Numerical solutions of the complete Navier-Stokes equations

Using ideas from the kinetic theory, the Navier-Stokes equations are modified in such a way that they can be cast as a set of first order hyperbolic equations. This is achieved by incorporating time dependent terms into the definition of the stress tensor and the heat flux vectors. The boundary conditions are then determined from the theory of characteristics. Because the resulting equations reduce to the traditional Navier-Stokes equations when the steady state is reached, the present approach provides a straightforward scheme for the determination of inflow and outflow boundary conditions. The method is validated by comparing its predictions with known exact solutions of the steady Navier-Stokes equations.