On Stationary Solutions for 2 - D Viscous Compressible Isothermal Navier-Stokes Equations

Remarks on Self-Similar Solutions to the Compressible Navier-Stokes Equations of a 1D Viscous Polytropic Ideal Gas

This paper is concerned with the self-similar solutions to the compressible Navier-Stokes equations of a 1D viscous polytropic ideal gas. Our results show that there exist neither forward nor backward selfsimilar solutions with finite total energy, which generalizes the results for the case of the isothermal compressible Navier-Stokes equations in Z. Guo and S. Jiang (Self-similar solutions to ...

A New High Resolution Scheme for Compressible Viscous Flow with Shocks

A new flux splitting and limiting technique which yields one-point stationary shock capturing is presented. The technique is applied to the full NavierStokes and Reynolds Averaged Navier-Stokes equations. Calculations of laminar boundary layers at subsonic and supersonic speeds are presented together with calculations of transonic flows around airfoils. The results exhibit very good agreement w...

Self-similar solutions to the isothermal compressible Navier–Stokes equations

We investigate the self-similar solutions to the isothermal compressible Navier–Stokes equations. The aim of this paper is to show that there exist neither forward nor backward self-similar solutions with finite total energy. This generalizes the results for the incompressible case in Nečas, J., Ru̇žička, M. & Šverák, V. (1996, On Leray’s self-similar solutions of the Navier-Stokes equations. Ac...

The Dirichlet Problem for Viscous Compressible Isothermal Navier-Stokes Equations in Two-Dimensions

Viscous potential flow

Potential flows u = ∇φ are solutions of the Navier–Stokes equations for viscous incompressible fluids for which the vorticity is identically zero. The viscous term μ∇u = μ∇∇φ vanishes, but the viscous contribution to the stress in an incompressible fluid (Stokes 1850) does not vanish in general. Here, we show how the viscosity of a viscous fluid in potential flow away from the boundary layers e...