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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 semi-smooth Newton method for solving elliptic equations with gradient constraints

Roland Griesse, Karl Kunisch (2009)

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

Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.

A shape optimization approach for a class of free boundary problems of Bernoulli type

Abdesslam Boulkhemair, Abdeljalil Nachaoui, Abdelkrim Chakib (2013)

Applications of Mathematics

We are interested in an optimal shape design formulation for a class of free boundary problems of Bernoulli type. We show the existence of the optimal solution of this problem by proving continuity of the solution of the state problem with respect to the domain. The main tools in establishing such a continuity are a result concerning uniform continuity of the trace operator with respect to the domain and a recent result on the uniform Poincaré inequality for variable domains.

A sharp Strichartz estimate for the wave equation with data in the energy space

Neal Bez, Keith M. Rogers (2013)

Journal of the European Mathematical Society

We prove a sharp bilinear estimate for the wave equation from which we obtain the sharp constant in the Strichartz estimate which controls the L t , x 4 ( 5 + 1 ) norm of the solution in terms of the energy. We also characterise the maximisers.

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