice particle-based stochastic reaction-diffusion
model that is a convergent approximation in the lattice spacing to an
underlying spatially-continuous particle dynamics model. The CRDME was designed
to be identical to the popular lattice reaction-diffusion master equation
(RDME) model for systems with only linear reactions, while overcoming the
RDME's loss of bimolecular reaction effects as the lattice spacing is taken to
zero. In our original work we developed the CRDME to handle bimolecular
association reactions on Cartesian grids. In this work we develop several
extensions to the CRDME to facilitate the modeling of cellular processes within
realistic biological domains. Foremost, we extend the CRDME to handle
reversible bimolecular reactions on unstructured grids. Here we develop a
generalized CRDME through discretization of the spatially continuous volume
reactivity model, extending the CRDME to encompass a larger variety of
particle-particle interactions. Finally, we conclude by examining several
numerical examples to demonstrate the convergence and accuracy of the CRDME in
approximating the volume reactivity model.
