Numerical solution of the Navier-Stokes equations for compressible fluids

Numerical methods for the solution of the Navier-Stokes equations for compressible fluids are discussed. A short review of the Navier-Stokes equations and of their qualitative mathematical properties, and a discussion of their interest in aerodynamics problems are presented. The following aspects of numerical methods are considered: limitation of the domain of calculation and boundary conditions on the outer boundary; various approaches in finite difference methods and properties of some representative schemes; treatment of the boundary condition at a solid wall; treatment of shock waves and general considerations on accuracy and computation times.