This paper is concerned with the numerical modelling of particle migration in concentrated suspensions by the finite volume method. The constitutive equation for the particle flux, originally proposed by Phillips et al., Phys. Fluids A, 4 (1992) 30-40, in one dimension, is implemented in general two-dimensional flows with arbitrary geometry and boundary conditions. The numerical implementation is benchmarked against the exact solution in circular Couette flow, including the transient case where a closed-form solution is not available. The numerical predictions in an eccentric circular geometry, where the inner cylinder is placed off the axis of the outer cylinder, are given, showing that particles migrate towards the outer cylinder, but at different rates depending on their azimuthal positions.