Objectivity tests for Navier-Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations

Alejandro C. Limache*, P. J. Sánchez, Lisandro D. Dalcín, Sergio R. Idelsohn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Laplace formulations are weak formulations of the Navier-Stokes equations commonly used in computational fluid dynamics. In these schemes, the viscous terms are given as a function of the Laplace diffusion operator only. Despite their popularity, recently, it has been proven that they violate a fundamental principle of continuum mechanics, the principle of objectivity. It is remarkable that such flaw has not being noticed before, neither detected in numerical experiments. In this work, a series of objectivity tests have been designed with the purpose of revealing such problem in real numerical experiments. Through the tests it is shown how, for slip boundaries or free-surfaces, Laplace formulations generate non-physical solutions which widely depart from the real fluid dynamics. These tests can be easily reproduced, not requiring complex simulation tools. Furthermore, they can be used as benchmarks to check consistency of developed or commercial software. The article is closed with a discussion of the mathematical aspects involved, including the issues of boundary conditions and objectivity.

Original languageEnglish (US)
Pages (from-to)4180-4192
Number of pages13
JournalComputer Methods in Applied Mechanics and Engineering
Issue number49-50
StatePublished - Sep 15 2008
Externally publishedYes


  • Annular cavity
  • Boundary conditions
  • Free-surfaces
  • Laplace diffusion operator
  • Navier-Stokes equations
  • Objectivity

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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