Conservation properties and accuracy of unstructured mesh schemes for the Navier Stokes equations

The Navier-Stokes equations is a general model that describes fluid flow by conserving mass and momentum. There are two main mesh discretizations for the computation of the Navier-Stokes equations, the collocated and staggered schemes. Collocated schemes locate the velocity field at the same grid points as the pressure ones, while staggered schemes locate variables at different points within the mesh. One of the most important characteristic of the discretization schemes, aside of accuracy, is their capacity to numerically conserve kinetic energy and momentum, specially when solving turbulent flow. This work analyzes the accuracy and conservation properties of two particular collocated and staggered schemes by solving different problems.