In this paper, we investigate the system of compressible Navier-Stokes equations with hyperbolic heat conduction, i.e., replacing the Fourier’s law by Cattaneo’s law. First, by using Kawashima’s condition on general hyperbolic parabolic systems, we show that for small relaxation time τ , global smooth solution exists for small initial data. Moreover, as τ goes to zero, we obtain the uniform con...

The aim of this work is to justify mathematically the derivation of a viscous free/congested zones two–phase model from the isentropic compressible Navier-Stokes equations with a singular pressure playing the role of a barrier. Titre et résumé en Français. Modèle bi-phasique gérant zones libres/zones congestionnées comme limite singulière d’un système de Navier-Stokes compressible. Le but de ce...

A finite difference lattice Boltzmann method based on the Bhatnagar–Gross–Krook-type modeled Boltzmann equation is proposed. Themethod relies on a different lattice equilibriumparticle distribution function and the use of a splitting method to solve the modeled lattice Boltzmann equation. The splitting technique permits the boundary conditions for the lattice Boltzmann equation to be set as con...

We present a fully discrete approximation technique for the compressible Navier–Stokes equations that is second-order accurate in time and space, semi-implicit, guaranteed to be invariant domain preserving. The restriction on step standard hyperbolic CFL condition, i.e. ? ? O ( h ) ? V where some reference velocity scale typical meshsize. • equations. method

In this paper, we prove the existence of global weak solutions to the compressible NavierStokes equations when the pressure law is in two variables. The method is based on the Lions argument and the Feireisl-Novotny-Petzeltova method. The main contribution of this paper is to develop a new argument for handling a nonlinear pressure law P (ρ, n) = ρ + n where ρ, n satisfy the mass equations. Thi...

The pseudo-incompressible approximation, which assumes small pressure perturbations from a one-dimensional reference state, has long been used to model large-scale dynamics in stellar and planetary atmospheres. However, existing implementations do not conserve energy when the state is time-dependent. We use variational formulation derive an energy-conserving evolves while remaining hydrostatic....

In this paper, we investigate the uniform regularity for the isentropic compressible Navier-Stokes system with general Navier-slip boundary conditions (1.6) and the inviscid limit to the compressible Euler system. It is shown that there exists a unique strong solution of the compressible Navier-Stokes equations with general Navier-slip boundary conditions in an interval of time which is uniform...

This paper is devoted to the study of the Navier~Stok.es équations descnbing the flow of an incompressible fluid in a shallow domain and to the hydrostatic approximation of these équations Wefirst study the behaviour of solutions of the Navier-Stokes équations when the depth of the domain tends to zero We then dérive the existence of solutions for the hydrostatic approximation Résumé — Ce papie...

The 2-D version of the non-hydrostatic fully compressible model MOLOCH developed at ISAC-CNR was used in idealized set-up to study the start-up and finite amplitude evolution of symmetric instability. The unstable basic state was designed by numerical integration of the equation which defines saturated equivalent potential vorticity q e . We present the structure and growth rates of the linear ...

In this paper we deal with a numerical solution of the compressible Navier-Stokes equations with the aid of higher order schemes. We use the discontinuous Galerkin finite element method for the space semi-discretization and a backward difference formula for the time discretization. Moreover, a linearization of inviscid/viscous fluxes and a suitable explicit extrapolation for nonlinear terms lea...