A Comparison of the Explicit and Implicit Hybridizable Discontinuous Galerkin Methods for Nonlinear Shallow Water Equations

Samii, Ali; Kazhyken, Kazbek; Michoski, Craig; Dawson, Clint

doi:10.1007/s10915-019-01007-z

Cited by 14 publications

(17 citation statements)

References 52 publications

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“…For transient flows, the HDG method has been combined with a variety of low and high-order time integrators [52, 71-73, 77, 94]. Although less explored, there are also works where the HDG method has been employed with explicit time-marching algorithms [114,115].…”

Section: Introductionmentioning

confidence: 99%

Hybridisable Discontinuous Galerkin Formulation of Compressible Flows

Vila-Pérez

Giacomini

Sevilla

et al. 2020

Arch Computat Methods Eng

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Section: Introductionmentioning

confidence: 99%

Hybridisable Discontinuous Galerkin Formulation of Compressible Flows

Vila-Pérez

Giacomini

Sevilla

et al. 2020

Arch Computat Methods Eng

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“…A similar idea is presented in [169] to devise an implicit-explicit (IMEX) HDG-DG scheme in which the linear part of the problem is solved using a hybridised DG method and a singly diagonally implicit Runge-Kutta (SDIRK) scheme and the nonlinear one is approximated by means of an explicit Runge-Kutta (RK) DG discretisation. A detailed comparison of explicit and implicit approaches to the nonlinear shallow water equations is provided in [229].…”

Section: Shallow Water Equationsmentioning

confidence: 99%

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

Giacomini

Sevilla

Huerta

2020

Arch Computat Methods Eng

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This paper presents , an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation available in . Ultimately, this is expected to make this relatively new advanced discretisation method more accessible to the computational engineering community. presents some features not available in other implementations of the HDG method that can be found in the free domain. First, it implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions. Second, it supports curved isoparametric simplicial elements in two and three dimensions. Third, it supports non-uniform degree polynomial approximations and it provides a flexible structure to devise degree adaptivity strategies. Finally, an interface with the open-source high-order mesh generator is provided to facilitate its application to practical engineering problems.

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“…where F h = F (q h ) and S h = S(q h ), F * h is a single valued approximation to F h n over element faces, called the numerical flux, and n is the unit outward normal vector to element face. The present work uses the numerical flux from the hybridized discontinuous Galerkin method developed by Samii et al in [36]. Therefore, the numerical flux is defined through q h ∈ M p,d+1 h , an approximation to q over the mesh skeleton called the numerical trace, as in [36]…”

Section: Decoupled Modelmentioning

confidence: 99%

Discontinuous Galerkin methods for a dispersive wave hydro-morphodynamic model with bed-load transport

Kazhyken,

Videman,

Dawson

2020

Preprint

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A dispersive wave hydro-morphodynamic model coupling the Green-Naghdi equations (the hydrodynamic part) with the sediment continuity Exner equation (the morphodynamic part) is presented. Numerical solution algorithms based on discontinuous Galerkin finite element discretizations of the model are proposed. The algorithms include both coupled and decoupled approaches for solving the hydrodynamic and morphodynamic parts simultaneously and separately from each other, respectively. The Strang operator splitting technique is employed to treat the dispersive terms separately, and it provides the ability to ignore the dispersive terms in specified regions, such as surf zones. Algorithms that can handle wetting-drying and detect wave breaking are presented. The numerical methods are verified and validated with two numerical experiments:(1) a simulation of water waves in the vicinity of the Faro-Olhão inlet of the Ria Formosa lagoon in Portugal, (2) an experiment that measures the flow and bed morphology induced by a solitary wave over a sloping beach. The results indicate that the model has the potential to be used in studies of coastal morphodynamics driven by dispersive water waves, given that the hydrodynamic part resolves the water motion and dispersive wave effects with sufficient accuracy up to swash zones, and the morphodynamic model can capture the major features of bed erosion and deposition.

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A Comparison of the Explicit and Implicit Hybridizable Discontinuous Galerkin Methods for Nonlinear Shallow Water Equations

Cited by 14 publications

References 52 publications

Hybridisable Discontinuous Galerkin Formulation of Compressible Flows

Hybridisable Discontinuous Galerkin Formulation of Compressible Flows

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

Discontinuous Galerkin methods for a dispersive wave hydro-morphodynamic model with bed-load transport

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