Consequences of Using the Splitting Method for Implementing Physical Forcings in a Semi-Implicit Semi-Lagrangian Model

Caya, Alain; Laprise, René; Zwack, Peter

doi:10.1175/1520-0493(1998)126<1707:coutsm>2.0.co;2

Cited by 35 publications

(38 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Including the source term S in this way ensures that the scheme obtains the exact steady-state solution (18), and thereby satisfies the fourth requirement -maintenance of the steady-state solution -whose importance was demonstrated by Caya et al (1998). Eliminating F * , F * * and F * * * , we obtain:…”

Section: Full Nonlinear Formmentioning

confidence: 99%

See 1 more Smart Citation

A monotonically‐damping second‐order‐accurate unconditionally‐stable numerical scheme for diffusion

Wood

Diamantakis

Staniforth

2007

Quart J Royal Meteoro Soc

View full text Add to dashboard Cite

ABSTRACT:We present a new two-step temporal discretization of the diffusion equation, which is formally secondorder-accurate and unconditionally stable. A novel aspect of the scheme is that it is monotonically damping: the damping rate is a monotonically-increasing function of the diffusion coefficient, independent of the size of the time step, when the diffusion coefficient is independent of the variable being diffused. Furthermore, the damping rate increases without bound as the diffusion coefficient similarly increases. We discuss the nonlinear behaviour of the scheme when the diffusion coefficient is a function of the diffused variable. The scheme is designed to maintain any steady-state solution. We present examples of the performance of the scheme.  Crown

show abstract

Section: Full Nonlinear Formmentioning

confidence: 99%

“…Maintenance of steady-state solutions. Some existing schemes do not properly maintain steady-state solutions, but instead wrongly distort them (Caya et al, 1998;Murthy and Nanjundiah, 2000;Dubal et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

A monotonically‐damping second‐order‐accurate unconditionally‐stable numerical scheme for diffusion

Wood

Diamantakis

Staniforth

2007

Quart J Royal Meteoro Soc

View full text Add to dashboard Cite

show abstract

“…introduced in SWC02a as an extension of the work by Caya et al (1998), is interpreted as follows. The first term on the right-hand side of (2) represents a sum of relaxation processes and the second term represents a sum of oscillatory forcings (with R α the forcing amplitude, k the wave number and α the frequency).…”

Section: Methodology and First Resultsmentioning

confidence: 99%

Stability and accuracy of the physics—dynamics coupling in spectral models

Termonia

Hamdi

2007

Quart J Royal Meteoro Soc

View full text Add to dashboard Cite

This article first reviews the existing spectral time-step organizations of the Integrated Forecast System (IFS) of the ECMWF and the ARPEGE/ALADIN/AROME models of Météo-France and the ALADIN partners. They are characterized according to four choices concerning the physics -dynamics coupling: (1) the order in which the physics parametrization and the dynamics are called and coupled inside the time-step computation, (2) the space-time location of the physics coupling on the semi-Lagrangian trajectory, (3) parallel or sequential time stepping of the different physics parametrizations and (4) parallel or sequential physics -dynamics coupling. It is found that according to this classification, IFS on the one hand and the ARPEGE/ALADIN/AROME models on the other hand exhibit two distinct structures.In the models, the dynamical cores of the semi-implicit semi-Lagrangian two-time-level schemes are linearized around a stationary reference state. This state differs from the real atmospheric state (i.e. the exact solution of the equations). This article generalizes the framework introduced by Staniforth, Wood and Côté to study the relation between the coupled physics parametrization and such reference and atmospheric states. Subsequently, the two above-mentioned time-step organizations are translated into this simplified frame. Extra degrees of freedom are added to allow for obvious improvements of the existing spectral time-step organizations. In order to deal with the complexity of the emerging structures and to avoid tedious algebraic manipulations, a numerical methodology is proposed to characterize their properties. This framework is then used to make a comparative study of the numerical stability and the accuracy of the physics -dynamics coupling within the two above-mentioned time-step organizations. Potential improvements are briefly discussed.

show abstract

“…Also, if the sequential scheme is run without any additional forcings besides S, the step (8) always directly follows step (10), except for the first and the last time step of the integration. However, following Caya et al (1998), the properties of these schemes will be determined with respect to their steady-state solution and, as will be shown below, these will be different for different values of η. Due to the nonlinearity and issues of stability, the updating of the damping is usually performed at least in a partly implicit way.…”

Section: Fractional Time-stepping Schemes For the Nonlinear Diffusionmentioning

confidence: 99%

On the role of tuning in parametrizations of unresolved diffusive processes in atmospheric models

Termonia

Smet

Bergh

2012

Quart J Royal Meteoro Soc

View full text Add to dashboard Cite

Consequences of Using the Splitting Method for Implementing Physical Forcings in a Semi-Implicit Semi-Lagrangian Model

Cited by 35 publications

References 11 publications

A monotonically‐damping second‐order‐accurate unconditionally‐stable numerical scheme for diffusion

A monotonically‐damping second‐order‐accurate unconditionally‐stable numerical scheme for diffusion

Stability and accuracy of the physics—dynamics coupling in spectral models

On the role of tuning in parametrizations of unresolved diffusive processes in atmospheric models

Contact Info

Product

Resources

About