Displaying similar documents to “Asymptotic-Preserving scheme for a two-fluid Euler-Lorentz model”

Interface model coupling via prescribed local flux balance

Annalisa Ambroso, Christophe Chalons, Frédéric Coquel, Thomas Galié (2014)

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

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This paper deals with the non-conservative coupling of two one-dimensional barotropic Euler systems at an interface at = 0. The closure pressure laws differ in the domains < 0 and > 0, and a Dirac source term concentrated at = 0 models singular pressure losses. We propose two numerical methods. The first one relies on ghost state reconstructions at the interface while the second is based on a suitable relaxation framework. Both methods satisfy a well-balanced property...

On power series solutions for the Euler equation, and the Behr–Nečas–Wu initial datum

Carlo Morosi, Mario Pernici, Livio Pizzocchero (2013)

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

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We consider the Euler equation for an incompressible fluid on a three dimensional torus, and the construction of its solution as a power series in time. We point out some general facts on this subject, from convergence issues for the power series to the role of symmetries of the initial datum. We then turn the attention to a paper by Behr, Nečas and Wu, 35 (2001) 229–238; here, the authors chose a very simple Fourier polynomial as an initial datum for the Euler equation and analyzed...

Analysis of an Asymptotic Preserving Scheme for Relaxation Systems

Francis Filbet, Amélie Rambaud (2013)

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

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We consider an asymptotic preserving numerical scheme initially proposed by F. Filbet and S. Jin [229 (2010)] and G. Dimarco and L. Pareschi [49 (2011) 2057–2077] in the context of nonlinear and stiff kinetic equations. Here, we propose a convergence analysis of such a scheme for the approximation of a system of transport equations with a nonlinear source term, for which the asymptotic limit is given by a conservation law. We investigate the convergence of the approximate solution ( ...

Two shallow-water type models for viscoelastic flows from kinetic theory for polymers solutions

Gladys Narbona-Reina, Didier Bresch (2013)

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

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In this work, depending on the relation between the Deborah, the Reynolds and the aspect ratio numbers, we formally derived shallow-water type systems starting from a micro-macro description for non-Newtonian fluids in a thin domain governed by an elastic dumbbell type model with a slip boundary condition at the bottom. The result has been announced by the authors in [G. Narbona-Reina, D. Bresch, Springer Verlag (2010)] and in the present paper, we provide a self-contained description,...

Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation

Clément Mouhot, Lorenzo Pareschi, Thomas Rey (2013)

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

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Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically ( ) where is the dimension of the velocity space. In this paper, following the ideas introduced in [C. Mouhot and L. Pareschi, 339 (2004) 71–76, C. Mouhot and L. Pareschi, 75 (2006) 1833–1852], we derive fast summation techniques for the evaluation of discrete-velocity schemes which...

Error Control and Andaptivity for a Phase Relaxation Model

Zhiming Chen, Ricardo H. Nochetto, Alfred Schmidt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The phase relaxation model is a diffuse interface model with small parameter which consists of a parabolic PDE for temperature and an ODE with double obstacles for phase variable . To decouple the system a semi-explicit Euler method with variable step-size is used for time discretization, which requires the stability constraint . Conforming piecewise linear finite elements over highly graded simplicial meshes with parameter are further employed for space discretization. error estimates...

Some special solutions of self similar type in MHD, obtained by a separation method of variables

Michel Cessenat, Philippe Genta (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We use a method based on a separation of variables for solving a first order partial differential equations system, using a very simple modelling of MHD. The method consists in introducing three unknown variables , , in addition to the time variable and then in searching a solution which is separated with respect to and only. This is allowed by a very simple relation, called a “metric separation equation”, which...

On Numerical Solution of the Gardner–Ostrovsky Equation

M. A. Obregon, Y. A. Stepanyants (2012)

Mathematical Modelling of Natural Phenomena

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A simple explicit numerical scheme is proposed for the solution of the Gardner–Ostrovsky equation ( + + + + ) = which is also known as the extended rotation-modified Korteweg–de Vries (KdV) equation. This equation is used for the description of internal oceanic waves affected by Earth’ rotation. Particular...

Nash equilibria for a model of traffic flow with several groups of drivers

Alberto Bressan, Ke Han (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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Traffic flow is modeled by a conservation law describing the density of cars. It is assumed that each driver chooses his own departure time in order to minimize the sum of a departure and an arrival cost. There are groups of drivers, The -th group consists of drivers, sharing the same departure and arrival costs (), (). For any given population sizes ,, , we prove the existence of a Nash equilibrium solution,...

Upper large deviations for maximal flows through a tilted cylinder

Marie Theret (2014)

ESAIM: Probability and Statistics

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We consider the standard first passage percolation model in ℤ for  ≥ 2 and we study the maximal flow from the upper half part to the lower half part (respectively from the top to the bottom) of a cylinder whose basis is a hyperrectangle of sidelength proportional to and whose height is () for a certain height function . We denote this maximal flow by (respectively ). We emphasize the fact that the cylinder may be tilted. We look at the probability that...