摘要：The Navier-Stokes Equations written in Laplace form are often the departure
point for the simulation of viscous newtonian flows and some studies of
numerical stability. Researchers may not be fully aware that the “physical
traction boundary conditions” are not the “natural boundary conditions”
of the Laplace form of the Navier-Stokes Equations. This is not a problem per
se, as long as one manages to rigurously incorporate the physical boundary
conditions into the formulation. However, we have discovered that if some
seemenly harmless assumptions are made, like using pseudo-tractions (i.e
the natural boundary conditions of the Laplace form) or neglecting viscous
terms on the free-surfaces, the resulting formulation violates 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.
