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An Adaptive Multi-level method for Convection Diffusion Problems

Martine MarionAdeline Mollard — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

In this article we introduce an adaptive multi-level method in space and time for convection diffusion problems. The scheme is based on a multi-level spatial splitting and the use of different time-steps. The temporal discretization relies on the characteristics method. We derive an error estimate and design a corresponding adaptive algorithm. The efficiency of the multi-level method is illustrated by numerical experiments, in particular for a convection-dominated problem.

Modelling of miscible liquids with the Korteweg stress

Ilya KostinMartine MarionRozenn Texier-PicardVitaly A. Volpert — 2003

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

When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients exist during some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical model consisting of the diffusion equation with convective terms and of the Navier-Stokes equations with the Korteweg stress. We prove the global existence...

Modelling of Miscible Liquids with the Korteweg Stress

Ilya KostinMartine MarionRozenn Texier-PicardVitaly A. Volpert — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients exist during some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical model consisting of the diffusion equation with convective terms and of the Navier-Stokes equations with the Korteweg stress. We prove the global...

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