hp Discontinuous Galerkin methods for advection dominated problems in shallow water flow

Kubatko, Ethan J.; Westerink, Joannes J.; Dawson, Clint

doi:10.1016/j.cma.2006.05.002

Cited by 132 publications

(95 citation statements)

References 29 publications

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“…Finally, the mass matrix is block diagonal, and for explicit computations, no linear solver is needed. We also observe a growing interest for the discontinuous Galerkin methods in coastal and estuarine modeling (Aizinger and Dawson 2002;Dawson and Aizinger 2005;Kubatko et al 2006;Aizinger and Dawson 2007;Bernard et al 2008a;Blaise et al 2010). For atmosphere modeling, the high-order capabilities of this scheme are really attractive (Nair et al 2005;Giraldo 2006), and the increasing use of DG follows the trend to replace spectral transform methods with local ones.…”

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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Section: Introductionmentioning

confidence: 99%

A discontinuous finite element baroclinic marine model on unstructured prismatic meshes

et al. 2010

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“…To simulate tidal flows in the Pentland Firth, we solve the shallow water equations using the discontinuous Galerkin (DG) version of ADCIRC [11,12]. This numerical scheme has been previously verified and validated for various applications such as modelling tidal flows and storm surges [13].…”

Section: Numerical Model (A) Numerical Schemementioning

confidence: 99%

The available power from tidal stream turbines in the Pentland Firth

et al. 2013

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This paper assesses an upper bound for the tidal stream power resource of the Pentland Firth. A depth-averaged numerical model of the tidal dynamics in the region is set-up and validated against field measurements. Actuator disc theory is used to model the effect of turbines on the flow, and to estimate the power available for generation after accounting for losses owing to mixing downstream of the turbines. It is found that three rows of turbines extending across the entire width of the Pentland Firth and blocking a large fraction of the channel can theoretically generate 1.9 GW, averaged over the spring–neap cycle. However, generation of significantly more power than this is unlikely to be feasible as the available power per additional swept area of turbine is too small to be viable. Our results differ from those obtained using simplified tidal channel models of the type used commonly in the literature. We also use our numerical model to investigate the available power from rows of turbines placed across various subchannels within the Pentland Firth, together with practical considerations such as the variation in power over the spring–neap tidal cycle and the changes to natural tidal flows which result from power extraction.

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“…It has been only very recent (since 2000) that the DG method first appeared in geophysical fluid dynamics (GFD) applications. However, implementations of the DG method in GFD have remained primarily restricted to shallow water flow (see [44,35,2,20,10,12,37,40,34,23,24]). To date, there has been no published work on either SE or DG methods for nonhydrostatic mesoscale atmospheric applications.…”

Section: Introductionmentioning

confidence: 99%

A study of spectral element and discontinuous Galerkin methods for the Navier–Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases

Giraldo

Restelli

2008

Journal of Computational Physics

222

333

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hp Discontinuous Galerkin methods for advection dominated problems in shallow water flow

Cited by 132 publications

References 29 publications

A discontinuous finite element baroclinic marine model on unstructured prismatic meshes

A discontinuous finite element baroclinic marine model on unstructured prismatic meshes

The available power from tidal stream turbines in the Pentland Firth

A study of spectral element and discontinuous Galerkin methods for the Navier–Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases

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