We focus here on an integral approach to compute compressible or incompressible fluid flows in physical congested domains with discontinuous fluid sections. This approach is based on a multidimensional integral formulation of the fluid model equations and aims at unifying the porous approach used at component scale and CFD used at local scale. Its discretization uses a semi-implicit collocated finite volume scheme with an incremental pressure-correction algorithm, implemented in the open-source CFD software Code Saturne, version 6.0. Numerical tests are completed by simulating a plane steady-channel flow with a fluid section jump. The results are compared to the analytical solution and the computation obtained with a standard equivalent porous model.