Multirate time stepping for accelerating explicit discontinuous Galerkin computations with application to geophysical flows

Seny, Bruno; Lambrechts, Jonathan; Comblen, Richard; Legat, Vincent; Remacle, Jean‐François

doi:10.1002/fld.3646

Cited by 44 publications

(33 citation statements)

References 44 publications

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“…To benefit from the multi-resolution capability even in cases when only a very small portion of the computational grid points have locally increased resolutions, multirate time stepping schemes are needed. Seny et al (2013) gave an example of such schemes applied in a discontinuous Galerkin model.…”

Section: Two-dimensional Meshmentioning

confidence: 99%

The Finite Element Sea Ice-Ocean Model (FESOM) v.1.4: formulation of an ocean general circulation model

et al. 2014

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Abstract. The Finite Element Sea Ice-Ocean Model (FE-SOM) is the first global ocean general circulation model based on unstructured-mesh methods that has been developed for the purpose of climate research. The advantage of unstructured-mesh models is their flexible multi-resolution modelling functionality. In this study, an overview of the main features of FESOM will be given; based on sensitivity experiments a number of specific parameter choices will be explained; and directions of future developments will be outlined. It is argued that FESOM is sufficiently mature to explore the benefits of multi-resolution climate modelling and that its applications will provide information useful for the advancement of climate modelling on unstructured meshes.

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Section: Two-dimensional Meshmentioning

confidence: 99%

The Finite Element Sea Ice-Ocean Model (FESOM) v.1.4: formulation of an ocean general circulation model

et al. 2014

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“…The latter is well suited for advectiondominated problems (Bassi and Rebay, 1997;Cockburn et al, 2000;Bernard et al, 2007) exhibiting strong gradients of the solution. Furthermore, it has different advantages, such as local and global conservativity, or the compactness of the stencil, which enables an easy and efficient parallel implementation (Seny et al, 2013(Seny et al, , 2014. The inter-element discontinuities of the solution constitute a good estimate of the discretisation error (Ainsworth, 2004;Bernard et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4 with an application to the thermocline oscillations of Lake Tanganyika

et al. 2018

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Abstract. The discontinuous Galerkin (DG) finite element method is well suited for the modelling, with a relatively small number of elements, of three-dimensional flows exhibiting strong velocity or density gradients. Its performance can be highly enhanced by having recourse to r-adaptivity. Here, a vertical adaptive mesh method is developed for DG finite elements. This method, originally designed for finite difference schemes, is based on the vertical diffusion of the mesh nodes, with the diffusivity controlled by the density jumps at the mesh element interfaces.The mesh vertical movement is determined by means of a conservative arbitrary Lagrangian-Eulerian (ALE) formulation. Though conservativity is naturally achieved, tracer consistency is obtained by a suitable construction of the mesh vertical velocity field, which is defined in such a way that it is fully compatible with the tracer and continuity equations at a discrete level.The vertically adaptive mesh approach is implemented in the three-dimensional version of the geophysical and environmental flow Second-generation Louvain-la-Neuve Iceocean Model (SLIM 3D; www.climate.be/slim). Idealised benchmarks, aimed at simulating the oscillations of a sharp thermocline, are dealt with. Then, the relevance of the vertical adaptivity technique is assessed by simulating thermocline oscillations of Lake Tanganyika. The results are compared to measured vertical profiles of temperature, showing similar stratification and outcropping events.

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“…Furthermore, it has different advantages, such as local and global conservativity, or the compactness of the stencil, which enables an easy and efficient parallel implementation (Seny et al, 2013(Seny et al, , 2014. The inter-element discontinuities of the solution constitute a good estimate of the discretisation error (Ainsworth, 2004;Bernard et al, 2007).…”

mentioning

confidence: 99%

A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4, a DG finite element hydrodynamic model, with an application to the thermocline oscillations of Lake Tanganyika

Delandmeter¹,

Lambrechts²,

Legat³

et al. 2017

Preprint

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Abstract. The discontinuous Galerkin (DG) finite element method is well suited to the modelling, with a relatively small number of elements, of three-dimensional flows exhibiting strong velocity or density gradients. Its performance can be highly enhanced by having recourse to r-adaptivity. Here, a vertical adaptive mesh method is developed for DG finite elements. This method, originally designed for finite difference schemes, is based on the vertical diffusion of the mesh nodes, with the diffusivity controlled by the density jumps at the mesh element interfaces. 5The mesh vertical movement is determined by means of a conservative Arbitrary Lagrangian-Eulerian (ALE) formulation.Though conservativity is naturally achieved, tracer consistency is obtained by a suitable construction of the mesh vertical velocity field, which is defined in such a way that it is fully compatible with the tracer and continuity equations at a discrete level.The vertically adaptive mesh approach is implemented in the geophysical and environmental flow model SLIM 3D (www. 10climate.be/slim). Idealised benchmarks, aimed at simulating the oscillations of a sharp thermocline, are dealt with. Then, the relevance of the vertical adaptivity technique is assessed by simulating thermocline oscillations of Lake Tanganyika. The results are compared to measured vertical profiles of temperature, showing similar stratification and outcropping events.

show abstract

Multirate time stepping for accelerating explicit discontinuous Galerkin computations with application to geophysical flows

Cited by 44 publications

References 44 publications

The Finite Element Sea Ice-Ocean Model (FESOM) v.1.4: formulation of an ocean general circulation model

The Finite Element Sea Ice-Ocean Model (FESOM) v.1.4: formulation of an ocean general circulation model

A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4 with an application to the thermocline oscillations of Lake Tanganyika

A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4, a DG finite element hydrodynamic model, with an application to the thermocline oscillations of Lake Tanganyika

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