Displaying similar documents to “Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension”

A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems

Thierry Gallouët, Jean-Marc Hérard, Nicolas Seguin (2002)

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

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The present paper is devoted to the computation of single phase or two phase flows using the single-fluid approach. Governing equations rely on Euler equations which may be supplemented by conservation laws for mass species. Emphasis is given on numerical modelling with help of Godunov scheme or an approximate form of Godunov scheme called VFRoe-ncv based on velocity and pressure variables. Three distinct classes of closure laws to express the internal energy in terms of pressure, density...

Adaptive multiscale scheme based on numerical density of entropy production for conservation laws

Mehmet Ersoy, Frédéric Golay, Lyudmyla Yushchenko (2013)

Open Mathematics

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We propose a 1D adaptive numerical scheme for hyperbolic conservation laws based on the numerical density of entropy production (the amount of violation of the theoretical entropy inequality). This density is used as an a posteriori error which provides information if the mesh should be refined in the regions where discontinuities occur or coarsened in the regions where the solution remains smooth. As due to the Courant-Friedrich-Levy stability condition the time step is restricted and...

Adaptive multiresolution methods

Margarete O. Domingues, Sônia M. Gomes, Olivier Roussel, Kai Schneider (2011)

ESAIM: Proceedings

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These lecture notes present adaptive multiresolution schemes for evolutionary PDEs in Cartesian geometries. The discretization schemes are based either on finite volume or finite difference schemes. The concept of multiresolution analyses, including Harten’s approach for point and cell averages, is described in some detail. Then the sparse point representation method is discussed. Different strategies for adaptive time-stepping, like local scale dependent time stepping and time step...

Transport of pollutant in shallow water : a two time steps kinetic method

Emmanuel Audusse, Marie-Odile Bristeau (2003)

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

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The aim of this paper is to present a finite volume kinetic method to compute the transport of a passive pollutant by a flow modeled by the shallow water equations using a new time discretization that allows large time steps for the pollutant computation. For the hydrodynamic part the kinetic solver ensures – even in the case of a non flat bottom – the preservation of the steady state of a lake at rest, the non-negativity of the water height and the existence of an entropy inequality....