An implicit discontinuous Galerkin finite element model for water waves

J.J.W. van der Vegt; S.K. Tomar

An implicit discontinuous Galerkin finite element model for water waves

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

An overview is given of a discontinuous Galerkin finite element method for linear free surface water waves. The method uses an implicit time integration method which is unconditionally stable and does not suffer from the frequently encountered mesh dependent saw-tooth type instability at the free surface. The numerical discretization has minimal dissipation and small dispersion errors in the wave propagation. The algorithm is second order accurate in time and has an optimal rate of convergence O(hp+1) in the L2- norm, both in the potential and wave height, with p the polynomial order and h the mesh size. The numerical discretization is demonstrated with the simulation of water waves in a basin with a bump at the bottom.

Original language	English
Title of host publication	Computational Mechanics
Subtitle of host publication	Proceedings of the Sixth World Congress on Computational Mechanics in conjunction with the Second Asian-Pacific Congress on Computational Mechanics, September 5-10, 2004, Beijing, China
Editors	Z.H. Yao, M.W. Yuan, W.X. Zhong
Place of Publication	Beijing
Publisher	Tsinghua University Press
Pages	690-695
Number of pages	6
ISBN (Print)	9787302093435
Publication status	Published - 5 Sep 2004
Event	6th World Congress on Computational Mechanics, WCCM 2004 - Beijing, China Duration: 5 Sep 2004 → 10 Sep 2004 Conference number: 6

Conference

Conference	6th World Congress on Computational Mechanics, WCCM 2004
Abbreviated title	WCCM VI
Country	China
City	Beijing
Period	5/09/04 → 10/09/04

Keywords

Discontinuous Galerkin method
Water waves
Elliptic partial differential equations

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van der Vegt, J. J. W., & Tomar, S. K. (2004). An implicit discontinuous Galerkin finite element model for water waves. In Z. H. Yao, M. W. Yuan, & W. X. Zhong (Eds.), Computational Mechanics: Proceedings of the Sixth World Congress on Computational Mechanics in conjunction with the Second Asian-Pacific Congress on Computational Mechanics, September 5-10, 2004, Beijing, China (pp. 690-695). Tsinghua University Press.

van der Vegt, J.J.W. ; Tomar, S.K. / An implicit discontinuous Galerkin finite element model for water waves. Computational Mechanics: Proceedings of the Sixth World Congress on Computational Mechanics in conjunction with the Second Asian-Pacific Congress on Computational Mechanics, September 5-10, 2004, Beijing, China. editor / Z.H. Yao ; M.W. Yuan ; W.X. Zhong. Beijing : Tsinghua University Press, 2004. pp. 690-695

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abstract = "An overview is given of a discontinuous Galerkin finite element method for linear free surface water waves. The method uses an implicit time integration method which is unconditionally stable and does not suffer from the frequently encountered mesh dependent saw-tooth type instability at the free surface. The numerical discretization has minimal dissipation and small dispersion errors in the wave propagation. The algorithm is second order accurate in time and has an optimal rate of convergence O(hp+1) in the L2- norm, both in the potential and wave height, with p the polynomial order and h the mesh size. The numerical discretization is demonstrated with the simulation of water waves in a basin with a bump at the bottom.",

keywords = "Discontinuous Galerkin method, Water waves, Elliptic partial differential equations",

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van der Vegt, JJW & Tomar, SK 2004, An implicit discontinuous Galerkin finite element model for water waves. in ZH Yao, MW Yuan & WX Zhong (eds), Computational Mechanics: Proceedings of the Sixth World Congress on Computational Mechanics in conjunction with the Second Asian-Pacific Congress on Computational Mechanics, September 5-10, 2004, Beijing, China. Tsinghua University Press, Beijing, pp. 690-695, 6th World Congress on Computational Mechanics, WCCM 2004, Beijing, China, 5/09/04.

An implicit discontinuous Galerkin finite element model for water waves. / van der Vegt, J.J.W.; Tomar, S.K.

Computational Mechanics: Proceedings of the Sixth World Congress on Computational Mechanics in conjunction with the Second Asian-Pacific Congress on Computational Mechanics, September 5-10, 2004, Beijing, China. ed. / Z.H. Yao; M.W. Yuan; W.X. Zhong. Beijing : Tsinghua University Press, 2004. p. 690-695.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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T1 - An implicit discontinuous Galerkin finite element model for water waves

AU - van der Vegt, J.J.W.

AU - Tomar, S.K.

N1 - Conference code: 6

PY - 2004/9/5

Y1 - 2004/9/5

N2 - An overview is given of a discontinuous Galerkin finite element method for linear free surface water waves. The method uses an implicit time integration method which is unconditionally stable and does not suffer from the frequently encountered mesh dependent saw-tooth type instability at the free surface. The numerical discretization has minimal dissipation and small dispersion errors in the wave propagation. The algorithm is second order accurate in time and has an optimal rate of convergence O(hp+1) in the L2- norm, both in the potential and wave height, with p the polynomial order and h the mesh size. The numerical discretization is demonstrated with the simulation of water waves in a basin with a bump at the bottom.

AB - An overview is given of a discontinuous Galerkin finite element method for linear free surface water waves. The method uses an implicit time integration method which is unconditionally stable and does not suffer from the frequently encountered mesh dependent saw-tooth type instability at the free surface. The numerical discretization has minimal dissipation and small dispersion errors in the wave propagation. The algorithm is second order accurate in time and has an optimal rate of convergence O(hp+1) in the L2- norm, both in the potential and wave height, with p the polynomial order and h the mesh size. The numerical discretization is demonstrated with the simulation of water waves in a basin with a bump at the bottom.

KW - Discontinuous Galerkin method

KW - Water waves

KW - Elliptic partial differential equations

M3 - Conference contribution

SN - 9787302093435

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EP - 695

BT - Computational Mechanics

A2 - Yao, Z.H.

A2 - Yuan, M.W.

A2 - Zhong, W.X.

PB - Tsinghua University Press

CY - Beijing

T2 - 6th World Congress on Computational Mechanics, WCCM 2004

Y2 - 5 September 2004 through 10 September 2004

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van der Vegt JJW, Tomar SK. An implicit discontinuous Galerkin finite element model for water waves. In Yao ZH, Yuan MW, Zhong WX, editors, Computational Mechanics: Proceedings of the Sixth World Congress on Computational Mechanics in conjunction with the Second Asian-Pacific Congress on Computational Mechanics, September 5-10, 2004, Beijing, China. Beijing: Tsinghua University Press. 2004. p. 690-695