A three-species model for steady-state negative corona discharge has been considered, with focus on geometries occurring in electrostatic precipitators and automotive spray painting. The model incorporates electrons as well as positive and negative ions, which are subject to ionization and attachment reactions. By using the three-species model it is possible to resolve the ionization region, which is not the case in one-species models for corona discharge, although these are commonly used in applications. In this work, we present an approach to solve the three-species problem by decomposing the domain into a one- and three-species part. This is based on that electrons and positive ions exclusively reside in the ionization region, which typically has a small spatial extent. It is an efficient approach as the one-species model is significantly less computationally demanding than the three-species model. The approach is implemented by coupling a structured finite-volume Newton solver for the one-species model and an unstructured finite-volume solver for the three-species model. The implemented solver is validated by considering a one dimensional test case with coaxial cylinders. The usefulness of the implemented solver is illustrated by solving the three-species problem for a range of geometries of interest to electrostatic precipitators and automotive spray painting. Specifically, we consider electrostatic precipitators with wires that are arranged between parallel plates. The results for these geometries are then used to perform coupled electrostatic-, fluidand particle-simulations to determine the particle collection efficiency, which is a performance measure for an electrostatic precipitator. Regarding automotive spray painting, we consider two dimensional analogs of the ABB G1 rotary spray bell. We indicate that the results from three-species simulations can be used to parametrize boundary conditions for a one-species solver. This could be a way to efficiently incorporate results from the three-species model in simulations that optimize the spray painting process.