On measure solutions to the zero-pressure gas model and their uniqueness
On numerical solution of compressible flow in time-dependent domains
The paper deals with numerical simulation of a compressible flow in time-dependent 2D domains with a special interest in medical applications to airflow in the human vocal tract. The mathematical model of this process is described by the compressible Navier-Stokes equations. For the treatment of the time-dependent domain, the arbitrary Lagrangian-Eulerian (ALE) method is used. The discontinuous Galerkin finite element method (DGFEM) is used for the space semidiscretization of the governing equations...
On symmetric equilibrium of an isothermal gas with a free boundary and a body force.
On the asymptotic behavior of the motion of a viscous, heat-conducting, one-dimensional real gas.
On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws
In this paper, we present some interesting connections between a number of Riemann-solver free approaches to the numerical solution of multi-dimensional systems of conservation laws. As a main part, we present a new and elementary derivation of Fey’s Method of Transport (MoT) (respectively the second author’s ICE version of the scheme) and the state decompositions which form the basis of it. The only tools that we use are quadrature rules applied to the moment integral used in the gas kinetic derivation...
On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws
In this paper, we present some interesting connections between a number of Riemann-solver free approaches to the numerical solution of multi-dimensional systems of conservation laws. As a main part, we present a new and elementary derivation of Fey's Method of Transport (MoT) (respectively the second author's ICE version of the scheme) and the state decompositions which form the basis of it. The only tools that we use are quadrature rules applied to the moment integral used in the...
On the nonhamiltonian character of shocks in 2-D pressureless gas
The paper deals with the 2-D system of gas dynamics without pressure which was introduced in 1970 by Ua. Zeldovich to describe the formation of largescale structure of the Universe. Such system occurs to be an intermediate object between the systems of ordinary differential equations and hyperbolic systems of PDE. The main its feature is the arising of singularities: discontinuities for velocity and d-functions of various types for density. The rigorous notion of generalized solutions in terms of...
On the rate of the volume growth for symmetric viscous heat-conducting gas flows with a free boundary.
On the solution of linear algebraic systems arising from the semi–implicit DGFE discretization of the compressible Navier–Stokes equations
We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier–Stokes equations by the backward difference formula – discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In this paper, we deal with these linear algebra systems with the aid of an iterative solver. We discuss...
On the solution of transonic flows with weak shocks
One-dimensional compressible viscous micropolar fluid model: stabilization of the solution for the Cauchy problem.
Problème de Cauchy et diffusion à données petites pour les modèles discrets de la cinétique des gaz
Regularity in kinetic formulations via averaging lemmas
We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best known regularizing effect in multidimensional scalar conservation laws. The new ingredient here is to use velocity...
Regularity in kinetic formulations via averaging lemmas
We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like γ = 3 in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best known regularizing effect in multidimensional scalar conservation laws. The new ingredient here is to...
Shock capturing and related numerical methods in computational fluid dynamics.
Solution globale de l'équation d'un gaz visqueux isotherme dans l'espace entier avec une grande force extérieure dérivant d'un potentiel
Solution of a mathematical model of a single piston pump with a more detailed description of the valve function
In this paper a mathematical model of a fluid flow in a tube with a valve and a pump is solved. The function of the valve is described in more detail than in [3], thus making the model more complete.
Solutions classiques globales des équations d'Euler pour un fluide parfait compressible
Soit , , , et les variables usuelles qui décrivent l’état d’un fluide en coordonnées eulériennes. Le domaine physique occupé par le fluide est a priori tout entier, mais peut être nul en dehors d’un compact . On choisit l’équation d’état d’un gaz parfait, , où est une constante. Le cas est celui du gaz mono-atomique.Dans la limite , les collisions sont rares et on est tenté d’approcher le mouvement des particules par un mouvement rectiligne uniforme : le champ de vitesse obéit alors...
Some elementary inequalities in gas dynamics equation.
Stability and Convergence of the Difference Schemes for Equations of Isentropic Gas Dynamics in Lagrangian Coordinates