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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 a depth-averaged
two-phase flow model. This model contains nonconservative products for which we
developed a discontinuous Galerkin finite element formulation in Rhebergen et al.
(2008) J. Comput. Phys. 227, 1887-1922. The goal is to qualitatively validate the
model against a laboratory experiment and to show the abilities of the model to
capture physical phenomena. To be able to perform these test cases, a WENO slope
limiter is investigated 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
1 Introduction
Debris flows are flows of water-saturated slurry mixtures (Iverson and Den-


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


Collections: Engineering