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In this paper, an efficient blending procedure based on the pressure-based algorithm is presented to solve the compressible Euler equations on a non-orthogonal mesh with collocated finite volume formulation. The boundedness criteria for this procedure are determined from total variation diminishing (TVD) schemes with and without applying of artificial compression method (ACM) of Harten as a control switch of dissipation. The fluxes of the convected quantities including mass flow rate are approximated by using the characteristic-based TVD and TVD/ACM methods. The algorithm is tested for steady-state inviscid flows at different Mach numbers ranging from the transonic to the supersonic regime and the results are compared with the existing numerical solutions. The comparisons show that the ACM is a useful technique to modify standard high-resolution schemes, which prevents the smearing of discontinuities and improves the resolution of shocks in the pressure-based algorithm. Aside from having the ability of accurately capturing shocked flows, this approach also accelerates the convergence rate of the solution in the supersonic flows with only a maximum increase of 5% in the operations with respect to standard second-order TVD schemes.

Shock waves for the compressible Navier-Stokes equations with heat conduction are analyzed. The shock wave is viewed as a strong discontinuity on which surface modified Rankine-Hugoniot conditions hold. These jump conditions are derived by the usual way from the system of viscous conservation laws. The linear instability of planar shock waves is proved. This points, in particular, to the inadequate character of numerical computations for viscous flows near blunt bodies with a bow discontinuous shock wave.

The structure of one-dimensional shock waves is investigated using the Navier-Stokes equations for the gas phase. The resulting system of three ordinary nonlinear differential equations is reduced to a system of two autonomous nonlinear differential equations which are solved exactly. This solution is obtained formally by assuming that the heat conductivity is temperature dependent, and that the viscosity is neglected. A deduction of the behaviour of entropy across inviscid shock waves is also given.

In the existing solutions of the extended integral equation method for transonic flows the shock wave has been assumed normal to the freestream. In this paper the effect of removing this assumption is investigated and flows with curved shock waves are examined.

A new reduction of the equations governing certain anisentropic non-steady flows of a polytropic gas to the study of a pair of partial differential equations is presented. The latter involve two functions, in terms of which flow variables are parametrised. A wide class of exact solutions to the original system is generated which, in particular, includes as a special case those obtained byGunderson and linked by a non-uniform shock to a gas at rest. New aspects ofGunderson's work are investigated and explicit forms for the shock locus and non-uniform density distribution in front of the shock are obtained.