Considering the increasing use of computer simulations to solve complex problems in industry and science, it is necessary to constantly work on the improvement of existing software so that the mathematical equations that describe real physical problems are a better representation of reality. Due to the nature of the mathematical models used in Computational Fluid Dynamics (CFD) to approximate real physical problems, errors occur when converting differential equations into discrete equations and performing iterative procedures. In this paper, the performance of the multigrid algorithm is studied, which enables the elimination of components of errors that classical iterative algorithms eliminate slowly. The theoretical background of classical iterative algorithms and the multigrid algorithm is presented. Different settings of the multigrid algorithm are tested on grids of different densities and shapes of control volumes in order to draw conclusions about the influence of the size and shape of the computational mesh on the speed of convergence of the multigrid algorithm. Also, two different algorithms were tested in the role of a smoother (an algorithm that smoothes the solution before and after the multigrid cycle) - ILU and Gauss-Seidel - and conclusions were drawn about their performance and conditions of use. At the end of the paper, a summary table of the conclusions was presented in order to make it easier for future users of the multigrid algorithm to use it.