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ESAIM: Proc., 2009, Vol. 27, pp. 272-288
DOI: 10.1051/proc/2009032
Viscous Problems with Inviscid Approximations in Subregions: a New Approach Based on Operator Factorization
Martin J. Gander1, Laurence Halpern2, Caroline Japhet2 and Veronique Martin31 Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, CP 64, CH-1211 Genève, SWITZERLAND.
2 LAGA,Institut Galilée, Université Paris XIII, Rue J.B. Clément, 93430 Villetaneuse, FRANCE.
3 LAMFA UMR-CNRS 6140, Université de Picardie Jules Verne, 33 Rue St. Leu, 80039 Amiens, FRANCE.
martin.gander@unige.ch
halpern@math.univ-paris13.fr
japhet@math.univ-paris13.fr
veronique.martin@u-picardie.fr
Published online: 25 June 2009
Abstract
In many applications the viscous terms become only important in
parts of the computational domain. As a typical example serves the
flow around the wing of an airplane, where close to the wing the
viscous terms in the Navier Stokes equations are essential for the
solution, while away from the wing, Euler's equations would suffice
for the simulation. This leads to the interesting problem of finding
coupling conditions between these two partial differential equations
of different type. While coupling conditions have been developed in
the literature, for example by using a limiting procedure on a
globally viscous problem, we are interested here to develop coupling
conditions which lead to coupled solutions which are as close as
possible to the fully viscous solution. We develop our new approach
on the one dimensional model problem of advection reaction diffusion
equations with pure advection reaction approximation in subregions,
which leads to the problem of coupling
first and second order operators.
Our guiding principle for finding transmission conditions
is an operator factorization, and we show both analytically and
numerically that the new coupling conditions lead to coupled
solutions which are much closer to the fully viscous ones than
other coupling conditions from the literature.
© EDP Sciences, ESAIM 2009
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