This work aims to verify different numerical algorithms under different types of mesh. Our area of interest is the algorithms for the numerical solution of partial differential equations describing the incompressible fluid movement. The numerical resolution of these partial differential equations is sensitive to the mesh used, especially for fluid simulations with complex geometry. We will do the numerical simulations based on Laplace, Burgers and Navier-Stokes equations using the finite volume method. For the simulations of the Navier-Stokes equation we will use the OpenFoam-2.1 solvers based in SIMPLE and PISO algorithms. To calculate the error, we will build analytical solutions based on the method of manufactured solutions. We will study the order convergence for several numerical schemes using different types of mesh, structured and unstructured under different boundary conditions. We will study the impact of mesh perturbation on the convergence. Finally, we will do comparisons of convergence orders for the errors given by the manufactured solution and by the interpolation error.