Successes and Failures of Discontinuous Galerkin Methods in Viscoelastic Fluid Analysis

To date, the more successful numerical methods in viscoelastic fluid dynamics are based upon the so called Discrete Elastic Viscous Stress Splitting (DEVSS) algorithm [6] together with a suitable form of upwinding of the hyperbolic part of the constitutive equation. An elegant way to perform upwinding on the viscoelastic stress tensor can be found in Discontinuous Galerkin techniques [4]. In particular the recently developed DEVSS/DG version [1], has proven to be successful in analyzing viscoelastic fluid flow problems in both smooth and non-smooth geometries. A particularly attractive feature of DG-based methods is that they allow for an efficient resolution of flow problems with multiple relaxation times, as was demonstrated in Baaijens et al. [1] which has recently been extended to three dimensional flows [2].