**3.1.2 Viscous fluxes**

The viscous terms are defined at the centre of the cell. The above procedure is repeated to approximate the contour integration of the viscous flux vector. The inclusion of diffusive transport terms requires a choice of the locations at which the derivatives of the primitive variables should be integrated. The grid used for gradient evaluation forms a second grid that is shifted a half cell in the axial and radial directions in relation to the original computational grid. The viscous flux vectors are approximated in such a manner to preserve cell conservations and maintain algorithm simplicity. The derivatives of primitive variables at the vertices of the cell are evaluated by discrete application of the divergence theorem (Peyret & Vivind, 1993) to the auxiliary cell of the secondary grid. The net convective flux is computed by summing the inviscid and viscous terms.
