Displaying similar documents to “An approximate nonlinear projection scheme for a combustion model”

Behaviour of the support of the solution appearing in some nonlinear diffusion equation with absorption

Tomoeda, Kenji

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Numerical experiments suggest interesting properties in the several fields of fluid dynamics, plasma physics and population dynamics. Among such properties, we may observe the interesting phenomena; that is, the repeated appearance and disappearance phenomena of the region penetrated by the fluid in the flow through a porous media with absorption. The model equation in two dimensional space is written in the form of the initial-boundary value problem for a nonlinear diffusion equation...

An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems

Molati, Motlatsi, Murakawa, Hideki

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This paper deals with nonlinear diffusion problems which include the Stefan problem, the porous medium equation and cross-diffusion systems. We provide a linear scheme for these nonlinear diffusion problems. The proposed numerical scheme has many advantages. Namely, the implementation is very easy and the ensuing linear algebraic systems are symmetric, which show low computational cost. Moreover, this scheme has the accuracy comparable to that of the wellstudied nonlinear schemes and...

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

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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...

Convergence of a variational lagrangian scheme for a nonlinear drift diffusion equation

Daniel Matthes, Horst Osberger (2014)

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

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We study a Lagrangian numerical scheme for solution of a nonlinear drift diffusion equation on an interval. The discretization is based on the equation’s gradient flow structure with respect to the Wasserstein distance. The scheme inherits various properties from the continuous flow, like entropy monotonicity, mass preservation, metric contraction and minimum/ maximum principles. As the main result, we give a proof of convergence in the limit of vanishing mesh size under a CFL-type condition....

A hyperbolic model for convection-diffusion transport problems in CFD: numerical analysis and applications.

Héctor Gómez, Ignasi Colominas, Fermín L. Navarrina, Manuel Casteleiro (2008)

RACSAM

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In this paper we present a numerical study of the hyperbolic model for convection-diffusion transport problems that has been recently proposed by the authors. This model avoids the infinite speed paradox, inherent to the standard parabolic model and introduces a new parameter called relaxation time. This parameter plays the role of an “inertia” for the movement of the pollutant. The analysis presented herein is twofold: first, we perform an accurate study of the 1D steady-state equations...

On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow

Vít Dolejší, Miloslav Feistauer, Christoph Schwab (2002)

Mathematica Bohemica

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The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—finite element method. Its advantage is the use of only one mesh (in contrast to the combined...