I am trying to develop a 2D unstructured cell-centered FV code for incompressible flow, with a SIMPLE-like scheme for the pressure-velocity coupling. This code must deal with elements with mixed and/or arbitrary topology, so a face-based (or, to be more precise, an edge-based ) structure is desirable. This structure carries information about the neighbor cells belonging to the edge. A BiCGstab solver is used to solve the linear system of equations resulting of the spatial discretization. A loop over the edges is carried out to evaluate the fluxes to/from the cells. My question is: with this data structure, how one can use this flux information to assemble the coefficient matrix of the linear system? Any references will be appreciated. Thanks in advance.

I don't see what the problem is: you get one coefficient for every face, you only need the information for the two cells around it and all is well. If you don't know how to calculate the face coefficient, that is described in all CFD books. If you want exactly the data structure you're talking about, have a look at my Thesis (it is available on-line):

@PhdThesis{Jasak:PhD, author = {Jasak, H.}, title = {Error analysis and estimation in the Finite Volume

method with applications to fluid flows}, school = {Imperial College, University of London}, year = 1996 }

Hrv