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An approximate nonlinear projection scheme for a combustion model

Christophe Berthon, Didier Reignier (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The paper deals with the numerical resolution of the convection-diffusion system which arises when modeling combustion for turbulent flow. The considered model is of compressible turbulent reacting type where the turbulence-chemistry interactions are governed by additional balance equations. The system of PDE's, that governs such a model, turns out to be in non-conservation form and usual numerical approaches grossly fail in the capture of viscous shock layers. Put in other words, classical finite...

An approximate nonlinear projection scheme for a combustion model

Christophe Berthon, Didier Reignier (2003)

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

The paper deals with the numerical resolution of the convection-diffusion system which arises when modeling combustion for turbulent flow. The considered model is of compressible turbulent reacting type where the turbulence-chemistry interactions are governed by additional balance equations. The system of PDE’s, that governs such a model, turns out to be in non-conservation form and usual numerical approaches grossly fail in the capture of viscous shock layers. Put in other words, classical finite...

Approximation of a solidification problem

Rajae Aboulaïch, Ilham Haggouch, Ali Souissi (2001)

International Journal of Applied Mathematics and Computer Science

A two-dimensional Stefan problem is usually introduced as a model of solidification, melting or sublimation phenomena. The two-phase Stefan problem has been studied as a direct problem, where the free boundary separating the two regions is eliminated using a variational inequality (Baiocchi, 1977; Baiocchi et al., 1973; Rodrigues, 1980; Saguez, 1980; Srunk and Friedman, 1994), the enthalpy function (Ciavaldini, 1972; Lions, 1969; Nochetto et al., 1991; Saguez, 1980), or a control problem (El Bagdouri,...

C++ Tools to construct our user-level language

Frédéric Hecht (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to present how to make a dedicaded computed language polymorphic and multi type, in C++ to solve partial differential equations with the finite element method. The driving idea is to make the language as close as possible to the mathematical notation.

C++ tools to construct our user-level language

Frédéric Hecht (2002)

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

The aim of this paper is to present how to make a dedicaded computed language polymorphic and multi type, in C++to solve partial differential equations with the finite element method. The driving idea is to make the language as close as possible to the mathematical notation.

Computation of bifurcated branches in a free boundary problem arising in combustion theory

Olivier Baconneau, Claude-Michel Brauner, Alessandra Lunardi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a parabolic 2D Free Boundary Problem, with jump conditions at the interface. Its planar travelling-wave solutions are orbitally stable provided the bifurcation parameter u * does not exceed a critical value u * c . The latter is the limit of a decreasing sequence ( u * k ) of bifurcation points. The paper deals with the study of the 2D bifurcated branches from the planar branch, for small k. Our technique is based on the elimination of the unknown front, turning the problem into a fully nonlinear...

Conservation schemes for convection-diffusion equations with Robin boundary conditions

Stéphane Flotron, Jacques Rappaz (2013)

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

In this article, we present a numerical scheme based on a finite element method in order to solve a time-dependent convection-diffusion equation problem and satisfy some conservation properties. In particular, our scheme is able to conserve the total energy for a heat equation or the total mass of a solute in a fluid for a concentration equation, even if the approximation of the velocity field is not completely divergence-free. We establish a priori errror estimates for this scheme and we give some...

Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems

Pedro Merino, Ira Neitzel, Fredi Tröltzsch (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.

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