All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 84 Next

Displaying 1661 – 1680 of 3470

Showing per page

Numerical approximation of Knudsen layer for the Euler-Poisson system

Fréderique Charles, Nicolas Vauchelet, Christophe Besse, Thierry Goudon, Ingrid Lacroix–Violet, Jean-Paul Dudon, Laurent Navoret (2011)

ESAIM: Proceedings

In this work, we consider the computation of the boundary conditions for the linearized Euler–Poisson derived from the BGK kinetic model in the small mean free path regime. Boundary layers are generated from the fact that the incoming kinetic flux might be far from the thermodynamical equilibrium. In [2], the authors propose a method to compute numerically the boundary conditions in the hydrodynamic limit relying on an analysis of the boundary layers....

Numerical approximation of nematic liquid crystal flows governed by the Ericksen-Leslie equations

Noel J. Walkington (2011)

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

Numerical approximation of the flow of liquid crystals governed by the Ericksen-Leslie equations is considered. Care is taken to develop numerical schemes which inherit the Hamiltonian structure of these equations and associated stability properties. For a large class of material parameters compactness of the discrete solutions is established which guarantees convergence.

Numerical approximation of nematic liquid crystal flows governed by the Ericksen-Leslie equations*

Noel J. Walkington (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Numerical approximation of the flow of liquid crystals governed by the Ericksen-Leslie equations is considered. Care is taken to develop numerical schemes which inherit the Hamiltonian structure of these equations and associated stability properties. For a large class of material parameters compactness of the discrete solutions is established which guarantees convergence.

Numerical approximation of the inviscid 3D primitive equations in a limited domain

Qingshan Chen, Ming-Cheng Shiue, Roger Temam, Joseph Tribbia (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

A new set of nonlocal boundary conditions is proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive equations are performed on a nested set of domains, and the results are discussed.

Numerical approximation of the inviscid 3D primitive equations in a limited domain

Qingshan Chen, Ming-Cheng Shiue, Roger Temam, Joseph Tribbia (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

A new set of nonlocal boundary conditions is proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive equations are performed on a nested set of domains, and the results are discussed.

Numerical Approximations of the Relative Rearrangement: The piecewise linear case. Application to some Nonlocal Problems

Jean-Michel Rakotoson, Maria Luisa Seoane (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We first prove an abstract result for a class of nonlocal problems using fixed point method. We apply this result to equations revelant from plasma physic problems. These equations contain terms like monotone or relative rearrangement of functions. So, we start the approximation study by using finite element to discretize this nonstandard quantities. We end the paper by giving a numerical resolution of a model containing those terms.

Numerical aspects of the nonlinear Schrödinger equation in the semiclassical limit in a supercritical regime

Rémi Carles, Bijan Mohammadi (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We study numerically the semiclassical limit for the nonlinear Schrödinger equation thanks to a modification of the Madelung transform due to Grenier. This approach allows for the presence of vacuum. Even if the mesh size and the time step do not depend on the Planck constant, we recover the position and current densities in the semiclassical limit, with a numerical rate of convergence in accordance with the theoretical results, before shocks appear in the limiting Euler equation. By using simple...

Numerical aspects of the nonlinear Schrödinger equation in the semiclassical limit in a supercritical regime

Rémi Carles, Bijan Mohammadi (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We study numerically the semiclassical limit for the nonlinear Schrödinger equation thanks to a modification of the Madelung transform due to Grenier. This approach allows for the presence of vacuum. Even if the mesh size and the time step do not depend on the Planck constant, we recover the position and current densities in the semiclassical limit, with a numerical rate of convergence in accordance with the theoretical results, before shocks appear in the limiting Euler equation. By using simple...

Numerical comparisons of two long-wave limit models

Stéphane Labbé, Lionel Paumond (2004)

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

The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations 16 (2003) 1039–1064; Pego and Quintero, Physica D 132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically...

Numerical comparisons of two long-wave limit models

Stéphane Labbé, Lionel Paumond (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations16 (2003) 1039–1064; Pego and Quintero, Physica D132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically...

Numerical evidence of nonuniqueness in the evolution of vortex sheets

Milton C. Lopes Filho, John Lowengrub, Helena J. Nussenzveig Lopes, Yuxi Zheng (2006)

ESAIM: Mathematical Modelling and Numerical Analysis


We consider a special configuration of vorticity that consists of a pair of externally tangent circular vortex sheets, each having a circularly symmetric core of bounded vorticity concentric to the sheet, and each core precisely balancing the vorticity mass of the sheet. This configuration is a stationary weak solution of the 2D incompressible Euler equations. We propose to perform numerical experiments to verify that certain approximations of this flow configuration converge to a non-stationary...

Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint

Florent Berthelin (2003)

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

We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.

Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint

Florent Berthelin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.

Numerical homogenization of well singularities in the flow transport through heterogeneous porous media: fully discrete scheme

Meiqun Jiang, Xingye Yue (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

Motivated by well-driven flow transport in porous media, Chen and Yue proposed a numerical homogenization method for Green function [Multiscale Model. Simul.1 (2003) 260–303]. In that paper, the authors focused on the well pore pressure, so the local error analysis in maximum norm was presented. As a continuation, we will consider a fully discrete scheme and its multiscale error analysis on the velocity field.

Numerical investigation of dynamic capillary pressure in two-phase flow in porous medium

Radek Fučík, Jiří Mikyška (2011)

Mathematica Bohemica

In order to investigate effects of the dynamic capillary pressure-saturation relationship used in the modelling of a flow in porous media, a one-dimensional fully implicit numerical scheme is proposed. The numerical scheme is used to simulate an experimental procedure using a measured dataset for the sand and fluid properties. Results of simulations using different models for the dynamic effect term in capillary pressure-saturation relationship are presented and discussed.

Numerical methods for fourth order nonlinear degenerate diffusion problems

Jürgen Becker, Günther Grün, Martin Lenz, Martin Rumpf (2002)

Applications of Mathematics

Numerical schemes are presented for a class of fourth order diffusion problems. These problems arise in lubrication theory for thin films of viscous fluids on surfaces. The equations being in general fourth order degenerate parabolic, additional singular terms of second order may occur to model effects of gravity, molecular interactions or thermocapillarity. Furthermore, we incorporate nonlinear surface tension terms. Finally, in the case of a thin film flow driven by a surface active agent (surfactant),...

Currently displaying 1661 – 1680 of 3470