Stability and Convergence of the Difference Schemes for Equations of Isentropic Gas Dynamics in Lagrangian Coordinates
Staggered schemes for all speed flows
We review in this paper a class of schemes for the numerical simulation of compressible flows. In order to ensure the stability of the discretizations in a wide range of Mach numbers and introduce sufficient decoupling for the numerical resolution, we choose to implement and study pressure correction schemes on staggered meshes. The implicit version of the schemes is also considered for the theoretical study. We give both algorithms for the barotropic Navier-Stokes equations, for the full Navier-Stokes...
Stationary spatially periodic compressible flows at high mach number
Stationary states and moving planes
Most of the paper deals with the application of the moving plane method to different questions concerning stationary accumulations of isentropic gases. The first part compares the concepts of stationarity arising from the points of view of dynamics and the calculus of variations. Then certain stationary solutions are shown to be unstable. Finally, using the moving plane method, a short proof of the existence of energy-minimizing gas balls is given.
Steady compressible Navier-Stokes-Fourier system in two space dimensions
We study steady flow of a compressible heat conducting viscous fluid in a bounded two-dimensional domain, described by the Navier-Stokes-Fourier system. We assume that the pressure is given by the constitutive equation , where is the density and is the temperature. For , we prove existence of a weak solution to these equations without any assumption on the smallness of the data. The proof uses special approximation of the original problem, which guarantees the pointwise boundedness of the...
Steady compressible Oseen flow with slip boundary conditions
We prove the existence of solution in the class H²(Ω) × H¹(Ω) to the steady compressible Oseen system with slip boundary conditions in a two dimensional, convex domain with boundary of class . The method is to regularize a weak solution obtained via the Galerkin method. The problem of regularization is reduced to the problem of solvability of a certain transport equation by application of the Helmholtz decomposition. The method works under an additional assumption on the geometry of the boundary....
Strong solutions for a compressible fluid model of Korteweg type
Sul decadimento delle onde di accelerazione in un fluido non viscoso entro una teoria termodinamica non-stazionaria
In according to a recent thermodynamic theory proposed by G. Grioli, we consider the growth of acceleration waves in a non viscous fluid. We determine the solutions for the growth of a plane or spherical wave advancing into the fluid in mechanical but not in thermal equilibrium.
Sul decadimento delle onde di accelerazione in un fluido non viscoso entro una teoria termodinamica non stazionaria
In according to a recent thermodynamic theory proposed by G. Grioli we consider the growth of acceleration waves in a non viscous fluid. We determine the solutions for the growth of a plane or spherical wave advancing into the fluid in mechanical but not in thermal equilibrium.
Sulla dinamica di una miscela di due fluidi comprimibili e non miscibili
Si dà un ulteriore contributo alla specificazione delle equazioni dinamiche di bilancio per una miscela di due fluidi non miscibili ma comprimibili.
Sur la Régularité des Solutions faibles des Equations de Navier-Stokes isentropiques en dimension deux
Sur la théorie globale des équations de Navier-Stokes compressible
Le but de cet article est de présenter quelques résultats mathématiques plus ou moins récents sur la théorie de l’existence globale en temps (solutions faibles et solutions fortes) pour les équations de Navier-Stokes compressibles en dimension supérieure ou égale à deux sans aucune hypothèse de symétrie sur le domaine et sans aucune hypothèse sur la taille des données initiales.
Symmetries and solutions to equations of two-dimensional motions of polytropic gas.
Symmetry group analysis and invariant solutions of hydrodynamic-type systems.