Mathematical models are being used more and more for understanding our environment. The Navier-Stokes equations and thermodynamical energy balances are used for describing hydrodynamical phenomena on a macroscopic scale. They are based on the principle of mass and momentum conservation. For describing the microscopic scale, we use methods such as molecular dynamics, which is used for describing the motion of particles and the Monte Carlo method, which is used for describing different physical phenomena and thermodynamic equilibria. A method is being used more and more for describing different physical and chemical phenomena on a mesoscopic scale is the lattice Boltzmann method. This is the method we used in this thesis to model two hydrodynamic phenomena: gravity flow and lid-driven cavity flow. Based on our models, we discovered that in order to approximate the results available in different literature, it is necessary to have enough time steps in the simulation. This is especially true for the lid-driven cavity flow, which needs more time to reach an equilibrium state.
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