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...

This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial diff...

In this article, we consider the free boundary value problem for one-dimensional compressible bipolar Navier-Stokes-Possion (BNSP) equations with density-dependent viscosities. For general initial data with finite energy and the density connecting with vacuum continuously, we prove the global existence of the weak solution. This extends the previous results for compressible NS [27] to NSP.

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...

We present a framework for applying the method of Proper Orthogonal Decomposition (POD) and Galerkin projection to compressible fluids. For incompressible flows, only the kinematic variables are important, and the techniques are well known. In a compressible flow, both the kinematic and thermodynamic variables are dynamically important, and must be included in the configuration space. We introd...

Obtrusions such as bends, constrictions and junctions occurring in confined flows give rise to turbulent flow structures and separation zones. The acoustic analysis of the flow-induced noise may be accomplished using two different approaches. The first is the highest modeling approach, wherein the full set of compressible Navier Stokes equations is solved. Difficulties lie in the amplitude disp...

In this paper we study the self-propelled motion of a single deformable body in a viscous compressible fluid which occupies whole 3-dimensional Euclidean space. The considered governing system for the fluid is the isentropic compressible Navier-Stokes equations. The main result of this paper is the existence of a weak solution on a time interval (0,+∞).

In [3,4,5], we have developed a new tool called the quasi solution which approximate in some sense the compressible Navier-Stokes equation. In particular it allows to obtain global strong solution for the compressible Navier-Stokes equations with large initial data on the irrotational part of the velocity ( large in the sense that the smallness assumption is subcritical in terms of scaling, it ...

In this paper, we are first interested in the compressible Navier-Stokes equations with densitydependent viscosities in bounded domains with non-homogeneous Dirichlet conditions. We study the wellposedness of such models with non-constant coefficients in non-stationary and stationary cases. We apply the last result in thin domains context, justifying the compressible Reynolds equations.

This paper studies the quasi-neutral limit of pressureless Navier-Stokes-Poisson equations in plasma physics in the torus T. For well prepared initial data the convergence of solutions of compressible Navier-Stokes-Poisson equations to the solutions of incompressible Navier-Stokes equations is justified rigorously by using the curl-div decomposition of the gradient. And a priori estimates with ...