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High order finite volume schemes for numerical solution of 2D and 3D transonic flows

Jiří Fürst, Karel Kozel, Petr Furmánek (2009)

Kybernetika

The aim of this article is a qualitative analysis of two modern finite volume (FVM) schemes. First one is the so called Modified Causon’s scheme, which is based on the classical MacCormack FVM scheme in total variation diminishing (TVD) form, but is simplified in such a way that the demands on computational power are much smaller without loss of accuracy. Second one is implicit WLSQR (Weighted Least Square Reconstruction) scheme combined with various types of numerical fluxes (AUSMPW+ and HLLC)....

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...

Hyperbolic relaxation models for granular flows

Thierry Gallouët, Philippe Helluy, Jean-Marc Hérard, Julien Nussbaum (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work we describe an efficient model for the simulation of a two-phase flow made of a gas and a granular solid. The starting point is the two-velocity two-pressure model of Baer and Nunziato [Int. J. Multiph. Flow16 (1986) 861–889]. The model is supplemented by a relaxation source term in order to take into account the pressure equilibrium between the two phases and the granular stress in the solid phase. We show that the relaxation process can be made thermodynamically coherent with an...

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