Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part II. Efficient flux quadrature

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Abstract

A new and efficient quadrature rule for the flux integrals arising in the space-time discontinuous Galerkin discretization of the Euler equations in a moving and deforming space-time domain is presented and analyzed. The quadrature rule is a factor three more efficient than the commonly applied quadrature rule and does not affect the local truncation error and stability of the numerical scheme. The local truncation error of the resulting numerical discretization is determined and is shown to be the same as when product Gauss quadrature rules are used. Details of the approximation of the dissipation in the numerical flux are presented, which render the scheme consistent and stable. The method is succesfully applied to the simulation of a three-dimensional, transonic flow over a deforming wing.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages46
ISBN (Print)0169-2960
Publication statusPublished - 2001

Publication series

NameMemoranda
PublisherDepartment of Applied Mathematics, University of Twente
No.1600
ISSN (Print)0169-2690

Keywords

  • MSC-76N15
  • IR-65787
  • MSC-65P25
  • EWI-3420
  • METIS-201430

Cite this

van der Ven, H. ; van der Vegt, Jacobus J.W. / Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part II. Efficient flux quadrature. Enschede : University of Twente, Department of Applied Mathematics, 2001. 46 p. (Memoranda; 1600).
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abstract = "A new and efficient quadrature rule for the flux integrals arising in the space-time discontinuous Galerkin discretization of the Euler equations in a moving and deforming space-time domain is presented and analyzed. The quadrature rule is a factor three more efficient than the commonly applied quadrature rule and does not affect the local truncation error and stability of the numerical scheme. The local truncation error of the resulting numerical discretization is determined and is shown to be the same as when product Gauss quadrature rules are used. Details of the approximation of the dissipation in the numerical flux are presented, which render the scheme consistent and stable. The method is succesfully applied to the simulation of a three-dimensional, transonic flow over a deforming wing.",
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author = "{van der Ven}, H. and {van der Vegt}, {Jacobus J.W.}",
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Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part II. Efficient flux quadrature. / van der Ven, H.; van der Vegt, Jacobus J.W.

Enschede : University of Twente, Department of Applied Mathematics, 2001. 46 p. (Memoranda; No. 1600).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part II. Efficient flux quadrature

AU - van der Ven, H.

AU - van der Vegt, Jacobus J.W.

N1 - Imported from MEMORANDA

PY - 2001

Y1 - 2001

N2 - A new and efficient quadrature rule for the flux integrals arising in the space-time discontinuous Galerkin discretization of the Euler equations in a moving and deforming space-time domain is presented and analyzed. The quadrature rule is a factor three more efficient than the commonly applied quadrature rule and does not affect the local truncation error and stability of the numerical scheme. The local truncation error of the resulting numerical discretization is determined and is shown to be the same as when product Gauss quadrature rules are used. Details of the approximation of the dissipation in the numerical flux are presented, which render the scheme consistent and stable. The method is succesfully applied to the simulation of a three-dimensional, transonic flow over a deforming wing.

AB - A new and efficient quadrature rule for the flux integrals arising in the space-time discontinuous Galerkin discretization of the Euler equations in a moving and deforming space-time domain is presented and analyzed. The quadrature rule is a factor three more efficient than the commonly applied quadrature rule and does not affect the local truncation error and stability of the numerical scheme. The local truncation error of the resulting numerical discretization is determined and is shown to be the same as when product Gauss quadrature rules are used. Details of the approximation of the dissipation in the numerical flux are presented, which render the scheme consistent and stable. The method is succesfully applied to the simulation of a three-dimensional, transonic flow over a deforming wing.

KW - MSC-76N15

KW - IR-65787

KW - MSC-65P25

KW - EWI-3420

KW - METIS-201430

M3 - Report

SN - 0169-2960

T3 - Memoranda

BT - Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part II. Efficient flux quadrature

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

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van der Ven H, van der Vegt JJW. Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part II. Efficient flux quadrature. Enschede: University of Twente, Department of Applied Mathematics, 2001. 46 p. (Memoranda; 1600).