Is your code solving the correct equations of Fluid and Solid Mechanics?

LIMACHE A.C.; IDELSOHN S.R.

Buenos Aires, Argentina

Conferencia; II Internat. Conf. on Approx. Methods for Design and Control (ICAMDC 2007); 2007

Asoc. Arg. de Matemática Aplicada, Comp. e Industrial

he Navier-Stokes Equations and the Equations of Conservation of Continuum Mechanics describe the motion and the deformation of incompressible viscous fluids and elastic solids, respectively. However, some approximations have been historically introduced into these exact equations leading to equations that are considered by most people as fully correct, or at least, as widely accepted valid approximations. In the case of fluids, the Navier-Stokes equations written in Laplace form lead to the widely used Laplacian Formulations. However, we have recently discovered that these widely accepted formulations violate a main axiom of continuum mechanics: The Principle of Objectivity. Here we will describe the potential consequences of this unexpected result, in fluids and solids. Finally, after all, is your code Objective?.