This paper is devoted to the study of convergence orders of several numericalmethods that are implemented in the TrioCFD code dedicatedto the simulation of turbulent flows and heat transfer in nuclear engineering applications. The spatialdiscretization is based on Finite Difference-Volume or Finite Element-Volumemethods. A projection method is applied to update the velocity andthe pressure. The time scheme can be either explicit or implicit, and hexahedral or tetrahedral meshes can be used for simulations. In this paper,the test cases are relative to steady Stokes problems, steady and unsteady Navier-Stokes problems, and finally the well-known lid-driven cavity flow case.The latter proposes several comparisons between our simulations and numerical data already published inthe literature, while the other cases yield the values of convergence orders by using the analytical solutions.The accuracy of the results obtained with TrioCFDdiffers according to the types of mesh used for simulations, theviscosity values or the source terms in the equations.