On the theory of one-dimensional unsteady motions of an ideal compressible fluid

A transformation is constructed of the independent variables and the unknown functions for the momentum and continuity equations of which one-dimensional unsteady motions of a perfect gas, relative to which the governing system of equations is invariant.When this transformation is used, the governing equation of state of the gas is transformed into a new equation which contains arbitrary parameters. This may enable approximation of the complex equation of state of a given medium to be carried out by selection of the parameters (in particular, for gases with respect of the equilibrium reactions taking place therein), and the use of this transformation may make it possible to reduce the problem to one with a simpler equation of state, for which the corresponding problem is more easily solved.The transformations investigated do not have singularities and do not impose any significant limitations on the hydrodynamic quantitiesthey are applicable both for variable entropy and for flows with shock waves.     

Nonlinear waves in a viscous compressible fluid with relaxation

The propagation and stability of nonlinear waves in a viscous compressible fluid with relaxation that satisfies a Theological equation of state of Oldroyd type are investigated. An equation that describes the structure of the wave perturbations and its evolution is derived subject to the condition of balance of the nonlinear dissipative and relaxation effects, and its solutions of the solitary wave type are analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 31–35, May–June, 1993.     

Study of nonstationary problems for a compressible viscous fluid

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 4, pp. 111–115, April, 1989.     

A finite element method for compressible viscous fluid flows

This work presents a mixed three‐dimensional finite element formulation for analyzing compressible viscous flows. The formulation is based on the primitive variables velocity, density, temperature and pressure. The goal of this work is to present a ‘stable’ numerical formulation, and, thus, the interpolation functions for the field variables are chosen so as to satisfy the inf–sup conditions. An exact tangent stiffness matrix is derived for the formulation, which ensures a quadratic rate of convergence. The good performance of the proposed strategy is shown in a number of steady‐state and transient problems where compressibility effects are important such as high Mach number flows, natural convection, Riemann problems, etc., and also on problems where the fluid can be treated as almost incompressible. Copyright © 2010 John Wiley & Sons, Ltd.     

Unsteady motion of a rigid cylinder in a compressible viscous fluid

International Applied Mechanics -