Discontinuous Galerkin finite element method for shallow two-phase flows

Sander Rhebergen; Onno Bokhove; Jacobus J.W. van der Vegt

doi:10.1016/j.cma.2008.10.019

Discontinuous Galerkin finite element method for shallow two-phase flows

Sander Rhebergen, Onno Bokhove, Jacobus J.W. van der Vegt

Research output: Contribution to journal › Article › Academic › peer-review

9 Citations (Scopus)

6 Downloads (Pure)

Abstract

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 Rhebergen 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.

Original language	Undefined
Article number	10.1016/j.cma.2008.10.019
Pages (from-to)	819-830
Number of pages	12
Journal	Computer methods in applied mechanics and engineering
Volume	198
Issue number	5-8
DOIs	https://doi.org/10.1016/j.cma.2008.10.019
Publication status	Published - 2009

Keywords

EWI-14851
MSC-65M60
MSC-76M10
MSC-76T99
MSC-35L65
MSC-35Q35
IR-62686
Discontinuity detector
Discontinuous Galerkin finite element methods
Nonconservative products
slope limiter
METIS-263715
Multiphase Flows

Access to Document

10.1016/j.cma.2008.10.019

http://eprints.eemcs.utwente.nl/secure2/14851/01/sdarticle.pdf

Cite this

@article{32dc398376f544dba2d8b9703f0989d7,

title = "Discontinuous Galerkin finite element method for shallow two-phase flows",

abstract = "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 Rhebergen 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.",

keywords = "EWI-14851, MSC-65M60, MSC-76M10, MSC-76T99, MSC-35L65, MSC-35Q35, IR-62686, Discontinuity detector, Discontinuous Galerkin finite element methods, Nonconservative products, slope limiter, METIS-263715, Multiphase Flows",

author = "Sander Rhebergen and Onno Bokhove and {van der Vegt}, {Jacobus J.W.}",

note = "10.1016/j.cma.2008.10.019 ",

year = "2009",

doi = "10.1016/j.cma.2008.10.019",

language = "Undefined",

volume = "198",

pages = "819--830",

journal = "Computer methods in applied mechanics and engineering",

issn = "0045-7825",

publisher = "Elsevier",

number = "5-8",

}

TY - JOUR

T1 - Discontinuous Galerkin finite element method for shallow two-phase flows

AU - Rhebergen, Sander

AU - Bokhove, Onno

AU - van der Vegt, Jacobus J.W.

N1 - 10.1016/j.cma.2008.10.019

PY - 2009

Y1 - 2009

N2 - 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 Rhebergen 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.

AB - 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 Rhebergen 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.

KW - EWI-14851

KW - MSC-65M60

KW - MSC-76M10

KW - MSC-76T99

KW - MSC-35L65

KW - MSC-35Q35

KW - IR-62686

KW - Discontinuity detector

KW - Discontinuous Galerkin finite element methods

KW - Nonconservative products

KW - slope limiter

KW - METIS-263715

KW - Multiphase Flows

U2 - 10.1016/j.cma.2008.10.019

DO - 10.1016/j.cma.2008.10.019

M3 - Article

SN - 0045-7825

VL - 198

SP - 819

EP - 830

JO - Computer methods in applied mechanics and engineering

JF - Computer methods in applied mechanics and engineering

IS - 5-8

M1 - 10.1016/j.cma.2008.10.019

ER -