TABLE OF CONTENTS There are several models describing viscous compressible flow. The most general is the model of a real heat-conductive gas which has to be used for the simulation of high speed flow. If the flow speed is not too high (i.e. the flow is subsonic, shock waves and contact discontinuities are not present and the entropy production can be neglected) and the viscosity coefficients are constant, it is possible to use the model of barotropic flow formulated in Section 1.2.18. In this case the energy equation is not considered, because it is replaced by a given relation between the pressure and the density.
As one can see from Chapter 2, there exists an extensive qualitative mathematical theory of viscous barotropic flow problems. In this section we shall be concerned with the application of the conforming finite element method to viscous compressible barotropic flow. Following the results from (Kellog and Liu, 1996), (Kellog and Liu, 1997), (Liu, 2000), we shall describe the finite element discretization of the initial-boundary value problem for barotropic flow with the streamline diffusion stabilization in the continuity equation and analyse the solvability of the discrete problem.
The model of nonstationary viscous compressible barotropic flow is described by the continuity equation, the Navier-Stokes equations and the equation of state, written in the form
considered in the space-time cylinder Q T = ? (0, T) and equipped with the boundary condition
and the initial...
