Emerging Numerical Methods for Atmospheric Modeling

Nair, Ramachandran D.; Levy, Michael; Lauritzen, P. H.

doi:10.1007/978-3-642-11640-7_9

Cited by 15 publications

(13 citation statements)

References 68 publications

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“…Because of these desirable properties, DG methods are becoming more and more popular in atmospheric modeling [4][5][6][7] on a variety of spherical meshes [8,9]. We refer the readers to the review paper [10] for details of the various DG applications in atmospheric science with an extensive list of references. 4 W. GUO, R. D. NAIR AND X. ZHONG Despite the great advantages, DG schemes may fail in approximating transport equations with discontinuous solution structures including strong shocks or sharp gradients.…”

Section: Introductionmentioning

confidence: 99%

An efficient WENO limiter for discontinuous Galerkin transport scheme on the cubed sphere

Guo

Nair

Zhong

2015

Int. J. Numer. Meth. Fluids

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SUMMARYThe discontinuous Galerkin (DG) transport scheme is becoming increasingly popular in the atmospheric modeling due to its distinguished features, such as high-order accuracy and high-parallel efficiency. Despite the great advantages, DG schemes may produce unphysical oscillations in approximating transport equations with discontinuous solution structures including strong shocks or sharp gradients. Nonlinear limiters need to be applied to suppress the undesirable oscillations and enhance the numerical stability. It is usually very difficult to design limiters to achieve both high-order accuracy and non-oscillatory properties and even more challenging for the cubed-sphere geometry. In this paper, a simple and efficient limiter based on the weighted essentially non-oscillatory (WENO) methodology is incorporated in the DG transport framework on the cubed sphere. The uniform high-order accuracy of the resulting scheme is maintained because of the high-order nature of WENO procedures. Unlike the classic WENO limiter, for which the wide halo region may significantly impede parallel efficiency, the simple limiter requires only the information from the nearest neighboring elements without degrading the inherent high-parallel efficiency of the DG scheme. A bound-preserving filter can be further coupled in the scheme that guarantees the highly desirable positivity-preserving property for the numerical solution. The resulting scheme is high-order accurate, non-oscillatory, and positivity preserving for solving transport equations based on the cubed-sphere geometry. Extensive numerical results for several benchmark spherical transport problems are provided to demonstrate good results, both in accuracy and in non-oscillatory performance.

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Section: Introductionmentioning

confidence: 99%

An efficient WENO limiter for discontinuous Galerkin transport scheme on the cubed sphere

Guo

Nair

Zhong

2015

Int. J. Numer. Meth. Fluids

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“…2D Smooth solid-body rotation The smooth solid-body rotation test with a smooth function is used for a grid convergence study [60,61]. A Gaussian hill q h ¼ exp À5 ðx À x c Þ 2 þ ðy À y c Þ 2 h i is originally centered in ðx c ; y c Þ ¼ ð0; 0Þ in a periodic domain X ¼ ½Àp; p Â ½Àp; p with prescribed velocity ðu; wÞ ¼ ðÀp y; pxÞ.…”

Section: Numerical Testingmentioning

confidence: 99%

Variational multiscale stabilization of high-order spectral elements for the advection–diffusion equation

Marras

Kelly

Giraldo

et al. 2012

Journal of Computational Physics

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“…1-4. For many practical applications monotonic solutions are required, and usually a monotonic limiter/filter is used to control or eliminate spurious oscillations [42].…”

Section: Non-divergent Casesmentioning

confidence: 99%

“…The discontinuous Galerkin (DG) method may be considered as a hybrid conservative approach combining the nice features of the finite-element and finite-volume methods [40]; and is becoming increasingly popular in atmospheric modeling applications [42]. Here, we briefly outline the DG transport scheme on the cubed-sphere, which is used for the deformational flow simulations.…”

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confidence: 99%

A class of deformational flow test cases for linear transport problems on the sphere

Nair

Lauritzen

2010

Journal of Computational Physics

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104

157

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a b s t r a c tA class of new benchmark deformational flow test cases for the two-dimensional horizontal linear transport problems on the sphere is proposed. The scalar field follows complex trajectories and undergoes severe deformation during the simulation; however, the flow reverses its course at half-time and the scalar field returns to its initial position and shape. This process makes the exact solution available at the end of the simulation, and facilitates assessment of the accuracy of the underlying transport scheme. A procedure to eliminate possible cancellations of errors when the flow reverses is proposed.The test suite consists of four cases. Three are based on non-divergent flow fields and one on a divergent flow. The initial conditions are prescribed in terms of regular latitude-longitude spherical coordinates and are easy to implement. The divergent flow is specifically aimed for conservative global transport schemes to test for conservation, consistency and monotonicity (or positivity) of limiters/filters in a challenging flow environment. In the context of semi-Lagrangian schemes, the time-varying flow fields can be used to test trajectory algorithms where the exact trajectories do not follow great-circle arcs. The characteristics of the test cases are demonstrated with two different transport schemes.

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Emerging Numerical Methods for Atmospheric Modeling

Cited by 15 publications

References 68 publications

An efficient WENO limiter for discontinuous Galerkin transport scheme on the cubed sphere

An efficient WENO limiter for discontinuous Galerkin transport scheme on the cubed sphere

Variational multiscale stabilization of high-order spectral elements for the advection–diffusion equation

A class of deformational flow test cases for linear transport problems on the sphere

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