Icosahedral Shallow Water Model (ICOSWM): results of shallow water  test cases and sensitivity to model parameters

Rípodas, Pilar; Gaßmann, Almut; Förstner, Jochen; Majewski, Detlev; Giorgetta, Marco; Korn, Peter; Kornblueh, Luis; Wan, Hui; Zängl, Günther; Bonaventura, Luca; Heinze, Thomas

doi:10.5194/gmdd-2-581-2009

Cited by 16 publications

(17 citation statements)

References 23 publications

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“…We have tested these transport schemes in the nonhydrostatic atmospheric solvers within the Icosahedral Nonhydrostatic (ICON; Gassmann 2010; Rípodas et al 2009;Gassmann and Herzog 2008) FIG. 11.…”

Section: D Test Resultsmentioning

confidence: 99%

Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Flux Operators for ODE-Based Time Integration

2011

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Higher-order finite-volume flux operators for transport algorithms used within Runge-Kutta time integration schemes on irregular Voronoi (hexagonal) meshes are proposed and tested. These operators are generalizations of third-and fourth-order operators currently used in atmospheric models employing regular, orthogonal rectangular meshes. Two-dimensional least squares fit polynomials are used to evaluate the higher-order spatial derivatives needed to cancel the leading-order truncation error terms of the standard second-order centered formulation. Positive definite or monotonic behavior is achieved by applying an appropriate limiter during the final Runge-Kutta stage within a given time step.The third-and fourth-order formulations are evaluated using standard transport tests on the sphere. The new schemes are more accurate and significantly more efficient than the standard second-order scheme and other schemes in the literature examined by the authors. The third-order formulation is equivalent to the fourth-order formulation plus an additional diffusion term that is proportional to the Courant number. An optimal value for the coefficient scaling this diffusion term is chosen based on qualitative evaluation of the test results. Improvements using the higher-order scheme in place of the traditional second-order centered approach are illustrated within 3D unstable baroclinic wave simulations produced using two global nonhydrostatic models employing spherical Voronoi meshes.

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Section: D Test Resultsmentioning

confidence: 99%

Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Flux Operators for ODE-Based Time Integration

2011

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“…Sensitivity of the comparison results to the amount of numerical diffusion has been highlighted in several model benchmarking exercises (see e.g. Ripodas et al, 2009).…”

Section: Numerical Resultsmentioning

confidence: 99%

A semi‐implicit, semi‐Lagrangian discontinuous Galerkin framework for adaptive numerical weather prediction

Tumolo

Bonaventura

2015

Quart J Royal Meteoro Soc

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We present an adaptive discretization approach for model equations typical of numerical weather prediction (NWP), which combines the semi-Lagrangian technique with a semiimplicit time discretization method, based on the Trapezoidal Rule second-order Backward Difference Formula scheme (TR-BDF2), and with a discontinuous Galerkin (DG) spatial discretization, with variable and adaptive element degree. The resulting method has full second-order accuracy in time, can employ polynomial bases of arbitrarily high degree in space, is unconditionally stable and can effectively adapt the number of degrees of freedom employed in each element at runtime, in order to balance accuracy and computational cost. Furthermore, although the proposed method can be implemented on arbitrary unstructured and non-conforming meshes, even its application on simple Cartesian meshes in spherical coordinates can reduce the impact of the coordinate singularity, by reducing the polynomial degree used in the polar elements. Numerical results are presented, obtained on classical benchmarks with two-dimensional models implementing discretizations of the shallowwater equations on the sphere and of the Euler equations on a vertical slice, respectively. The results confirm that the proposed method has a significant potential for NWP applications.

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“…However, whereas in the literature [13] on the hexagonal C-grid that reconstruction is already known for the equilateral case (though obtained by different means), many different methods [1,5,8] are in use for the triangular C-grid.…”

Section: Perform a Piecewise Constant Vector Reconstruction In The Cementioning

confidence: 97%

Inspection of hexagonal and triangular C-grid discretizations of the shallow water equations

Gaßmann

2011

Journal of Computational Physics

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Icosahedral Shallow Water Model (ICOSWM): results of shallow water test cases and sensitivity to model parameters

Cited by 16 publications

References 23 publications

Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Flux Operators for ODE-Based Time Integration

Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Flux Operators for ODE-Based Time Integration

A semi‐implicit, semi‐Lagrangian discontinuous Galerkin framework for adaptive numerical weather prediction

Inspection of hexagonal and triangular C-grid discretizations of the shallow water equations

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