4. Turbulence model

The Navier-Stokes equations model both laminar and turbulent flows. In the case of turbulent flow, the length and time scales are so small that extremely fine meshing and extremely small time steps are required for discretization. To deal with such turbulent problems, and given the power limitations of computers, it is necessary to introduce a macroscopic model, also known as a turbulence model, to take account of these small-scale phenomena. These turbulence models were first introduced by Reynolds. For such models, velocity and pressure are written as the sum of a mean value and an oscillating disturbance, i.e.