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A robust entropy−satisfying finite volume scheme for the isentropic Baer−Nunziato model

Frédéric Coquel, Jean-Marc Hérard, Khaled Saleh, Nicolas Seguin (2014)

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

We construct an approximate Riemann solver for the isentropic Baer−Nunziato two-phase flow model, that is able to cope with arbitrarily small values of the statistical phase fractions. The solver relies on a relaxation approximation of the model for which the Riemann problem is exactly solved for subsonic relative speeds. In an original manner, the Riemann solutions to the linearly degenerate relaxation system are allowed to dissipate the total energy in the vanishing phase regimes, thereby enforcing...

A second order anti-diffusive Lagrange-remap scheme for two-component flows

Marie Billaud Friess, Benjamin Boutin, Filipa Caetano, Gloria Faccanoni, Samuel Kokh, Frédéric Lagoutière, Laurent Navoret (2011)

ESAIM: Proceedings

We build a non-dissipative second order algorithm for the approximate resolution of the one-dimensional Euler system of compressible gas dynamics with two components. The considered model was proposed in [1]. The algorithm is based on [8] which deals with a non-dissipative first order resolution in Lagrange-remap formalism. In the present paper we describe, in the same framework, an algorithm that is second order accurate in time and space, and that...

A second-order multi-fluid model for evaporating sprays

Guillaume Dufour, Philippe Villedieu (2005)

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

The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. Using the underlying kinetic interpretation of the sectional method [Y. Tambour, Combust. Flame 60 (1985) 15–28] exposed in [F. Laurent and M. Massot, Combust. Theory Model. 5 (2001) 537–572], we propose an extension of this approach based on a more accurate representation of the droplet size number density in each...

A second-order multi-fluid model for evaporating sprays

Guillaume Dufour, Philippe Villedieu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. Using the underlying kinetic interpretation of the sectional method [Y. Tambour, Combust. Flame60 (1985) 15–28] exposed in [F. Laurent and M. Massot, Combust. Theory Model.5 (2001) 537–572], we propose an extension of this approach based on a more accurate representation of the droplet size number density in each...

A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations

Robert Renka (2013)

Open Mathematics

The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trustregion radius is defined by a Sobolev norm and the trust-region subproblems are solved by a dogleg method. Numerical test results show the method to be effective.

A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations

Vivette Girault, Béatrice Rivière, Mary F. Wheeler (2005)

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

In this paper we solve the time-dependent incompressible Navier-Stokes equations by splitting the non-linearity and incompressibility, and using discontinuous or continuous finite element methods in space. We prove optimal error estimates for the velocity and suboptimal estimates for the pressure. We present some numerical experiments.

A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations

Vivette Girault, Béatrice Rivière, Mary F. Wheeler (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we solve the time-dependent incompressible Navier-Stokes equations by splitting the non-linearity and incompressibility, and using discontinuous or continuous finite element methods in space. We prove optimal error estimates for the velocity and suboptimal estimates for the pressure. We present some numerical experiments.

A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes

Malte Braack (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

It is well known that the classical local projection method as well as residual-based stabilization techniques, as for instance streamline upwind Petrov-Galerkin (SUPG), are optimal on isotropic meshes. Here we extend the local projection stabilization for the Navier-Stokes system to anisotropic quadrilateral meshes in two spatial dimensions. We describe the new method and prove an a priori error estimate. This method leads on anisotropic meshes to qualitatively better convergence behavior...

A two-fluid hyperbolic model in a porous medium

Laëtitia Girault, Jean-Marc Hérard (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The paper is devoted to the computation of two-phase flows in a porous medium when applying the two-fluid approach. The basic formulation is presented first, together with the main properties of the model. A few basic analytic solutions are then provided, some of them corresponding to solutions of the one-dimensional Riemann problem. Three distinct Finite-Volume schemes are then introduced. The first two schemes, which rely on the Rusanov scheme, are shown to give wrong approximations in some...

A unified convergence analysis for local projection stabilisations applied to the Oseen problem

Gunar Matthies, Piotr Skrzypacz, Lutz Tobiska (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

The discretisation of the Oseen problem by finite element methods may suffer in general from two shortcomings. First, the discrete inf-sup (Babuška-Brezzi) condition can be violated. Second, spurious oscillations occur due to the dominating convection. One way to overcome both difficulties is the use of local projection techniques. Studying the local projection method in an abstract setting, we show that the fulfilment of a local inf-sup condition between approximation and projection spaces...

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