A flux‐form conservative semi‐Lagrangian multitracer transport scheme (FF‐CSLAM) for icosahedral‐hexagonal grids

Dubey, S.; Mittal, R. C.; Lauritzen, P. H.

doi:10.1002/2013ms000259

Cited by 8 publications

(4 citation statements)

References 55 publications

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“…In order to attain more accurate interpolation results, high-order polynomial fitting was utilized. It needs a local grid stencil in 3D Cartesian spaces, and then the grid points in this local stencil would be mapped onto a local two-dimensional (2D) coordinate system by a general stereography projection [26,27], and then a bivariate polynomial was utilized to fit the values at grid points on the stencil. In order to obtain an approximate value at the departure point, first, find the nearest vertex for each departure point, and then a polynomial least-squares fit is calculated using values at the vertex and its nearest first-layer neighbor points.…”

Section: Local Polynomial Fitting By Least-square Methods (Poly-lsq)mentioning

confidence: 99%

High-Order Semi-Lagrangian Schemes for the Transport Equation on Icosahedron Spherical Grids

Zhang

Tian

et al. 2022

Atmosphere

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The transport process is an important part of the research of fluid dynamics, especially when it comes to tracer advection in the atmosphere or ocean dynamics. In this paper, a series of high-order semi-Lagrangian methods for the transport process on the sphere are considered. The methods are formulated entirely in three-dimensional Cartesian coordinates, thus avoiding any apparent artificial singularities associated with surface-based coordinate systems. The underlying idea of the semi-Lagrangian method is to find the value of the field/tracer at the departure point through interpolating the values of its surrounding grid points to the departure point. The implementation of the semi-Lagrangian method is divided into the following two main procedures: finding the departure point by integrating the characteristic equation backward and then interpolate on the departure point. In the first procedure, three methods are utilized to solve the characteristic equation for the locations of departure points, including the commonly used midpoint-rule method and two explicit high-order Runge–Kutta (RK) methods. In the second one, for interpolation, four new methods are presented, including 1) linear interpolation; 2) polynomial fitting based on the least square method; 3) global radial basis function stencils (RBFs), and 4) local RBFs. For the latter two interpolation methods, we find that it is crucial to select an optimal value for the shape parameter of the basis function. A Gauss hill advection case is used to compare and contrast the methods in terms of their accuracy, and conservation properties. In addition, the proposed method is applied to standard test cases, which include solid body rotation, shear deformation of twin slotted cylinders, and the evolution of a moving vortex. It demonstrates that the proposed method could simulate all test cases with reasonable accuracy and efficiency.

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Section: Local Polynomial Fitting By Least-square Methods (Poly-lsq)mentioning

confidence: 99%

High-Order Semi-Lagrangian Schemes for the Transport Equation on Icosahedron Spherical Grids

Zhang

Tian

et al. 2022

Atmosphere

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“…Potentially more accurate transport schemes, such as the one by Dubey et al (2014), are under consideration for future use. However, the trade-off between accuracy and computational effort remains an issue.…”

Section: Flux-corrected Transportmentioning

confidence: 99%

A Vertically Flow-Following Icosahedral Grid Model for Medium-Range and Seasonal Prediction. Part I: Model Description

Bleck

Bao

Benjamin

et al. 2015

Monthly Weather Review

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A hydrostatic global weather prediction model based on an icosahedral horizontal grid and a hybrid terrainfollowing/isentropic vertical coordinate is described. The model is an extension to three spatial dimensions of a previously developed, icosahedral, shallow-water model featuring user-selectable horizontal resolution and employing indirect addressing techniques. The vertical grid is adaptive to maximize the portion of the atmosphere mapped into the isentropic coordinate subdomain. The model, best described as a stacked shallow-water model, is being tested extensively on real-time medium-range forecasts to ready it for possible inclusion in operational multimodel ensembles for medium-range to seasonal prediction.

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“…In this study, it was shown that the although Miura-simplification is unstable (depending on reconstruction function's order) for Courant numbers larger than approximately 1/2, but it can lead to more accurate solutions for low Courant numbers compared to rigorous remapping scheme on quadrilateral grid. Moreover the studies of [12,32] on icosahedral grids also pointed out that the geometrical errors (errors due to incorrect flux area approximation) are not as significant as the derivative errors (errors related to the sub-grid reconstructions). Therefore in second order advection scheme, where main source of error is derivative error, use of crude flux area simplification is justified.…”

Section: Finite Volume Advection Schemesmentioning

confidence: 99%

On the inter-comparison of two tracer transport schemes on icosahedral grids

Dubey

Dubos

Hourdin

et al. 2015

Applied Mathematical Modelling

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a b s t r a c tTwo simple finite volume advection schemes based on linear sub-grid reconstruction are implemented over spherical icosahedral-hexagonal grids. One of theses schemes is fully discrete in space and time, while the other one is a semi-discrete scheme with third order Runge-Kutta time integration. For the linear sub-grid reconstruction, we propose two possible candidates for consistent gradient discretization over general grids. These gradients are designed in a finite volume sense with an adequate modification to guarantee convergence in the absence of special grid optimization. To generate our computational mesh from triangular grid, we either use centroids (BT grid) or circumcenters (VT grid) of the spherical triangular mesh. A numerical convergence study is used to show that for a first order convergence of our discrete gradients grid modification is sufficient, whereas to achieve second order convergence grid optimization is mandatory. This study also implicates that BT grid offers a better rate of convergence than VT grid.Monotonicity of the advection schemes is enforced by a slope limiter as well as flux-corrected transport (FCT). We compared aforementioned space-time coupled and space-time decoupled advection schemes in terms of their performance for the recently proposed advection test cases. Our findings advocate that space-time coupled advection scheme is performing better than its counterpart. Furthermore, we used the fully discrete advection scheme to carried out a comparison of slope limitation and FCT approach to achieve monotonicity.

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A flux‐form conservative semi‐Lagrangian multitracer transport scheme (FF‐CSLAM) for icosahedral‐hexagonal grids

Cited by 8 publications

References 55 publications

High-Order Semi-Lagrangian Schemes for the Transport Equation on Icosahedron Spherical Grids

High-Order Semi-Lagrangian Schemes for the Transport Equation on Icosahedron Spherical Grids

A Vertically Flow-Following Icosahedral Grid Model for Medium-Range and Seasonal Prediction. Part I: Model Description

On the inter-comparison of two tracer transport schemes on icosahedral grids

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