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The violation of objectivity in Laplace formulations of the Navier–Stokes equations
Author(s) -
Limache A.,
Idelsohn S.,
Rossi R.,
Oñate E.
Publication year - 2007
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.1480
Subject(s) - mathematics , laplace transform , laplace operator , laplace's equation , boundary value problem , objectivity (philosophy) , mathematical analysis , stokes flow , calculus (dental) , geometry , medicine , philosophy , flow (mathematics) , dentistry , epistemology
Abstract The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural boundary conditions of the Laplace form or neglecting the viscous contributions on free surfaces are traditionally considered reasonable and harmless assumptions. With these boundary conditions any formulation derived from integral methods (like finite elements or finite volumes) recovers the pure Laplacian aspect of the strong form of the equations. This approach has also the advantage of being convenient in terms of computational effort and, as a consequence, it is used extensively. However, we have recently discovered that these resulting Laplacian formulations violate a basic axiom of continuum mechanics: the principle of objectivity. In the present article we give an accurate account about these topics. We also show that unexpected differences may sometimes arise between Laplace discretizations and divergence discretizations. Copyright © 2007 John Wiley & Sons, Ltd.