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...

Hybrid methods represent a classic discretization paradigm for elliptic equations. More recently, hybrid methods have been formulated for convection-diffusion problems, in particular compressible fluid flow. In [25], we have introduced a hybrid mixed method for the compressible Navier-Stokes equations as a combination of a hybridized DG scheme for the convective terms, and an H(div,Ω)-method fo...

Abstract: The mass and momentum transfer phenomena in a compressible fluid represented by the Navier–Stokes equations are shown to convert into the Schrödinger equation for quantum mechanics. The complete Navier–Stokes equations render into an extended generalized version of Schrödinger equation. These results complement the Madelung’s (Zeitschrift für Physik 40 (3–4), pp. 322–326, 1926–1927) d...

We describe a novel Eulerian interface-sharpening approach for the efficient numerical resolution of interfaces arising from inviscid compressible flow in more than one space dimension. The algorithm uses the single-phase compressible Euler equations as the model system, and introduces auxiliary differential terms to the model so as to neutralize numerical diffusion that is inevitable when the ...

The self-consistent Eulerian rate-type elastoplastic model based on the logarithmic rate is used to study finite bending of a compressible elastic-perfectly plastic rectangular block. It is found that an explicit closed-form solution for this typical inhomogeneous finite deformation mode may be available in a general case of compressible deformation with a stretch normal to the bending plane, w...

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...

For the numerical resolution of the compressible Navier-Stokes equations (NS) with Finite Volumes (FV) two main approaches have called the attention of researchers and engineers. First, following the hyperbolic nature of the compressible NS equations, the Godunov-like schemes discretize the numerical fluxes by a characteristic analysis. Second, disregarding the hyperbolicity of the equations, t...

We introduce and launch a study of compression bases in unital groups. The family of all compressions on a compressible group and the family of all direct compressions on a unital group are examples of compression bases. In this article we show that the properties of the compatibility relation in a compressible group generalize to unital groups with compression bases. AMS Classification: Primar...

Abstract. This work is concerned with the simulation of compressible flow in time dependent domains. We present an ALE (Arbitrary Lagrangian-Eulerian) formulation of the Navier-Stokes equations describing compressible flow, discretize them in space by the discontinous Galerkin method and introduce a semi-implicit linearized time stepping for the numerical solution of the complete problem. We pr...

In this paper we focus on an existence of a weak solution to a system describing a self-propelled motion of a single deformable body in a viscous compressible fluid which occupies a bounded domain in the 3 dimensional Euclidean space. The considered governing system for the fluid is the isentropic compressible Navier-Stokes equation. We prove an existence of a weak solution up to a collision.