The numerical solution of differential equations is an algorithmic process with various parameters controlling the accuracy, stability and computational time of the simulation. In Computational Fluid Mechanics (CFD) there are numerous softwares designed to solve multiphase flow problems. One such software is OpenFoam, an open-source CFD software. In this thesis we use OpenFoam to simulate two special cases: first the rising of a single air bubble in liquid water, and then a turbulent dispersed two-phase flow. The simulation result obtained from the single rising air bubble case is compared with benchmark data obtained from the literature. By analysing the solutions from the two simulation cases we identify numerical parameters affecting the solution process in terms of accuracy and simulation time. Furthermore we derive an optimisation algorithm to find optimum numerical parameters. In addition we show that the residual provided by OpenFoam is not sufficient to judge the accuracy of the solutions. To this end we show that the Grid Convergence Index method, an extension of the Richardson extrapolation method, is very adequate to compute discretisation errors for local solutions.