Solving the incompressible Navier-Stokes equations in 3-D to model gas flow in a room

Abstract: The thesis proposes to model the flow of gases in a room by solving the incompressible Navier-Stokes equations in three dimensions. The transportationof scalars such as temperature and concentration of CO2 is modeled by solving the advection-diffusion equation, and the effects of temperature on thevelocity is accounted for by employing the Boussinesq approximation. Theequations are solved numerically in Matlab by using the finite volume methodon a cubic domain with Cartesian coordinates. The code is verified by comparison with the well studied case of a lid-driven cavity. Different boundaryconditions are discussed and boundary conditions to model inlets and outlets along with radiators and windows are proposed. A simplified model of aroom is created and is shown to provide reasonable results for low Reynoldsnumbers (Re ≈ 200). It is also shown that the model is not efficient enoughto run simulations with higher Reynolds numbers (Re ≈ 20000) that resultfrom a realistic choice of parameters.Teknisk-naturvetenskapliga fakult