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2D–3D hybrid stabilized finite element method for tsunami runup simulations

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Abstract

This paper presents a two-dimensional (2D)–three-dimensional (3D) hybrid stabilized finite element method that enables us to predict a propagation process of tsunami generated in a hypocentral region, which ranges from offshore propagation to runup to urban areas, with high accuracy and relatively low computational costs. To be more specific, the 2D shallow water equation is employed to simulate the propagation of offshore waves, while the 3D Navier–Stokes equation is employed for the runup in urban areas. The stabilized finite element method is utilized for numerical simulations for both of the 2D and 3D domains that are independently discretized with unstructured meshes. The multi-point constraint and transmission methods are applied to satisfy the continuity of flow velocities and pressures at the interface between the resulting 2D and 3D meshes, since neither their spatial dimensions nor node arrangements are consistent. Numerical examples are presented to demonstrate the performance of the proposed hybrid method to simulate tsunami behavior, including offshore propagation and runup to urban areas, with substantially lower computation costs in comparison with full 3D computations.

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Acknowledgments

This study is conducted with support from the Grants-in-Aid for Scientific Research (A) (Research Project No.: 25246043) “Multi-scale Numerical Experiments for Evaluation of Interaction between Runup Tsunami and Structures”. We are grateful for the support.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Tohoku University, Aza-Aoba 6-6, Aramaki, Aoba-ku, Sendai, 980-0845, Japan

    S. Takase, J. Kato, T. Kyoya & T. Kotani

  2. International Research Institute of Disaster Science, Tohoku University, Aza-Aoba 468-1, Aramaki, Aoba-ku, Sendai, 980-0845, Japan

    S. Moriguchi & K. Terada

  3. Department of Civil and Environmental Engineering, Chuo University, Kasuga 1-13-27, Bunkyou-ku, Tokyo, 112-8521, Japan

    K. Kashiyama

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  1. S. Takase
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  2. S. Moriguchi
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  3. K. Terada
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  4. J. Kato
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  5. T. Kyoya
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  6. K. Kashiyama
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  7. T. Kotani
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Correspondence to S. Takase.

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Takase, S., Moriguchi, S., Terada, K. et al. 2D–3D hybrid stabilized finite element method for tsunami runup simulations. Comput Mech 58, 411–422 (2016). https://doi.org/10.1007/s00466-016-1300-4

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  • DOI: https://doi.org/10.1007/s00466-016-1300-4

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