On the use of Characteristic Variables in Viscoelastic Flow Calculations

Abstract

The development of accurate and stable timedependent approximations to viscoelastic flow problems remains a priority and challenge for researchers in this field. The mathematical statement of viscoelastic flow problems is invariably in terms of velocity, pressure and extra-stress, the so-called mixed formulation. This class of flow problems is characterized by a nonlinear rheological equation of state which relates the extra-stress tensor to the rate of deformation tensor. For high values of the Deborah or Weissenberg numbers it is the discretization of this equation which is the cause of so many numerical difficulties due to the dominating influence of the convective terms.