Hi, The interpolation schemes are used to calculate the cell face values from the cell centered values. You may already know that in the finite volume approach, the cell centred values are the ones used for computation. For each cell, in time, these cell centred values get updated based on the fluxes on its faces. And these fluxes are calculated from the available centre values of the 2 cells (in higher order interpolation, even more) adjacent to the face. In the code excerpt that you've attached, the flux being calculated is the mass flux at the cell faces. Since phi, which is basically face values of dot product of velocity and face area vector, is already face centred values, only rho, the density needs interpolating and that's what the code has done. Hope this answers your question.