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Successes and failures of discontinuous Galerkin methods in viscoelastic fluid analysis. (English) Zbl 0989.76042

Cockburn, Bernardo (ed.) et al., Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24-26, 1999. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 11, 263-270 (2000).
Summary: To date, the more successful numerical methods in viscoelastic fluid dynamics are based upon the so-called discrete elastic viscous stress splitting (DEVSS) algorithm together with a suitable form of upwinding of the hyperbolic part of constitutive equation. An elegant way to perform upwinding on the viscoelastic stress tensor can be found in discontinuous Galerkin techniques. In particular, the recently developed DEVSS/DG version 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. However, one of the key issues in simulations of viscoelastic flows remains the assessment of temporal stability of the computational method. Especially, increasing elasticity beyond critical values of Weissenberg number can give rise to numerical instabilities in flows that are otherwise mathematically stable.
For the entire collection see [Zbl 0935.00043].

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76A10 Viscoelastic fluids
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