Displaying similar documents to “Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system.”

Numerical simulation of a point-source initiated flame ball with heat losses

Jacques Audounet, Jean-Michel Roquejoffre, Hélène Rouzaud (2002)

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

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This article is devoted to the numerical study of a flame ball model, derived by Joulin, which obeys to a singular integro-differential equation. The numerical scheme that we analyze here, is based upon a one step method, and we are interested in its long-time behaviour. We recover the same dynamics as in the continuous case: quenching, or stabilization of the flame, depending on heat losses, and an energy input parameter.

Plane wave stability of some conservative schemes for the cubic Schrödinger equation

Morten Dahlby, Brynjulf Owren (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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The plane wave stability properties of the conservative schemes of Besse [ (2004) 934–952] and Fei [ (1995) 165–177] for the cubic Schrödinger equation are analysed. Although the two methods possess many of the same conservation properties, we show that their stability behaviour is very different. An energy preserving generalisation of the Fei method with improved stability is presented.

Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants

John W. Barrett, Linda El Alaoui (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a system of degenerate parabolic equations modelling a thin film, consisting of two layers of immiscible Newtonian liquids, on a solid horizontal substrate. In addition, the model includes the presence of insoluble surfactants on both the free liquid-liquid and liquid-air interfaces, and the presence of both attractive and repulsive van der Waals forces in terms of the heights of the two layers. We show that this system formally satisfies a Lyapunov structure, and a...