This thesis explores the possibility of using graphics processing units (GPUs) to compute approximations of the Navier-Stokes equations for usage in real-time simulation. The Navier-Stokes equations describe the change in mass and momentum of fluids, e.g., liquids or gases. Typical applications for such a simulator can be computer games to increase realism by simulating, e.g., clouds or smoke that interact with the environment. A new, efficient solver that supports arbitrary boundaries is presented. Support for objects following the flow whilst acting as obstacles themselves is also discussed. The simulation is performed solely on the GPU, and offers high quality simulations at a modest cost.