A Nonhydrostatic Finite-Element Model for Three-Dimensional Stratified Oceanic Flows. Part I: Model Formulation

Ford, Rupert; Pain, Christopher C.; Piggott, Matthew D.; Goddard, A.J.H.; Oliveira, C.R.E. de; Umpleby, A.

doi:10.1175/mwr2824.1

Cited by 82 publications

(68 citation statements)

References 42 publications

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“…The FE method provides an easy conservation of energy and a natural treatment of geometric boundaries (Danilov et al, 2004;Wang et al, 2008a;Timmermann et al, 2009). There have been only a few FE ocean general circulation models developed so far that employ the capability of unstructured meshes (Danilov et al, 2004;Ford et al, 2004;White et al, 2008a). In this paper we use the Finite-Element Sea-Ice Ocean Model (FESOM) (Danilov et al, 2004(Danilov et al, , 2005Wang et al, 2008b;Timmermann et al, 2009), which is an ocean general circulation model coupled to a dynamic thermodynamic sea-ice model.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of a Finite-Element Sea-Ice Ocean Model (FESOM) set-up to study the interannual to decadal variability in the deep-water formation rates

et al. 2013

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The characteristics of a global setup of the Finite-Element Sea-Ice Ocean Model (FESOM) under forcing of the period 1958-2004 are presented. The model setup is designed to study the variability in the deep-water mass formation areas and was therefore regionally better resolved in the deep-water formation areas in the Labrador Sea, Greenland Sea, Weddell Sea and Ross Sea. The sea-ice model reproduces realistic sea-ice distributions and variabilities in the sea ice extent of both hemispheres as well as sea ice transport that compares well with observational data. Based on a comparison between model and Ocean Weather Ship data in the North Atlantic, we observe that the vertical structure is well captured in areas with a high resolution. In our model setup we are able to simulate decadal ocean variability including several salinity anomaly events and corresponding fingerprint in the vertical hydrography. The ocean state of the model setup features pronounced variability in the Atlantic Meridional Overturning Circulation (AMOC) as well as the associated mixed layer depth pattern in the North Atlantic deep-water formation areas.

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Section: Introductionmentioning

confidence: 99%

Evaluation of a Finite-Element Sea-Ice Ocean Model (FESOM) set-up to study the interannual to decadal variability in the deep-water formation rates

et al. 2013

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“…Nonhydrostatic finite element methods are found in Labeur and Wells (2009) for small-scale problems. For large-scale ocean modeling, continuous finite element methods are used in FEOM (Finite Element Ocean Model) (Wang et al 2008a, b;Timmermann et al 2009), and Imperial College Ocean Model (Ford et al 2004a) relies on mesh adaptivity to capture the multiscale aspects of the flow (Piggott et al 2008).…”

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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“…Weak Dirichlet boundary conditions, corresponding to (16), are applied to the viscous term. The equations are discretised in time using the pressure projection method described in Ford et al [54], consisting of a Crank-Nicolson discretisation (implicit midpoint rule) with the non-linear system approximately solved to second order accuracy in time via two Picard iterations. The pressure projection equations are solved with UMFPACK [55] via PETSc [56], and the velocity equations solved via PETSc with Bi-CGSTAB [57] preconditioned with incomplete LU factorisation.…”

Section: Incompressible Navier-stokesmentioning

confidence: 99%

“…The P 1 DG − P 2 velocity-pressure element pair has the important property that the discrete Laplacian matrix formed in the pressure projection step (the −C T M −1 C matrix in the notation of Ford et al [54]) is identical to the discrete Laplacian formed by multiplying the Laplacian operator by a P 2 test function and integrating by parts [58]. The former construction requires the separate assembly of divergence and mass matrices, and then the application of linear algebra operations.…”

Section: Incompressible Navier-stokesmentioning

confidence: 99%

Rapid development and adjoining of transient finite element models

Maddison

Farrell

2014

Computer Methods in Applied Mechanics and Engineering

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Recent advances in high level finite element systems have allowed for the symbolic representation of discretisations and their efficient automated implementation as model source code. This allows for the extremely compact implementation of complex non-linear models in a handful of lines of high level code. In this work we extend the high level finite element FEniCS system to introduce an abstract representation of the temporal discretisation: this enables the similarly rapid development of transient finite element models. Efficiency is achieved via aggressive optimisations that exploit the temporal structure, such as automated pre-assembly and caching of forms, and the robust re-use of matrix factorisations and preconditioner data. The resulting models are as fast or faster than hand-optimised finite element codes. The high level representation of the system remains extremely compact and easily manipulated. This structure is exploited to derive the associated discrete adjoint model automatically, with the adjoint model inheriting the performance advantages of the forward model. Combined, this provides a system for the rapid development of efficient transient models, together with their discrete adjoints.

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A Nonhydrostatic Finite-Element Model for Three-Dimensional Stratified Oceanic Flows. Part I: Model Formulation

Cited by 82 publications

References 42 publications

Evaluation of a Finite-Element Sea-Ice Ocean Model (FESOM) set-up to study the interannual to decadal variability in the deep-water formation rates

Evaluation of a Finite-Element Sea-Ice Ocean Model (FESOM) set-up to study the interannual to decadal variability in the deep-water formation rates

A discontinuous finite element baroclinic marine model on unstructured prismatic meshes

Rapid development and adjoining of transient finite element models

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