On the use of characteristic variables in viscoelastic flow problems (Q2716587)

The authors consider the system of partial differential equations describing the flow of upper-convected Maxwell fluid. The equations are of mixed elliptic-hyperbolic type. The authors identify two characteristic variables which are transported along the streamlines. Then the authors describe a spectral element method in which continuity of characteristic variables is used to couple extra stress components between contiguous elements. The velocity and pressure can be determined from a doubly constrained weak formulation. Both the pressure and the extra stress tensor are discontinuous. Numerical results demonstrate the procedure.