Construction of Gas-Dynamic Equations by Using Conservation Laws

In this chapter, we recall physical principles serving as a base in deducing equations of the classical gas dynamics and the new quasi-gas-dynamic (QGD) and quasihydrodynamic (QHD) systems. As the Navier–Stokes equations, the QGD/QHD equations are a consequence of integral conservation laws, have a dissipative character, and can be obtained from the general system of conservation laws. A principal and substantial distinction of the QGD/QHD equations from the Navier–Stokes equations is the use of the time-spatial averaging procedure in order to find the main hydrodynamic quantities—the density, the velocity, and the temperature. The use of spatial averages leads to the Navier–Stokes system. For time-spatial averages, we propose two variants of closing the general system of equations, which lead to QGD/QHD systems. In this chapter, we present the expressions for the vectors of mass flux density, heat flux, and the tensor of viscous stresses for QGD/QHD systems without any deduction. Two methods for constructing these quantities for the QGD system are presented in Chap. 3. We discuss the physical meaning of the vector of mass flux. The presentation of this chapter is mainly based on [84, 181, 184, 190].