A computer program for the analysis of two-dimensional turbulent fluid flow has been developed. The program is based on the finite volume method on unstructured locally orthogonal grid with the same nodes for all variables (collocated grid). In the used grid each cell face is orthogonal to the connection line of two adjacent nodes and divides it in two equal parts. Two variants of finite volume method have been proposed: one using the SIMPLE algorithm and the other using the SIMPLER algorithm which has not been used on the unstructured collocated grids yet. The following differencing schemes have been implemented: first order Upwind Differencing Scheme – UDS, Central Differencing Scheme – CDS, the combination of UDS and CDS, Exponential Differencing Scheme – EDS and Exponential Differencing Scheme Improved – EDSI. Results of proposed variants of the finite volume method have been compared with the results obtained with the public CFD program CAFFA on a structured non-orthogonal grid (author M. Perić) in terms of convergence rate and accuracy. It is concluded that the grid non-orthogonality increases the number of iterations needed to achieve prescribed accuracy. Due to the grid non-orthogonality the domain of under relaxation factors, in which SIMPLE algorithm converges, becomes smaller. It has been demonstrated that the numerical results obtained on locally orthogonal grid are more accurate than the corresponding results obtained on non-orthogonal grid. In the case of the unstructured grid, local orthogonality enables the application of the SIMPLER algorithm which is superior to the SIMPLE algorithm with respect to rate of convergence in most test cases without turbulence. In case of turbulent flow, the convergence of numerical method is mainly influenced by the convergence of turbulence model equations. Consequently, the superiority of the SIMPLER over SIMPLE algorithm is abated. A general conclusion is that the proposed locally orthogonal grid enables good discretisation of complex geometries and a robust and accurate numerical procedure.