Non-ideal Compressible Fluids

Abstract

The chapter deals with a model that merges compressibility and viscosity. The momentum equation is a combination of the Euler equation for ideal compressible fluids and the Navier–Stokes equation for viscous incompressible fluids. Instead of the barotropic relation between the pressure and density we use the full energy equation. While in the case of a viscous incompressible fluid the only dissipative mechanism is viscosity, now we have a second dissipative process, which is thermal conduction. Hence, the efficiency of dissipation is defined by two dimensionless numbers, the Reynolds and Peclet numbers. We use this model to study the damping of sound waves. Then we obtain the solution describing the structure of shock waves. Finally, we derive Burgers’ equation, which describes the propagation of nonlinear waves with small amplitude. We also study the main properties of this equation.