An efficient Eulerian finite element method for the shallow water equations

Hanert, Emmanuel; Roux, Daniel Y. Le; Legat, Vincent; Deleersnijder, Éric

doi:10.1016/j.ocemod.2004.06.006

Cited by 101 publications

(56 citation statements)

References 35 publications

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“…In the final numerical test, we solve the equatorial Rossby soliton analytically studied by Boyd [5], and used to validate numerical models in [12,17] among others. The rotational effect of the Earth is included through the Coriolis force.…”

Section: Solitary Rossby Wavementioning

confidence: 99%

A multi-moment finite volume formulation for shallow water equations on unstructured mesh

Akoh

Satoshi

Xiao

2010

Journal of Computational Physics

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Section: Solitary Rossby Wavementioning

confidence: 99%

A multi-moment finite volume formulation for shallow water equations on unstructured mesh

Akoh

Satoshi

Xiao

2010

Journal of Computational Physics

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“…More recent mathematical and numerical analysis of finite element pairs for gravity and Rossby waves are provided in Le Roux et al (2007, , and . Hanert et al (2005) proposed to use the P NC 1 -P 1 pair, following Hua and Thomasset (1984). It appears that the P NC 1 -P 1 pair is a stable discretization, but its rate of convergence is suboptimal on unstructured grids (Bernard et al 2008b).…”

Section: Introductionmentioning

confidence: 99%

A discontinuous finite element baroclinic marine model on unstructured prismatic meshes

et al. 2010

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We describe the space discretization of a three-dimensional baroclinic finite element model, based upon a discontinuous Galerkin method, while the companion paper (Comblen et al. 2010a) describes the discretization in time. We solve the hy- drostatic Boussinesq equations governing marine flows on a mesh made up of triangles extruded from the surface toward the seabed to obtain prismatic threedimensional elements. Diffusion is implemented using the symmetric interior penalty method. The tracer equation is consistent with the continuity equation. A Lax-Friedrichs flux is used to take into account internal wave propagation. By way of illustration, a flow exhibiting internal waves in the lee of an isolated seamount on the sphere is simulated. This enables us to show the advantages of using an unstructured mesh, where the resolution is higher in areas where the flow varies rapidly in space, the mesh being coarser far from the region of interest. The solution exhibits the expected wave structure. Linear and quadratic shape functions are used, and the extension to higher-order discretization is straightforward.

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“…Earlier experiments with P NC 1 − P 1 code revealed problems with spatial noise and instability of the momentum advection when the discretisation is used as described by Hanert et al (2005). A modified implementation without upwinding terms was found to work well when paired with rather high viscous dissipation to remove small-scale noise in the velocity field.…”

Section: Momentum Advection Schemementioning

confidence: 93%

“…The main reason to choose finite elements is the computational mesh that can be adapted to cover basins with irregular bottom topography and coastlines. The spatial discretisation of TsunAWI is based on the finite element approach by Hanert et al (2005) with modifications like added viscous and bottom friction terms, corrected momentum advection terms, radiation boundary condition, and nodal lumping of mass matrix in the continuity equation. The basic principles of discretisation follow Hanert et al (2005) with linear conforming elements P 1 for sea surface height ζ and water depth h, and linear non-conforming elements P NC 1 for the velocity v. Thus, values for sea surface are computed at element nodes, while the velocity components are regarded at the edges.…”

Section: Finite Element Methodsmentioning

confidence: 99%

Operational tsunami modelling with TsunAWI – recent developments and applications

Rakowsky

Androsov

Fuchs

et al. 2013

Nat. Hazards Earth Syst. Sci.

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In this article, the tsunami model TsunAWI (Alfred Wegener Institute) and its application for hindcasts, inundation studies, and the operation of the tsunami scenario repository for the Indonesian tsunami early warning system are presented. TsunAWI was developed in the framework of the German-Indonesian Tsunami Early Warning System (GITEWS) and simulates all stages of a tsunami from the origin and the propagation in the ocean to the arrival at the coast and the inundation on land. It solves the non-linear shallow water equations on an unstructured finite element grid that allows to change the resolution seamlessly between a coarse grid in the deep ocean and a fine representation of coastal structures. During the GITEWS project and the following maintenance phase, TsunAWI and a framework of pre- and postprocessing routines was developed step by step to provide fast computation of enhanced model physics and to deliver high quality results

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An efficient Eulerian finite element method for the shallow water equations

Cited by 101 publications

References 35 publications

A multi-moment finite volume formulation for shallow water equations on unstructured mesh

A multi-moment finite volume formulation for shallow water equations on unstructured mesh

A discontinuous finite element baroclinic marine model on unstructured prismatic meshes

Operational tsunami modelling with TsunAWI – recent developments and applications

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