Displaying similar documents to “Flow-oriented difference scheme for multidimensional convection-diffusion equation.”

Diffusion limit of the Lorentz model : asymptotic preserving schemes

Christophe Buet, Stéphane Cordier, Brigitte Lucquin-Desreux, Simona Mancini (2002)

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

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This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the diffusion coefficient as in the continuous case. We are also naturally interested with a discretization which can be used with few...

Resolution of the time dependent equations by a Godunov type scheme having the diffusion limit

Patricia Cargo, Gérald Samba (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the model to approximate the time dependent transport equation in one dimension of space. In a diffusive regime, the solution of this system is solution of a diffusion equation. We are looking for a numerical scheme having the diffusion limit property: in a diffusive regime, it has to give the solution of the limiting diffusion equation on a mesh at the diffusion scale. The numerical scheme proposed is an extension of the Godunov type scheme proposed by...

Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids

Bruno Després, Frédéric Lagoutière (2001)

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

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We study a family of non linear schemes for the numerical solution of linear advection on arbitrary grids in several space dimension. A proof of weak convergence of the family of schemes is given, based on a new Longitudinal Variation Diminishing (LVD) estimate. This estimate is a multidimensional equivalent to the well-known TVD estimate in one dimension. The proof uses a corollary of the Perron-Frobenius theorem applied to a generalized Harten formalism.

Stable upwind schemes for the magnetic induction equation

Franz G. Fuchs, Kenneth H. Karlsen, Siddharta Mishra, Nils H. Risebro (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the magnetic induction equation for the evolution of a magnetic field in a plasma where the velocity is given. The aim is to design a numerical scheme which also handles the divergence constraint in a suitable manner. We design and analyze an upwind scheme based on the symmetrized version of the equations in the non-conservative form. The scheme is shown to converge to a weak solution of the equations. Furthermore, the discrete divergence produced by the scheme is...

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

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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.

High order finite volume schemes for numerical solution of 2D and 3D transonic flows

Jiří Fürst, Karel Kozel, Petr Furmánek (2009)

Kybernetika

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The aim of this article is a qualitative analysis of two modern finite volume (FVM) schemes. First one is the so called Modified Causon’s scheme, which is based on the classical MacCormack FVM scheme in total variation diminishing (TVD) form, but is simplified in such a way that the demands on computational power are much smaller without loss of accuracy. Second one is implicit WLSQR (Weighted Least Square Reconstruction) scheme combined with various types of numerical fluxes (AUSMPW+...