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Calculation of low Mach number acoustics : a comparison of MPV, EIF and linearized Euler equations

Sabine Roller, Thomas Schwartzkopff, Roland Fortenbach, Michael Dumbser, Claus-Dieter Munz (2005)

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

The calculation of sound generation and propagation in low Mach number flows requires serious reflections on the characteristics of the underlying equations. Although the compressible Euler/Navier-Stokes equations cover all effects, an approximation via standard compressible solvers does not have the ability to represent acoustic waves correctly. Therefore, different methods have been developed to deal with the problem. In this paper, three of them are considered and compared to each other. They...

Calculation of low Mach number acoustics: a comparison of MPV, EIF and linearized Euler equations

Sabine Roller, Thomas Schwartzkopff, Roland Fortenbach, Michael Dumbser, Claus-Dieter Munz (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The calculation of sound generation and propagation in low Mach number flows requires serious reflections on the characteristics of the underlying equations. Although the compressible Euler/Navier-Stokes equations cover all effects, an approximation via standard compressible solvers does not have the ability to represent acoustic waves correctly. Therefore, different methods have been developed to deal with the problem. In this paper, three of them are considered and compared to each other....

Cascade of phases in turbulent flows

Christophe Cheverry (2006)

Bulletin de la Société Mathématique de France

This article is devoted to incompressible Euler equations (or to Navier-Stokes equations in the vanishing viscosity limit). It describes the propagation of quasi-singularities. The underlying phenomena are consistent with the notion of a cascade of energy.

Cauchy problem for the non-newtonian viscous incompressible fluid

Milan Pokorný (1996)

Applications of Mathematics

We study the Cauchy problem for the non-Newtonian incompressible fluid with the viscous part of the stress tensor τ V ( 𝕖 ) = τ ( 𝕖 ) - 2 μ 1 Δ 𝕖 , where the nonlinear function τ ( 𝕖 ) satisfies τ i j ( 𝕖 ) e i j ≥ c | 𝕖 | p or τ i j ( 𝕖 ) e i j ≥ c ( | 𝕖 | 2 + | 𝕖 | p ) . First, the model for the bipolar fluid is studied and existence, uniqueness and regularity of the weak solution is proved for p > 1 for both models. Then, under vanishing higher viscosity μ 1 , the Cauchy problem for the monopolar fluid is considered. For the first model the existence of the weak solution is proved for p > 3 n n + 2 , its uniqueness and...

Cell centered Galerkin methods for diffusive problems

Daniele A. Di Pietro (2012)

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

In this work we introduce a new class of lowest order methods for diffusive problems on general meshes with only one unknown per element. The underlying idea is to construct an incomplete piecewise affine polynomial space with optimal approximation properties starting from values at cell centers. To do so we borrow ideas from multi-point finite volume methods, although we use them in a rather different context. The incomplete polynomial space replaces classical complete polynomial spaces in discrete...

Cell centered Galerkin methods for diffusive problems

Daniele A. Di Pietro (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work we introduce a new class of lowest order methods for diffusive problems on general meshes with only one unknown per element. The underlying idea is to construct an incomplete piecewise affine polynomial space with optimal approximation properties starting from values at cell centers. To do so we borrow ideas from multi-point finite volume methods, although we use them in a rather different context. The incomplete polynomial space replaces classical complete polynomial spaces...

Central-upwind schemes for the Saint-Venant system

Alexander Kurganov, Doron Levy (2002)

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

We present one- and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central schemes...

Central-Upwind Schemes for the Saint-Venant System

Alexander Kurganov, Doron Levy (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present one- and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central...

Characterization of collision kernels

Laurent Desvillettes, Francesco Salvarani (2003)

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

In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.

Characterization of collision kernels

Laurent Desvillettes, Francesco Salvarani (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.

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