In order to solve numerically the differential equations described in chapter 3 we employed the finite volume method in the discretization of those equations. To obtain the approximated equations we evaluated properties balances in the considered elemental volumes. Time discretization was done using a fully implicit formulation. We used CDS, UDS and WUDS as interpolation functions and in the boundary conditions we used fictitious volumes.

A co-located arrange was employed in the solution, and all variables occupy the same elemental volume. The SIMPLE and SIMPLEC method was employed in the pressure-velocity coupling. 

The physical domain, evaluated in csfl-lib-1.0, is fitted to the computational field using a generalized coordinate system, which is coincident to the boundary. This kind of technique makes possible the solution of a wide range of different geometries. Grids can be generated in own software using the grid editor or we can import grids generated in other software developed in Sinmec, for example Germal.

The linear system can be solved by TDMA line-by-line, Gauss-Seidel, Conjugate Gradient or Jacobi (for teaching purposes) and the matrix has 9 diagonals. 

This document has for objective detailing all numerical methodology used in developed of numerical library, as well as implementation os the CFD Studio software, as the general equation showed in Section 3 and it discretization in Section 4.

The interpolation functions used were described in Section 5, showing the diffusive coefficients in next chapter. The pressure-velocity coupling used is described in Section 7; it had all different conditions details on boundary described in Section 8.

The iterative solution to the linear system is described in section 9, as well as the iterative cycle of the solution (Section 10). The metrics transformations are discussed in Section 11, and the solid blocks concept is presented in Section 12. And the methodologies used in the evaluation of heat fluxes and Nusselt’s number is presented in Section 13 and 14, respectively.