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An adaptive enrichment algorithm for advection‐dominated problems
Author(s) -
Abgrall Rémi,
Krust Arnaud
Publication year - 2012
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3745
Subject(s) - advection , representation (politics) , finite element method , algorithm , resolution (logic) , scheme (mathematics) , dirichlet boundary condition , path (computing) , mathematics , boundary layer , boundary (topology) , adaptive mesh refinement , dirichlet distribution , computer science , boundary value problem , computational science , mathematical analysis , mechanics , artificial intelligence , structural engineering , engineering , physics , politics , political science , law , thermodynamics , programming language
SUMMARY We are interested in developing a numerical framework well suited for advection–diffusion problems when the advection part is dominant. In that case, given Dirichlet type boundary condition, it is well known that a boundary layer develops. To resolve correctly this layer, standard methods consist in increasing the mesh resolution and possibly increasing the formal accuracy of the numerical method. In this paper, we follow another path: we do not seek to increase the formal accuracy of the scheme but, by a careful choice of finite element, to lower the mesh resolution in the layer. Indeed the finite element representation we choose is locally the sum of a standard one plus an enrichment. This paper proposes such a method and with several numerical examples, we show the potential of this approach. In particular, we show that the method is not very sensitive to the choice of the enrichment and develop an adaptive algorithm to automatically choose the enrichment functions.Copyright © 2012 John Wiley & Sons, Ltd.