Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation

Allan Peter Engsig-Karup; Claes Eskilsson; Daniele Bigoni

Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation

Allan Peter Engsig-Karup, Claes Eskilsson, Daniele Bigoni

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Abstract

We introduce a new stabilized high-order and unstructured numerical model for modeling fully nonlinear and dispersive water waves. The model is based on a nodal spectral element method of arbitrary order in space and a -transformed formulation due to Cai, Langtangen, Nielsen and Tveito (1998). In the present paper we use a single layer of quadratic (in 2D) and prismatic (in 3D) elements. The model has been stabilized through a combination of over-integration of the Galerkin projections and a mild modal filter. We present numerical tests of nonlinear waves serving as a proof-of-concept validation for this new high-order model. The model is shown to exhibit exponential convergence even for very steep waves and there is a good agreement to analytic and experimental data.

Original language	English
Title of host publication	Proceedings of the 26th International Ocean and Polar Engineering Conference (ISOPE 2016)
Editors	Jin S. Chung, Michael Muskulus, Ted Kokkinis, Alan M. Wang
Publisher	International Society of Offshore & Polar Engineers
Publication date	2016
Pages	661-668
Article number	ISOPE-I-16-455
ISBN (Print)	978-1-880653-88-3
Publication status	Published - 2016
Event	26th International Ocean and Polar Engineering Conference (ISOPE 2016) - Rhodes, Greece Duration: 26 Jun 2016 → 2 Jul 2016 Conference number: 26

Conference

Conference	26th International Ocean and Polar Engineering Conference (ISOPE 2016)
Number	26
Country/Territory	Greece
City	Rhodes
Period	26/06/2016 → 02/07/2016

Series	Proceedings of the International Offshore and Polar Engineering Conference
ISSN	1098-6189

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Engsig-Karup, A. P., Eskilsson, C., & Bigoni, D. (2016). Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation. In J. S. Chung, M. Muskulus, T. Kokkinis, & A. M. Wang (Eds.), Proceedings of the 26th International Ocean and Polar Engineering Conference (ISOPE 2016) (pp. 661-668). Article ISOPE-I-16-455 International Society of Offshore & Polar Engineers.

Engsig-Karup, Allan Peter ; Eskilsson, Claes ; Bigoni, Daniele. / Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation. Proceedings of the 26th International Ocean and Polar Engineering Conference (ISOPE 2016). editor / Jin S. Chung ; Michael Muskulus ; Ted Kokkinis ; Alan M. Wang. International Society of Offshore & Polar Engineers, 2016. pp. 661-668 (Proceedings of the International Offshore and Polar Engineering Conference).

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title = "Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation",

abstract = "We introduce a new stabilized high-order and unstructured numerical model for modeling fully nonlinear and dispersive water waves. The model is based on a nodal spectral element method of arbitrary order in space and a -transformed formulation due to Cai, Langtangen, Nielsen and Tveito (1998). In the present paper we use a single layer of quadratic (in 2D) and prismatic (in 3D) elements. The model has been stabilized through a combination of over-integration of the Galerkin projections and a mild modal filter. We present numerical tests of nonlinear waves serving as a proof-of-concept validation for this new high-order model. The model is shown to exhibit exponential convergence even for very steep waves and there is a good agreement to analytic and experimental data.",

author = "Engsig-Karup, \{Allan Peter\} and Claes Eskilsson and Daniele Bigoni",

year = "2016",

language = "English",

isbn = "978-1-880653-88-3",

series = "Proceedings of the International Offshore and Polar Engineering Conference",

publisher = "International Society of Offshore \& Polar Engineers",

pages = "661--668",

editor = "Chung, \{Jin S. \} and Muskulus, \{Michael \} and Kokkinis, \{Ted \} and Wang, \{Alan M. \}",

booktitle = "Proceedings of the 26th International Ocean and Polar Engineering Conference (ISOPE 2016)",

note = "26th International Ocean and Polar Engineering Conference (ISOPE 2016) ; Conference date: 26-06-2016 Through 02-07-2016",

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Engsig-Karup, AP, Eskilsson, C & Bigoni, D 2016, Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation. in JS Chung, M Muskulus, T Kokkinis & AM Wang (eds), Proceedings of the 26th International Ocean and Polar Engineering Conference (ISOPE 2016)., ISOPE-I-16-455, International Society of Offshore & Polar Engineers, Proceedings of the International Offshore and Polar Engineering Conference, pp. 661-668, 26th International Ocean and Polar Engineering Conference (ISOPE 2016), Rhodes, Greece, 26/06/2016.

Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation. / Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele.
Proceedings of the 26th International Ocean and Polar Engineering Conference (ISOPE 2016). ed. / Jin S. Chung; Michael Muskulus; Ted Kokkinis; Alan M. Wang. International Society of Offshore & Polar Engineers, 2016. p. 661-668 ISOPE-I-16-455 (Proceedings of the International Offshore and Polar Engineering Conference).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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T1 - Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation

AU - Engsig-Karup, Allan Peter

AU - Eskilsson, Claes

AU - Bigoni, Daniele

N1 - Conference code: 26

PY - 2016

Y1 - 2016

N2 - We introduce a new stabilized high-order and unstructured numerical model for modeling fully nonlinear and dispersive water waves. The model is based on a nodal spectral element method of arbitrary order in space and a -transformed formulation due to Cai, Langtangen, Nielsen and Tveito (1998). In the present paper we use a single layer of quadratic (in 2D) and prismatic (in 3D) elements. The model has been stabilized through a combination of over-integration of the Galerkin projections and a mild modal filter. We present numerical tests of nonlinear waves serving as a proof-of-concept validation for this new high-order model. The model is shown to exhibit exponential convergence even for very steep waves and there is a good agreement to analytic and experimental data.

AB - We introduce a new stabilized high-order and unstructured numerical model for modeling fully nonlinear and dispersive water waves. The model is based on a nodal spectral element method of arbitrary order in space and a -transformed formulation due to Cai, Langtangen, Nielsen and Tveito (1998). In the present paper we use a single layer of quadratic (in 2D) and prismatic (in 3D) elements. The model has been stabilized through a combination of over-integration of the Galerkin projections and a mild modal filter. We present numerical tests of nonlinear waves serving as a proof-of-concept validation for this new high-order model. The model is shown to exhibit exponential convergence even for very steep waves and there is a good agreement to analytic and experimental data.

M3 - Article in proceedings

SN - 978-1-880653-88-3

T3 - Proceedings of the International Offshore and Polar Engineering Conference

SP - 661

EP - 668

BT - Proceedings of the 26th International Ocean and Polar Engineering Conference (ISOPE 2016)

A2 - Chung, Jin S.

A2 - Muskulus, Michael

A2 - Kokkinis, Ted

A2 - Wang, Alan M.

PB - International Society of Offshore & Polar Engineers

T2 - 26th International Ocean and Polar Engineering Conference (ISOPE 2016)

Y2 - 26 June 2016 through 2 July 2016

ER -

Engsig-Karup AP, Eskilsson C, Bigoni D. Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation. In Chung JS, Muskulus M, Kokkinis T, Wang AM, editors, Proceedings of the 26th International Ocean and Polar Engineering Conference (ISOPE 2016). International Society of Offshore & Polar Engineers. 2016. p. 661-668. ISOPE-I-16-455. (Proceedings of the International Offshore and Polar Engineering Conference).

Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation

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