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On numerical solution of compressible flow in time-dependent domains

Miloslav Feistauer, Jaromír Horáček, Václav Kučera, Jaroslava Prokopová (2012)

Mathematica Bohemica

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 the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws

Tim Kröger, Sebastian Noelle, Susanne Zimmermann (2004)

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

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

Tim Kröger, Sebastian Noelle, Susanne Zimmermann (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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

Yu. G. Rykov (2002)

Bollettino dell'Unione Matematica Italiana

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 solution of linear algebraic systems arising from the semi–implicit DGFE discretization of the compressible Navier–Stokes equations

Vít Dolejší (2010)

Kybernetika

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...

Regularity in kinetic formulations via averaging lemmas

Pierre-Emmanuel Jabin, Benoît Perthame (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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 use velocity...

Regularity in kinetic formulations via averaging lemmas

Pierre-Emmanuel Jabin, Benoît Perthame (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Solutions classiques globales des équations d'Euler pour un fluide parfait compressible

Denis Serre (1997)

Annales de l'institut Fourier

Soit ρ , u , e , S et p les variables usuelles qui décrivent l’état d’un fluide en coordonnées eulériennes. Le domaine physique occupé par le fluide est a priori ℝ d tout entier, mais ρ peut être nul en dehors d’un compact K ( t ) . On choisit l’équation d’état d’un gaz parfait, p = ( γ - 1 ) ρ e , où γ ∈ [ 1 , 1 + 2 / d ] est une constante. Le cas γ = 1 + 2 / d est celui du gaz mono-atomique.Dans la limite ρ → 0 , 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...

Stationary states and moving planes

Gerhard Ströhmer (2008)

Banach Center Publications

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.

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