A Semi-implicit Semi-Lagrangian Scheme Using the Height Coordinate for a Nonhydrostatic and Fully Elastic Model of Atmospheric Flows

Bonaventura, Luca

doi:10.1006/jcph.1999.6414

Cited by 79 publications

(79 citation statements)

References 38 publications

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“…The continuous one-dimensional (1D) governing equations derived from those used in the Met Office's operational forecast model (Staniforth et al 2004) or equivalently from those used by Bonaventura (2000) are written as: where D/Dt ≡ ∂/∂t + w∂/∂z, w is vertical velocity, ≡ (p/p 0 ) κ is Exner pressure, p is pressure, p 0 = p(z = 0), κ ≡ R/c p , R is the gas constant, c p is specific heat of dry air at constant pressure, θ is potential temperature, g is gravity, ρ is density, t is time, z is height above the surface, and z T is the height of the top boundary.…”

Section: The Model (A) the Continuous Equationsmentioning

confidence: 99%

Impact of semi-Lagrangian trajectories on the discrete normal modes of a non-hydrostatic vertical-column model

Cordero

Wood

Staniforth

2005

Q. J. R. Meteorol. Soc.

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SUMMARYThe impact of one-and two-term extrapolated-trajectory schemes on the stability properties of centred semiimplicit semi-Lagrangian schemes is analysed by examining the behaviour of the discrete (acoustic) normal modes of a prototypical column model. It is found that, in the absence of any controlling mechanism, both extrapolated-trajectory schemes are unstable. Additionally, they can significantly distort the vertical structure of the modes. Though not studied herein, the analogous distortion of Rossby and gravity waves could be expected to be deleterious to a forecast model.

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Section: The Model (A) the Continuous Equationsmentioning

confidence: 99%

Impact of semi-Lagrangian trajectories on the discrete normal modes of a non-hydrostatic vertical-column model

Cordero

Wood

Staniforth

2005

Q. J. R. Meteorol. Soc.

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“…Almost all nonhydrostatic mesoscale models currently in existence are based on the finite difference (FD) method; examples include the following list of models: [4,5,11,17,25,26,[29][30][31][32]39,42,43,46,48,57,58], and [60]. Included in this list are models such as ARPS (University of Oklahoma), COAMPS (US Navy), LM (German Weather Service), MC2 (Environment Canada), MM5 (Penn State/NCAR), NMM (National Center for Environmental Prediction), and WRF (NCAR).…”

Section: Introductionmentioning

confidence: 99%

A study of spectral element and discontinuous Galerkin methods for the Navier–Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases

Giraldo

Restelli

2008

Journal of Computational Physics

225

333

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“…In addition, small cells are generally created in the vicinity of lower boundary, resulting in a huge computational cost because the time interval of integration depends on the size of the smallest cell in the whole region. Steppeler et al (2002) introduced a "thin wall" approximation, which extended the method proposed by Bonaventura (2000), to an advective form of the the nonhydrostatic atmospheric model in order to reduce the computational cost associated with the cut-cell method and obtain the most numerical stability. In the approximation, topography was represented using flux limiters at the flanks of cells and the volume of a cut cell is treated as well as that of uncut cells.…”

Section: Introductionmentioning

confidence: 99%

A Conserved Topographical Representation Scheme Using a Thin-Wall Approximation in Z-Coordinates

Nishikawa

Satoh

2016

SOLA

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As nonhydrostatic models have higher resolution, a topographical representation scheme is desirable as an alternative to the terrain-following approach, which is unstable for steep topography. We developed a conserved topographical representation scheme using a thin-wall approximation in z-coordinates (the CT scheme). This scheme is formulated by the flux-form finite-volume method with a flux limiter, so that the total integrals over the entire domain of prognostic variables are conserved: this is advantageous compared to the conventional thin-wall approximation method. The CT scheme is easily implemented for existing models that use the finite-volume method. We constructed the scheme to satisfy conservation of mass, horizontal momentum, and total energy. We compared the results of the CT scheme for an isolated mountain case with those of a step-mountain (SM) method. The CT scheme represents the propagation of gravity waves more accurately than the SM method. The upward flux of horizontal momentum becomes more vertically uniform for the CT scheme than for the SM method over time. In addition, the horizontal momentum budget shows that the total momentum is reduced by reaction force at the lower boundary with changes due to numerical damping in the upper layers and numerical filters in the free layers.(Citation: Nishikawa, Y., and M. Satoh, 2016: A conserved topographical representation scheme using a thin-wall approximation in z-coordinates. SOLA, 12, 232−236,

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A Semi-implicit Semi-Lagrangian Scheme Using the Height Coordinate for a Nonhydrostatic and Fully Elastic Model of Atmospheric Flows

Cited by 79 publications

References 38 publications

Impact of semi-Lagrangian trajectories on the discrete normal modes of a non-hydrostatic vertical-column model

Impact of semi-Lagrangian trajectories on the discrete normal modes of a non-hydrostatic vertical-column model

A study of spectral element and discontinuous Galerkin methods for the Navier–Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases

A Conserved Topographical Representation Scheme Using a Thin-Wall Approximation in Z-Coordinates

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