All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 213

Showing per page

Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid

Jiří Neustupa (1988)

Aplikace matematiky

The paper contains the proof of global existence of weak solutions to the mixed initial-boundary value problem for a certain modification of a system of equations of motion of viscous compressible fluid. The modification is based on an application of an operator of regularization to some terms appearing in the system of equations and it does not contradict the laws of fluid mechanics. It is assumed that pressure is a known function of density. The method of discretization in time is used and finally,...

Global weak solvability to the regularized viscous compressible heat conductive flow

Jiří Neustupa, Antonín Novotný (1991)

Applications of Mathematics

The concept of regularization to the complete system of Navier-Stokes equations for viscous compressible heat conductive fluid is developed. The existence of weak solutions for the initial boundary value problem for the modified equations is proved. Some energy and etropy estimates independent of the parameter of regularization are derived.

Homogenization of the compressible Navier–Stokes equations in a porous medium

Nader Masmoudi (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We study the homogenization of the compressible Navier–Stokes system in a periodic porous medium (of period ε ) with Dirichlet boundary conditions. At the limit, we recover different systems depending on the scaling we take. In particular, we rigorously derive the so-called “porous medium equation”.

Homogenization of the compressible Navier–Stokes equations in a porous medium

Nader Masmoudi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the homogenization of the compressible Navier–Stokes system in a periodic porous medium (of period ε) with Dirichlet boundary conditions. At the limit, we recover different systems depending on the scaling we take. In particular, we rigorously derive the so-called “porous medium equation”.

Hybrid central-upwind schemes for numerical resolution of two-phase flows

Steinar Evje, Tore Flåtten (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...

Hybrid central-upwind schemes for numerical resolution of two-phase flows

Steinar Evje, Tore Flåtten (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the Jacobian matrix of the model. The two-fluid model possesses a highly nonlinear pressure law. From the mass conservation equations we develop an evolution equation which...

Les théorèmes de Leray et de Fujita-Kato pour le système de Boussinesq partiellement visqueux

Raphaël Danchin, Marius Paicu (2008)

Bulletin de la Société Mathématique de France

Dans cet article, on étudie le système de Boussinesq décrivant le phénomène de convection dans un fluide incompressible et visqueux. Ce système est composé des équations de Navier-Stokes incompressibles avec un terme de force verticale dont l’amplitude est transportée sans dissipationpar le flot du champ de vitesses. On montre que les résultats classiques pour le système de Navier-Stokes standard demeurent vrais pour le système de Boussinesq bien qu’il n’y ait pas d’amortissement sur le terme de...

Limite incompressible de solutions du système d’Euler compressible 2-D dans certains cas mal préparés

Alexandre Dutrifoy (2002/2003)

Séminaire Équations aux dérivées partielles

Les effets dispersifs permettent de passer à la limite dans le système d’Euler compressible 2-D isentropique, quand le nombre de Mach tend vers zéro, même si les données initiales ne sont pas uniformément régulières.Ceci mène à des résultats de convergence vers des solutions non régulières du système d’Euler incompressible, comme les poches de tourbillon ou les solutions de Yudovich.

Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting fluids

Ewa Zadrzyńska, Wojciech Zajączkowski (1998)

Applicationes Mathematicae

The local existence and the uniqueness of solutions for equations describing the motion of viscous compressible heat-conducting fluids in a domain bounded by a free surface is proved. First, we prove the existence of solutions of some auxiliary problems by the Galerkin method and by regularization techniques. Next, we use the method of successive approximations to prove the local existence for the main problem.

Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids

G. Ströhmer, W. Zajączkowski (1999)

Applicationes Mathematicae

Local existence of solutions is proved for equations describing the motion of a viscous compressible barotropic and self-gravitating fluid in a domain bounded by a free surface. First by the Galerkin method and regularization techniques the existence of solutions of the linearized momentum equations is proved, next by the method of successive approximations local existence to the nonlinear problem is shown.

Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic compressible fluid

Piotr Kacprzyk (2004)

Applicationes Mathematicae

Local existence of solutions for the equations describing the motion of a magnetohydrodynamic compressible fluid in a domain bounded by a free surface is proved. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. First by the Galerkin method and regularization techniques the existence of solutions of the linearized equations is proved, next by the method of successive aproximations local existence to the nonlinear problem is shown....

Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid

Piotr Kacprzyk (2003)

Applicationes Mathematicae

Local existence of solutions is proved for equations describing the motion of a magnetohydrodynamic incompressible fluid in a domain bounded by a free surface. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. First by the Galerkin method and regularization techniques the existence of solutions of the linarized equations is proved; next by the method of successive aproximations the local existence is shown for the nonlinear problem....

Low Mach number limit for viscous compressible flows

Raphaël Danchin (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this survey paper, we are concerned with the zero Mach number limit for compressible viscous flows. For the sake of (mathematical) simplicity, we restrict ourselves to the case of barotropic fluids and we assume that the flow evolves in the whole space or satisfies periodic boundary conditions. We focus on the case of ill-prepared data. Hence highly oscillating acoustic waves are likely to propagate through the fluid. We nevertheless state the convergence to the incompressible Navier-Stokes equations...

Low Mach number limit for viscous compressible flows

Raphaël Danchin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this survey paper, we are concerned with the zero Mach number limit for compressible viscous flows. For the sake of (mathematical) simplicity, we restrict ourselves to the case of barotropic fluids and we assume that the flow evolves in the whole space or satisfies periodic boundary conditions. We focus on the case of ill-prepared data. Hence highly oscillating acoustic waves are likely to propagate through the fluid. We nevertheless state the convergence to the incompressible Navier-Stokes...

Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations

Kučera, Václav, Lukáčová-Medviďová, Mária, Noelle, Sebastian, Schütz, Jochen (2021)

Programs and Algorithms of Numerical Mathematics

In this note, we give an overview of the authors’ paper [6] which deals with asymptotic consistency of a class of linearly implicit schemes for the compressible Euler equations. This class is based on a linearization of the nonlinear fluxes at a reference state and includes the scheme of Feistauer and Kučera [3] as well as the class of RS-IMEX schemes [8,5,1] as special cases. We prove that the linearization gives an asymptotically consistent solution in the low-Mach limit under the assumption of...

Currently displaying 61 – 80 of 213