2012 , Volume 17, № 3, p.3-12

We consider the complete system of Navier Stokes equations whose solutions describe the flow of a compressible viscous heat-conducting ideal gas at constant values of the coefficients of viscosity and thermal conductivity. We deviate from the traditional use of the density and temperature as independent thermodynamic variables, and re-formulate the equation of state and the complete system of Navier-Stokes equations in terms of the specific volume and pressure. In this case the complete system of Navier-Stokes equations can be written in the normal form with respect to time derivatives of the unknown functions with polynomial right hand side. In the case of one-dimensional plane symmetric flows, it allows using the Galerkin method (infinite series of harmonics in the spatial variable) for finding solutions. Conditions of adhesion and thermal insulation at the boundaries of the interval are satisfied for this formulation. We are looking at finding of the coefficients of these series as functions of time. The method reduces the problem to an infinite system of differential equations for these coefficients. When a finite number of harmonics are considered, we numerically solve the corresponding finite system of ordinary differential equations. In particular, it describes the motion of a traveling shock transition, which has no significant oscillations in the vicinity of its front.