A<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:math>-discontinuous Galerkin method for the stationary quasi-geostrophic equations of the ocean

Kim, Tae Yeon; Park, Eun Jae; Shin, Dong wook

doi:10.1016/j.cma.2015.11.022

Cited by 15 publications

(6 citation statements)

References 26 publications

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“…The FEM is particularly appealing because it combines advantages of multiple methods. It can easily handle adaptive mesh refinement and complex geometries (like the FVMs), but also can create higher-order schemes (like pseudospectral methods) at the same time, like the discretization used in [30,60], which is shown in Figure 2 (see also [61][62][63]). The first FE approximation of the QGE, to the best of our knowledge, was a scheme based on the mixed formulation developed in [64].…”

Section: Finite Element Methods For the Qgementioning

confidence: 99%

“…Triangulation of the Mediterranean Sea suitable for simulations with finite element methods which was used in [30,60] (see also [61][62][63]).…”

Section: Finite Element Methods For the Qgementioning

confidence: 99%

“…Several numerical tests, commonly employed in the geophysical literature, showed the accuracy of the finite element discretization and illustrated the theoretical estimates. Other recent developments of FEM for QGE include discontinuous Galerkin formulation using C 0 elements [62] and B-splines [69][70][71][72][73]. In particular, an adaptive refinement algorithm for B-splines finite element approximation was presented in [71] for the streamfunction formulation.…”

Section: Finite Element Methods For the Qgementioning

confidence: 99%

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Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey

Mou

Wang

Wells

et al. 2020

Fluids

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Reduced order models (ROMs) are computational models whose dimension is significantly lower than those obtained through classical numerical discretizations (e.g., finite element, finite difference, finite volume, or spectral methods). Thus, ROMs have been used to accelerate numerical simulations of many query problems, e.g., uncertainty quantification, control, and shape optimization. Projection-based ROMs have been particularly successful in the numerical simulation of fluid flows. In this brief survey, we summarize some recent ROM developments for the quasi-geostrophic equations (QGE) (also known as the barotropic vorticity equations), which are a simplified model for geophysical flows in which rotation plays a central role, such as wind-driven ocean circulation in mid-latitude ocean basins. Since the QGE represent a practical compromise between efficient numerical simulations of ocean flows and accurate representations of large scale ocean dynamics, these equations have often been used in the testing of new numerical methods for ocean flows. ROMs have also been tested on the QGE for various settings in order to understand their potential in efficient numerical simulations of ocean flows. In this paper, we survey the ROMs developed for the QGE in order to understand their potential in efficient numerical simulations of more complex ocean flows: We explain how classical numerical methods for the QGE are used to generate the ROM basis functions, we outline the main steps in the construction of projection-based ROMs (with a particular focus on the under-resolved regime, when the closure problem needs to be addressed), we illustrate the ROMs in the numerical simulation of the QGE for various settings, and we present several potential future research avenues in the ROM exploration of the QGE and more complex models of geophysical flows.

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Section: Finite Element Methods For the Qgementioning

confidence: 99%

“…Triangulation of the Mediterranean Sea suitable for simulations with finite element methods which was used in [30,60] (see also [61][62][63]).…”

Section: Finite Element Methods For the Qgementioning

confidence: 99%

Section: Finite Element Methods For the Qgementioning

confidence: 99%

See 1 more Smart Citation

Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey

Mou

Wang

Wells

et al. 2020

Fluids

View full text Add to dashboard Cite

show abstract

“…The FEM is particularly appealing because it combines advantages of multiple methods. It can easily handle adaptive mesh refinement and complex geometries (like the FVMs), but also can create higher-order schemes (like pseudospectral methods) at the same time, like the discretization used in [27,26], which is shown in Figure 2 (see also [31,44,98]). The first FE approximation of the QGE, to the best of our knowledge, was a scheme based on the mixed formulation developed in [25].…”

Section: Finite Elementmentioning

confidence: 99%

“…Several numerical tests, commonly employed in the geophysical literature, showed the accuracy of the finite element discretization and illustrated the theoretical estimates. Other recent developments of FEM for QGE include discontinuous Galerkin formulation using C 0 elements [44] and Bsplines [45,41,5,43,87]. In particular, an adaptive refinement algorithm for B-splines finite element approximation was presented in [5] for the streamfunction formulation.…”

Section: Finite Elementmentioning

confidence: 99%

Data-driven correction reduced order models for the quasi-geostrophic equations: a numerical investigation

Mou

Liu

Wells

et al. 2020

International Journal of Computational Fluid Dynamics

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This paper investigates the recently introduced data-driven correction reduced order model (DDC-ROM) in the numerical simulation of the quasi-geostrophic equations. The DDC-ROM uses available data to model the correction term that is generally used to represent the missing information in low-dimensional ROMs. Physical constraints are added to the DDC-ROM to create the constrained data-driven correction reduced order model (CDDC-ROM) in order to further improve its accuracy and stability. Finally, the DDC-ROM is tested on time intervals that are longer than the time interval over which it was trained. The numerical investigation shows that, for low-dimensional ROMs, both the DDC-ROM and CDDC-ROM perform better than the standard Galerkin ROM (G-ROM) and the CDDC-ROM provides the best results.(CM, HL,TI)

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Phase field simulations of coupled microstructure solidification problems via the strong form particle difference method

Song

Kim

et al. 2017

Int J Mech Mater Des

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AC0-discontinuous Galerkin method for the stationary quasi-geostrophic equations of the ocean

Cited by 15 publications

References 26 publications

Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey

Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey

Data-driven correction reduced order models for the quasi-geostrophic equations: a numerical investigation

Phase field simulations of coupled microstructure solidification problems via the strong form particle difference method

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