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Discontinuous Galerkin finite element method for shallow two-phase flows

Summary: Discontinuous Galerkin finite element method
for shallow two-phase flows
S. Rhebergen , O. Bokhove and J.J.W. van der Vegt
Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500
AE, Enschede, The Netherlands
We present a discontinuous Galerkin finite element method for two depth-averaged
two-phase flow models. One of these models contains nonconservative products for
which we developed a discontinuous Galerkin finite element formulation in Rhe-
bergen et al. (2008) J. Comput. Phys. 227, 1887-1922. The other model is a new
depth-averaged two-phase flow model we introduce for shallow two-phase flows that
does not contain nonconservative products. We will compare numerical results of
both models and qualitatively validate the models against a laboratory experiment.
Furthermore, because of spurious oscillations that may occur near discontinuities,
a WENO slope limiter is applied in conjunction with a discontinuity detector to
detect regions where spurious oscillations appear.
Key words: discontinuous Galerkin finite element methods, multiphase flows,
nonconservative products, slope limiter, discontinuity detector
PACS: 02.60.Cb, 02.70.Dh, 47.55.-t
1991 MSC: 35L65, 35Q35, 65M60, 76M10, 76T99


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering