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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 asymptotic preserving scheme for P1 model using classical diffusion schemes on unstructured polygonal meshes

Emmanuel Franck, Philippe Hoch, Pierre Navaro, Gérald Samba (2011)

ESAIM: Proceedings

A new scheme for discretizing the P1 model on unstructured polygonal meshes is proposed. This scheme is designed such that its limit in the diffusion regime is the MPFA-O scheme which is proved to be a consistent variant of the Breil-Maire diffusion scheme. Numerical tests compare this scheme with a derived GLACE scheme for the P1 system.

An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier–Stokes flows

Andrea Manzoni (2014)

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

We present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier–Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [S. Deparis, SIAM J. Numer. Anal. 46 (2008) 2039–2067; A. Quarteroni and G. Rozza, Numer. Methods Partial Differ. Equ. 23 (2007) 923–948; K. Veroy and A.T. Patera, Int. J. Numer. Methods Fluids 47 (2005) 773–788]) to more general affine and nonaffine parametrizations (such as volume-based...

An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment

François Bouchut, Tomás Morales de Luna (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water. The difficulty in this system comes from the coupling terms involving some derivatives of the unknowns that make the system nonconservative, and eventually nonhyperbolic. Due to these terms, a numerical scheme obtained by performing an arbitrary scheme to each layer, and using time-splitting or other similar techniques leads to instabilities in...

An entropy stable finite volume method for a compressible two phase model

Eduard Feireisl, Mădălina Petcu, Bangwei She (2023)

Applications of Mathematics

We study a binary mixture of compressible viscous fluids modelled by the Navier-Stokes-Allen-Cahn system with isentropic or ideal gas law. We propose a finite volume method for the approximation of the system based on upwinding and artificial diffusion approaches. We prove the entropy stability of the numerical method and present several numerical experiments to support the theory.

An entropy-correction free solver for non-homogeneous shallow water equations

Tomás Chacón Rebollo, Antonio Domínguez Delgado, Enrique D. Fernández Nieto (2003)

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

In this work we introduce an accurate solver for the Shallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme.

An entropy-correction free solver for non-homogeneous shallow water equations

Tomás Chacón Rebollo, Antonio Domínguez Delgado, Enrique D. Fernández Nieto (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work we introduce an accurate solver for the Shallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme.

An error estimate uniform in time for spectral Galerkin approximations for the equations for the motion of a chemical active fluid.

M. A. Rojas-Medar, S. A. Lorca (1995)

Revista Matemática de la Universidad Complutense de Madrid

We study error estimates and their convergence rates for approximate solutions of spectral Galerkin type for the equations for the motion of a viscous chemical active fluid in a bounded domain. We find error estimates that are uniform in time and also optimal in the L2-norm and H1-norm. New estimates in the H(-1)-norm are given.

An example in the gradient theory of phase transitions

Camillo De Lellis (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We prove by giving an example that when n ≥ 3 the asymptotic behavior of functionals ∫ Ω ε | ∇ 2 u | 2 + ( 1 - | ∇ u | 2 ) 2 / ε is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.

An example in the gradient theory of phase transitions

Camillo De Lellis (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We prove by giving an example that when n ≥ 3 the asymptotic behavior of functionals ∫ Ω ε | ∇ 2 u | 2 + ( 1 - | ∇ u | 2 ) 2 / ε is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see [2]) is no longer true in higher dimensions.

An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit

Didier Bresch, Marguerite Gisclon, Chi-Kun Lin (2005)

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

The purpose of this work is to study an example of low Mach (Froude) number limit of compressible flows when the initial density (height) is almost equal to a function depending on x . This allows us to connect the viscous shallow water equation and the viscous lake equations. More precisely, we study this asymptotic with well prepared data in a periodic domain looking at the influence of the variability of the depth. The result concerns weak solutions. In a second part, we discuss the general low...

Currently displaying 361 – 380 of 3487