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INTEGRAL EQUATIONS FOR THE GENERALIZED STOKES OPERATOR. APPLICATIONS TO HIGH REYNOLDS NUMBER FLOWS.
 

Summary: INTEGRAL EQUATIONS FOR THE GENERALIZED STOKES OPERATOR.
APPLICATIONS TO HIGH REYNOLDS NUMBER FLOWS.
(May 92)
Y. Achdou (*).
Abstract
This paper deals with a boundary integral equation for the Generalized Stokes Problem and its
approximation by simpler integral equations when the Reynolds number tends to infinity. The
2­dimensional case has been treated in [1]. This paper addresses the 3­dimensional case.
0. Introduction
Viscous flows at high Reynolds numbers are quite difficult to compute. The boundary layers are
extremely thin and the meshes must be either extremely dense or have a very high aspect ratio.
In this work we wish to show that high Reynolds number flows have certain features which have
been underestimated so far and which can make the numerical simulation easier.
The basic idea is that an operator such as 1
ffit I \Gamma š \Delta is numerically equivalent to 1
ffit I if the mesh is
coarser than
p
ffitš or numerically equivalent to 1
ffit I \Gamma š @ 2

  

Source: Achdou, Yves - Laboratoire Jacques-Louis Lions, Université Pierre-et-Marie-Curie, Paris 6

 

Collections: Mathematics