Laplace Form of Navier-Stokes Equations: a safe path or a wrong way?

LIMACHE A.; IDELSOHN S.

Santa Fe, Argentina

Congreso; ENIEF 2006: XV Congreso sobre Métodos Numéricos y sus Aplicaciones; 2006

Asociación Argentina de Mecánica Computacional y CIMEC

The Navier-Stokes Equations written in Laplace form are often the departure point for thesimulation of viscous newtonian flows and some studies of numerical stability. Researchers may not befully aware that the physical traction boundary conditions are not the natural boundary conditions ofthe Laplace form of the Navier-Stokes Equations. This is not a problem per se, as long as one managesto rigurously incorporate the physical boundary conditions into the formulation. However, we havediscovered that if some seemenly harmless assumptions are made, like using pseudo-tractions (i.e thenatural boundary conditions of the Laplace form) or neglecting viscous terms on the free-surfaces, theresulting formulation violates a basic axiom of continuum mechanics: the principle of objectivity. In thepresent article we give an accurate account about these topics. We also show that unexpected differencesmay sometimes arise between Laplace discretizations and Divergence discretizations.