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Non-Hydrostatic Discontinuous/Continuous Galerkin Model for Wave Propagation, Breaking and Runup

1
Centro de Investigaciones Hidráulicas e Hidrotécnicas, Universidad Tecnológica de Panamá, Panamá 0819-07289, Panama
2
DICATECh—Department. of Civil, Environmental, Land, Building Engineering and Chemistry, Polytechnic University of Bari, Via E. Orabona 4, 70125 Bari, Italy
3
Departamento de Recursos Hídricos e Meio Ambiente (DRHIMA), Federal University of Rio de Janeiro, Rio de Janeiro, RJ 21941-901, Brazil
*
Author to whom correspondence should be addressed.
Academic Editor: Sergey A. Karabasov
Computation 2021, 9(4), 47; https://doi.org/10.3390/computation9040047
Received: 15 March 2021 / Revised: 8 April 2021 / Accepted: 11 April 2021 / Published: 14 April 2021
(This article belongs to the Section Computational Engineering)
This paper presents a new depth-integrated non-hydrostatic finite element model for simulating wave propagation, breaking and runup using a combination of discontinuous and continuous Galerkin methods. The formulation decomposes the depth-integrated non-hydrostatic equations into hydrostatic and non-hydrostatic parts. The hydrostatic part is solved with a discontinuous Galerkin finite element method to allow the simulation of discontinuous flows, wave breaking and runup. The non-hydrostatic part led to a Poisson type equation, where the non-hydrostatic pressure is solved using a continuous Galerkin method to allow the modeling of wave propagation and transformation. The model uses linear quadrilateral finite elements for horizontal velocities, water surface elevations and non-hydrostatic pressures approximations. A new slope limiter for quadrilateral elements is developed. The model is verified and validated by a series of analytical solutions and laboratory experiments. View Full-Text
Keywords: depth-integrated; discontinuous galerkin finite element method; non-hydrostatic; wave breaking; wave propagation; wave runup depth-integrated; discontinuous galerkin finite element method; non-hydrostatic; wave breaking; wave propagation; wave runup
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MDPI and ACS Style

Calvo, L.; De Padova, D.; Mossa, M.; Rosman, P. Non-Hydrostatic Discontinuous/Continuous Galerkin Model for Wave Propagation, Breaking and Runup. Computation 2021, 9, 47. https://doi.org/10.3390/computation9040047

AMA Style

Calvo L, De Padova D, Mossa M, Rosman P. Non-Hydrostatic Discontinuous/Continuous Galerkin Model for Wave Propagation, Breaking and Runup. Computation. 2021; 9(4):47. https://doi.org/10.3390/computation9040047

Chicago/Turabian Style

Calvo, Lucas, Diana De Padova, Michele Mossa, and Paulo Rosman. 2021. "Non-Hydrostatic Discontinuous/Continuous Galerkin Model for Wave Propagation, Breaking and Runup" Computation 9, no. 4: 47. https://doi.org/10.3390/computation9040047

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