Vorticity–divergence mass-conserving semi-Lagrangian shallow-water model using the reduced grid on the sphere

Tolstykh, M. A.; Shashkin, V. V.

doi:10.1016/j.jcp.2012.02.016

Cited by 22 publications

(28 citation statements)

References 58 publications

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“…In particular, we plan to implement the hybrid σ -p vertical coordinate and the reduced lat.-long. grid (Fadeev, 2013), as we did for the shallow-water model (Tolstykh and Shashkin, 2012). Furthermore, consistent transport formulation similar to Wong et al (2013) is considered.…”

Section: Discussionmentioning

confidence: 99%

“…(8), (9), and (11). The horizontal wind components u and v at time step n+1 are restored from known ζ n+1 and D n+1 using the algorithm from Tolstykh and Shashkin (2012). The algorithm solves the direct problem,…”

Section: Basic (Nonconservative) Sl-av Dynamical Core Formulationmentioning

confidence: 99%

“…The horizontal wind V n+1 is reconstructed from known D n+1 and ζ n+1 using the solver described in Tolstykh and Shashkin (2012).…”

Section: Mass-conservative Sl Discretization Of the Continuity Equationmentioning

confidence: 99%

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Inherently mass-conservative version of the semi-Lagrangian absolute vorticity (SL-AV) atmospheric model dynamical core

Shashkin

Tolstykh

2014

Geosci. Model Dev.

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Abstract. The semi-Lagrangian absolute vorticity (SL-AV) atmospheric model is the global semi-Lagrangian hydrostatic model used for operational medium-range and seasonal forecasts at the Hydrometeorological Centre of Russia. The distinct feature of the SL-AV dynamical core is the semiimplicit, semi-Lagrangian vorticity-divergence formulation on the unstaggered grid. A semi-implicit, semi-Lagrangian approach allows for long time steps but violates the global and local mass conservation. In particular, the total mass in simulations with semi-Lagrangian models can drift significantly if no a posteriori mass-fixing algorithm is applied. However, the global mass-fixing algorithms degrade the local mass conservation.The new inherently mass-conservative version of the SL-AV model dynamical core presented here ensures global and local mass conservation without mass-fixing algorithms. The mass conservation is achieved with the introduction of the finite-volume, semi-Lagrangian discretization for a continuity equation based on the 3-D extension of the conservative cascade semi-Lagrangian transport scheme (CCS). Numerical experiments show that the new version of the SL-AV dynamical core presented combines the accuracy and stability of the standard SL-AV dynamical core with the massconservation properties. The results of the mountain-induced Rossby-wave test and baroclinic instability test for the massconservative dynamical core are found to be in agreement with the results available in the literature.

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Section: Discussionmentioning

confidence: 99%

Section: Basic (Nonconservative) Sl-av Dynamical Core Formulationmentioning

confidence: 99%

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Inherently mass-conservative version of the semi-Lagrangian absolute vorticity (SL-AV) atmospheric model dynamical core

Shashkin

Tolstykh

2014

Geosci. Model Dev.

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“…The spherical shallow water equations are usually used as the first step to examine new numerical algorithms to be used in more complex global climate and weather prediction models. In recent years, much research (such as [3,4,5,6,7,8,9]) have been devoted to the development of new efficient numerical algorithms for the spherical shallow water equations.…”

Section: Introductionmentioning

confidence: 99%

High‐order compact finite difference schemes for the vorticity–divergence representation of the spherical shallow water equations

Ghader

Nordström

2015

Numerical Methods in Fluids

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SUMMARYThis work is devoted to the application of the super compact finite difference (SCFDM) and the combined compact finite difference (CCFDM) methods for spatial differencing of the spherical shallow water equations in terms of vorticity, divergence and height. The fourth-order compact, the sixth-order and eighth-order SCFDM and the sixth-order and eighth-order CCFDM schemes are used for the spatial differencing. To advance the solution in time, a semi-implicit Runge-Kutta method is used. In addition, to control the non-linear instability an eighth-order compact spatial filter is employed. For the numerical solution of the elliptic equations in the problem, a direct hybrid method which consists of a high-order compact scheme for spatial differencing in the latitude coordinate and a fast Fourier transform in longitude coordinate is utilized. The accuracy and convergence rate for all methods are verified against exact analytical solutions. Qualitative and quantitative assessment of the results for an unstable barotropic mid-latitude zonal jet employed as an initial condition, is addressed. It is revealed that the sixth-order and eighth-order CCFDM and SCFDM methods lead to a remarkable improvement of the solution over the fourth-order compact method.

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“…Examples include the spectral transform method (Jakob-Chien et al, 1995), semi-Lagrangian methods (Ritchie, 1988;Bates et al, 1990;Tolstykh, 2002;Zerroukat et al, 2009;Tolstykh and Shashkin, 2012;Qaddouri et al, 2012), finite-difference methods (Heikes and Randall, 1995;Ronchi et al, 1996), Godunov-type finite-volume methods (Rossmanith, 2006;Ullrich et al, 2010), staggered finite-volume methods (Lin and Rood, 1997;Ringler et al, 2008Ringler et al, , 2011, multi-moment finite-volume methods Li et al, 2008;Chen et al, 2014) and finite-element methods (Taylor et al, 1997;Côté and Staniforth, 1990;Thomas and Loft, 2005;Giraldo et al, 2002;Nair et al, 2005;Läuter et al, 2008;Comblen et al, 2009;Bao et al, 2014). This paper introduces a novel discrete derivative operator that is applied to the shallow-water equations on a manifold using continuous and discontinuous finite elements.…”

Section: Introductionmentioning

confidence: 99%

A global finite-element shallow-water model supporting continuous and discontinuous elements

Ullrich

2014

Geosci. Model Dev.

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Abstract. This paper presents a novel nodal finite-element method for either continuous and discontinuous elements, as applied to the 2-D shallow-water equations on the cubed sphere. The cornerstone of this method is the construction of a robust derivative operator that can be applied to compute discrete derivatives even over a discontinuous function space. A key advantage of the robust derivative is that it can be applied to partial differential equations in either a conservative or a non-conservative form. However, it is also shown that discontinuous penalization is required to recover the correct order of accuracy for discontinuous elements. Two versions with discontinuous elements are examined, using either the g 1 and g 2 flux correction function for distribution of boundary fluxes and penalty across nodal points. Scalar and vector hyperviscosity (HV) operators valid for both continuous and discontinuous elements are also derived for stabilization and removal of grid-scale noise. This method is validated using four standard shallow-water test cases, including geostrophically balanced flow, a mountain-induced Rossby wave train, the Rossby-Haurwitz wave and a barotropic instability. The results show that although the discontinuous basis requires a smaller time step size than that required for continuous elements, the method exhibits better stability and accuracy properties in the absence of hyperviscosity.

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Vorticity–divergence mass-conserving semi-Lagrangian shallow-water model using the reduced grid on the sphere

Cited by 22 publications

References 58 publications

Inherently mass-conservative version of the semi-Lagrangian absolute vorticity (SL-AV) atmospheric model dynamical core

Inherently mass-conservative version of the semi-Lagrangian absolute vorticity (SL-AV) atmospheric model dynamical core

High‐order compact finite difference schemes for the vorticity–divergence representation of the spherical shallow water equations

A global finite-element shallow-water model supporting continuous and discontinuous elements

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