On the use of characteristic variables in viscoelastic flow problems

The system of partial differential equations governing the how of an upper converted Maxwell fluid is known to be of mixed elliptic-hyperbolic type. T he hyperbolic nature of the constitutive equation requires that, where appr opriate, inflow conditions are prescribed in order to obtain a well-posed p roblem. Although there are three convective derivatives in the constitutive equation there are only two characteristic quantities which are transporte d along the streamlines. These characteristic quantities are identified. A spectral element method is described in which continuity of the characteris tic variables is used to couple the extra stress components between contigu ous elements. The continuity of the characteristic variables is treated as a constraint on the constitutive equation. These conditions do not necessar ily impose continuity on the extra-stress components. The velocity and pres sure follow from the doubly constrained weak formulation which enforces a d ivergence-free velocity field and irrotational polymeric stress forces. Thi s means that both the pressure and the extra-stress tensor are discontinuou s. Numerical results are presented to demonstrate this procedure. The theor y is applied to the upper convected Maxwell model with vanishing Reynolds n umber. No regularization techniques such as streamline upwind Petrov Galerk in (SUPG), elastic viscous split stress (EVSS) or explicitly elliptic momen tum equation (EEME) are used.