Conservative finite‐volume schemes for the quasi‐geostrophic equation on coastal‐conforming unstructured primal–dual meshes

Chen, Qingshan; Ju, Lili

doi:10.1002/qj.3277

Cited by 6 publications

(5 citation statements)

References 34 publications

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“…These generalized C-grid methods are applicable to a wide class of meshes including latitude-longitude grids, Delaunay triangulations, Centroidal Voronoi tessellation (CVT), and spherical CVT. A different approach to overcome this issue was considered in [50], where the non-staggered Z-grid scheme [51] was used for the QGE model.…”

Section: Finite Volume Methods For the Qgementioning

confidence: 99%

“…where {a j (t)} r j=1 are the sought time-varying ROM coefficients. We note that we made two important choices in our approach: (i) We enforced the coupling between the POD vorticity and streamfunction basis functions in (15); and (ii) We used the same ROM coefficients in the ROM vorticity approximation (16) and in the ROM streamfunction approximation (17). The motivation for making these two choices is efficiency.…”

Section: Galerkin Reduced Order Model (G-rom)mentioning

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 Volume Methods For the Qgementioning

confidence: 99%

Section: Galerkin Reduced Order Model (G-rom)mentioning

confidence: 99%

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

“…These generalized C-grid methods are applicable to a wide class of meshes including latitude-longitude grids, Delaunay triangulations, Centroidal Voronoi tessellation (CVT), and spherical CVT. A different approach to overcome this issue was considered in [15], where the non-staggered Z-grid scheme [85] was used for the QGE model.…”

Section: 2mentioning

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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“…Following [20], we also use an adapted version of the SWSTC #2 on the northern hemishpere. Finally, we also make use of a new test case of our own ( [21]) involving a freely evolving gyre in the northern Atlantic.…”

Section: Numerical Evaluationsmentioning

confidence: 99%

Conservative numerical schemes with optimal dispersive wave relations -- Part II. Numerical evaluations

Chen¹,

Ju²,

Témam³

2020

Preprint

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A new energy and enstrophy conserving scheme is evaluated using a suite of test cases over the global spherical domain or bounded domains. The evaluation is organized around a set of pre-defined properties: accuracy of individual opeartors, accuracy of the whole scheme, conservation, control of the divergence variable, representation of the energy and enstrophy spectra, and simulation of nonlinear dynamics. The results confirm that the scheme is between the first and second order accurate, and conserves the total energy and potential enstrophy up to the time truncation errors. The scheme is capable of producing more physically realistic energy and enstrophy spectra, indicating that the new scheme can help prevent the unphysical energy cascade towards the finest resolvable scales. With an optimal representation of the dispersive wave relations, the scheme is able to keep the flow close to being non-divergent, maintain the geostrophically balanced structures with large-scale geophysical flows over longterm simulations.

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Conservative finite‐volume schemes for the quasi‐geostrophic equation on coastal‐conforming unstructured primal–dual meshes

Cited by 6 publications

References 34 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

Conservative numerical schemes with optimal dispersive wave relations -- Part II. Numerical evaluations

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