Application of low-order Discontinuous Galerkin methods to the analysis of viscoelastic flows

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Abstract

The performance of two low-order discretization schemes in combination with the Discontinuous Galerkin method for the analysis of viscoelastic flows is investigated. An (extended) linear interpolation of the velocity-pressure variables is used in combination with a piecewise discontinuous constant and linear approximation of the extra stresses. Galerkin-leastsquares methodology is applied to stabilize the velocity-pressure discretization. As test problems, the falling sphere in a tube and the stick-slip configuration are studied. The constant stress triangular element converges to high Deborah numbers for a wide variety of material parameters of the Phan-Thien-Tanner model. In particular, for the upper convected Maxwell model, the falling sphere problem converges at least up to Deborah number of 4, while the stick-slip problem converges up to a Deborah number of 25.5.
Original languageEnglish
Pages (from-to)37-57
Number of pages11
JournalJournal of Non-Newtonian Fluid Mechanics
Volume52
Issue number1
DOIs
Publication statusPublished - 1994

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