Splitting schemes for the stress formulation of the incompressible Navier–Stokes equations

Abstract

This paper presents a novel approach to the Navier–Stokes equations which reformulates them in terms of a new tensor variable. In the first formulation discussed in the paper this variable is proportional to the gradient of the velocity field with the pressure added to the diagonal components. In the second formulation it is identical to the stress tensor. At first glance the resulting tensorial problem is more difficult than the problem in the primitive variables. However, if combined with a proper splitting, it yields locally one dimensional schemes with attractive properties, that are very competitive to the most widely used schemes for the formulation in primitive variables. In addition, it has an advantage if applied to fluid–structure interaction problems.