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Numerical methods for phase transition problems

Claudio Verdi (1998)

Bollettino dell'Unione Matematica Italiana

Nel presente articolo si illustrano alcuni dei principali metodi numerici per l'approssimazione di modelli matematici legati ai fenomeni di transizione di fase. Per semplificare e contenere l'esposizione ci siamo limitati a discutere con un certo dettaglio i metodi più recenti, presentandoli nel caso di problemi modello, quali il classico problema di Stefan e l'evoluzione di superficie per curvatura media, solo accennando alle applicazioni e modelli più generali.

Numerical modeling of the movement of a rigid particle in viscous fluid

Josef Ježek, Stanislav Saic, Karel Segeth (1999)

Applications of Mathematics

Modeling the movement of a rigid particle in viscous fluid is a problem physicists and mathematicians have tried to solve since the beginning of this century. A general model for an ellipsoidal particle was first published by Jeffery in the twenties. We exploit the fact that Jeffery was concerned with formulae which can be used to compute numerically the velocity field in the neighborhood of the particle during his derivation of equations of motion of the particle. This is our principal contribution...

Numerical modelling of algebraic closure models of oceanic turbulent mixing layers

Anne-Claire Bennis, Tomas Chacón Rebollo, Macarena Gómez Mármol, Roger Lewandowski (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce in this paper some elements for the mathematical and numerical analysis of algebraic turbulence models for oceanic surface mixing layers. In these models the turbulent diffusions are parameterized by means of the gradient Richardson number, that measures the balance between stabilizing buoyancy forces and destabilizing shearing forces. We analyze the existence and linear exponential asymptotic stability of continuous and discrete equilibria states. We also analyze the well-posedness...

Numerical realization of the Bayesian inversion accelerated using surrogate models

Bérešová, Simona (2023)

Programs and Algorithms of Numerical Mathematics

The Bayesian inversion is a natural approach to the solution of inverse problems based on uncertain observed data. The result of such an inverse problem is the posterior distribution of unknown parameters. This paper deals with the numerical realization of the Bayesian inversion focusing on problems governed by computationally expensive forward models such as numerical solutions of partial differential equations. Samples from the posterior distribution are generated using the Markov chain Monte...

Numerical resolution of an “unbalanced” mass transport problem

Jean-David Benamou (2003)

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

We introduce a modification of the Monge–Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented lagrangian numerical method introduced in [6] is adapted to this “unbalanced” problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology.

Numerical resolution of an “unbalanced” mass transport problem

Jean-David Benamou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce a modification of the Monge–Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented Lagrangian numerical method introduced in [6] is adapted to this “unbalanced” problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology.

Numerical schemes for a three component Cahn-Hilliard model

Franck Boyer, Sebastian Minjeaud (2011)

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

In this article, we investigate numerical schemes for solving a three component Cahn-Hilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the stability of the method. We study three different schemes and prove existence and convergence theorems. Theoretical results are illustrated by...

Numerical schemes for a three component Cahn-Hilliard model

Franck Boyer, Sebastian Minjeaud (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article, we investigate numerical schemes for solving a three component Cahn-Hilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the stability of the method. We study three different schemes and prove existence and convergence theorems. Theoretical results are illustrated by...

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

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.

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

Jacques Audounet, Jean-Michel Roquejoffre, Hélène Rouzaud (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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.

Numerical simulation of chemotactic bacteria aggregation via mixed finite elements

Americo Marrocco (2003)

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

We start from a mathematical model which describes the collective motion of bacteria taking into account the underlying biochemistry. This model was first introduced by Keller-Segel [13]. A new formulation of the system of partial differential equations is obtained by the introduction of a new variable (this new variable is similar to the quasi-Fermi level in the framework of semiconductor modelling). This new system of P.D.E. is approximated via a mixed finite element technique. The solution algorithm...

Numerical simulation of chemotactic bacteria aggregation via mixed finite elements

Americo Marrocco (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We start from a mathematical model which describes the collective motion of bacteria taking into account the underlying biochemistry. This model was first introduced by Keller-Segel [13]. A new formulation of the system of partial differential equations is obtained by the introduction of a new variable (this new variable is similar to the quasi-Fermi level in the framework of semiconductor modelling). This new system of P.D.E. is approximated via a mixed finite element technique. The solution...

Numerical simulation of generalized Newtonian and Oldroyd-B fluids flow

Keslerová, Radka, Kozel, Karel (2013)

Programs and Algorithms of Numerical Mathematics

This work deals with the numerical solution of generalized Newtonian and Oldroyd-B fluids flow. The governing system of equations is based on the system of balance laws for mass and momentum for incompressible laminar viscous and viscoelastic fluids. Two different definition of the stress tensor are considered. For viscous case Newtonian model is used. For the viscoelastic case Oldroyd-B model is tested. Both presented models can be generalized. In this case the viscosity is defined as a shear rate...

Numerical simulations for nodal domains and spectral minimal partitions

Virginie Bonnaillie-Noël, Bernard Helffer, Gregory Vial (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We recall here some theoretical results of Helffer et al. [Ann. Inst. H. Poincaré Anal. Non Linéaire (2007) doi:10.1016/j.anihpc.2007.07.004] about minimal partitions and propose numerical computations to check some of their published or unpublished conjectures and exhibit new ones.

Currently displaying 541 – 560 of 603