We design a numerical approximation of a system of partial differential
equations modelling the miscible displacement of a fluid by another in a porous
medium. The advective part of the system is discretised using a characteristic
method, and the diffusive parts by a finite volume method. The scheme is
applicable on generic (possibly non-conforming) meshes as encountered in
applications. The main features of our work are the reconstruction of a Darcy
velocity, from the discrete pressure fluxes, that enjoys a local consistency
property, an analysis of implementation issues faced when tracking, via the
characteristic method, distorted cells, and a new treatment of cells near the
injection well that accounts better for the conservativity of the injected
fluid