In this paper we write, analyze and experimentally compare three different numerical schemes dedicated to the one dimensional barotropic Navier-Stokes equations: a staggered scheme based on Rusanov for inviscid (Euler) system, pseudo-Lagrangian in which mesh “follows” fluid, Eulerian projection (on fixed mesh) of preceding scheme. All these only involve resolution linear systems (all nonlinear ...

The heat conducting compressible viscous flows are governed by the Navier–Stokes–Fourier (NSF) system. In this paper, we study NSF system accomplished Newton law of cooling for transfer at boundary. On one part boundary, consider Navier slip boundary condition, while in remaining inlet and outlet occur. These effects unique sink/source to problem under study, others such as gravity dissipation ...

In this paper, we study the global well-posedness of the 2D compressible NavierStokes equations with large initial data and vacuum. It is proved that if the shear viscosity μ is a positive constant and the bulk viscosity λ is the power function of the density, that is, λ(ρ) = ρβ with β > 3, then the 2D compressible Navier-Stokes equations with the periodic boundary conditions on the torus T2 ad...