Abstract: A new method for stabilizing viscoelastic flows is proposed suitable for high-order discretizations. It employs a mode-dependent diffusion operator that guarantees monotonicity while maintaining the formal accuracy of the discretization. Other features of the method are: a high-order time-splitting scheme, modal spectral element expansions on a single grid, and the use of a finitely extensible non-linear elastic-Peterlin (FENE-P) model. The convergence of the method is established through analytic examples and benchmark problems in two and three dimensions, and unsteady flow past a three-dimensional (3D) ellipsoid is studied at high Reynolds number.

Keywords: Spectral methods; FENE-P; Numerical diffusion; Unsteady flow