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Building generalized open boundary conditions for fluid dynamics problems
Author(s) -
Blayo Eric,
Martin Véronique
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.3675
Subject(s) - grid , extrapolation , mathematics , simple (philosophy) , boundary value problem , operator (biology) , boundary (topology) , laplace transform , partial differential equation , richardson extrapolation , mathematical analysis , geometry , philosophy , biochemistry , chemistry , epistemology , repressor , transcription factor , gene
SUMMARY This paper deals with the design of an efficient open boundary condition (OBC) for fluid dynamics problems. Such problematics arise, for instance, when one solves a local model on a fine grid that is nested in a coarser one of greater extent. Usually, the local solution U loc is computed from the coarse solution U ext , thanks to an OBC formulated as B h U loc = B H U ext , where B h and B H are discretizations of the same differential operator B ( B h being defined on the fine grid and B H on the coarse grid). In this paper, we show that such an OBC cannot lead to the exact solution, and we propose a generalized formulation B h U loc = B H U ext + g , where g is a correction term. When B h and B H are discretizations of a transparent operator, g can be computed analytically, at least for simple equations. Otherwise, we propose to approximate g by a Richardson extrapolation procedure. Numerical test cases on a 1D Laplace equation and on a 1D shallow water system illustrate the improved efficiency of such a generalized OBC compared with usual ones. Copyright © 2012 John Wiley & Sons, Ltd.