The expansion waves for the compressible Navier-Stokes equations have recently been shown to be nonlinear stable. The nonlinear stability results are called local stability or global stability depending on whether theH1−norm of the initial perturbation is small or not. Up to now, local stability results have been well established. However, for global stability, only partial results have been ob...

Abstract. In this paper we introduce a new class of numerical schemes for the incompressible Navier-Stokes equations, which are inspired by the theory of discrete kinetic schemes for compressible fluids. For these approximations it is possible to give a stability condition, based on a discrete velocities version of the Boltzmann H–theorem. Numerical tests are performed to investigate their accu...

We consider a singular limit problem for the NavierStokes system of a rotating compressible fluid, where the Rossby and Mach numbers tend simultaneously to zero. The limit problem is identified as the 2-D Navier-Stokes system in the “horizontal” variables containing an extra term that accounts for compressibility in the original system.

Compressible Navier–Stokes models for quantum fluids are reviewed. They are derived from a collisional Wigner equation by a moment method and a Chapman–Enskog expansion around the quantum equilibrium. Introducing a new velocity variable, the barotropic quantum Navier-Stokes model can be reformulated as a viscous quantum Euler system, which possesses a new Lyapunov (energy) functional. This func...

This paper describes a very general absorbing layer model for hyperbolic-parabolic systems of partial differential equations. For linear systems with constant coefficients it is shown that the model possesses the perfect matching property, i.e., it is a perfectly matched layer (PML). The model is applied to two linear systems: a linear wave equation with a viscous damping term and the linearize...

This paper concerns the existence of global weak solutions \`a la Leray for compressible Navier-Stokes equations with a pressure law that depends on density and time space variables $t$ $x$. The assumptions contain only locally Lipschitz assumption respect to variable some hypothesis extra variables. It may be seen as first step consider heat-conducting physical laws such truncated virial assum...

We present a procedure to adapt and repair meshes in the general solution of Navier–Stokes incompressible and compressible fluid flows, including structural interactions. For fluid-structure interactions, FSI, the fluid is described by an arbitrary-Lagrangian–Eulerian formulation fully coupled to general solids and structures described by Lagrangian formulations. The solids and structures can u...