A standard test set for numerical approximations to the shallow water equations in spherical geometry

Williamson, David L.; Drake, John B.; Hack, James J.; Jakob, Rüdiger; Swarztrauber, Paul N.

doi:10.1016/s0021-9991(05)80016-6

Cited by 779 publications

(575 citation statements)

References 17 publications

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“…sin Â + ∇ × V is the absolute vorticity. Details on the other forms of writing the SW equations and their development can be found in References [57,58].…”

Section: Extension To 2-d: Global Shallow Water Equations Modelmentioning

confidence: 99%

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A comparative study of the performance of high resolution advection schemes in the context of data assimilation

Akella

Navon

2006

Int. J. Numer. Meth. Fluids

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SUMMARYHigh resolution advection schemes have been developed and studied to model propagation of ows involving sharp fronts and shocks. So far the impact of these schemes in the framework of inverse problem solution has been studied only in the context of linear models. A detailed study of the impact of various slope limiters and the piecewise parabolic method (PPM) on data assimilation is the subject of this work, using the nonlinear viscous Burgers equation in 1-D. Also provided are results obtained in 2-D using a global shallow water equations model. The results obtained in this work may point out to suitability of these advection schemes for data assimilation in more complex higher dimensional models.

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“…sin Â + ∇ × V is the absolute vorticity. Details on the other forms of writing the SW equations and their development can be found in References [57,58].…”

Section: Extension To 2-d: Global Shallow Water Equations Modelmentioning

confidence: 99%

“…A suite of several test cases that have been widely used to compare di erent algorithmic formulations and numerical schemes for the SW equations was suggested by Williamson et al [57]. Therefore, results obtained from these tests could be used as a guide towards developing more complex models in higher dimensions.…”

Section: Case 3: 2-d Global Sw Equationsmentioning

confidence: 99%

A comparative study of the performance of high resolution advection schemes in the context of data assimilation

Akella

Navon

2006

Int. J. Numer. Meth. Fluids

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“…In addition, formulas involving the two coordinates are often not symmetric which means the flow is not isodirectional; this is certainly the case for standard lat-lon schemes (Williamson et al, 1992) or spectral harmonic schemes (Temperton, 1991); (Swarztrauber, 1993).…”

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confidence: 99%

“…Computations are performed on local spherical coordinates or on the local tangent plane after which the horizontal velocity components are resurrected or time integrated by manipulating spatial derivatives of scalar quantities; spatial derivatives of vector components are not needed. Such forms include vector-invariant (Ringler et al, 2010), vorticity-divergence (Williamson et al, 1992), or stream function and velocity potential (Masuda and Ohnishi, 1986), but the equations and pro-20 gramming can be complex.…”

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confidence: 99%

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Symmetric Equations on the Surface of a Sphere as Used by Model GISS:IB

Russell¹,

Rind²,

Jonas³

2018

Preprint

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Abstract. Standard vector calculus formulas of Cartesian three space are projected onto the surface of a sphere. This produces symmetric equations with three nonindependent horizontal velocity components. Each orthogonal axis has a velocity component that rotates around its axis (eastward velocity rotates around the north-south axis) and a specific angular momentum component that is the product of the velocity component times the cosine of axis' latitude. Angular momentum components align with the fixed axes and simplify several formulas, whereas the rotating velocity components are not orthogonal and vary 5 with location. Three symmetric coordinates allow vector resolution and calculus operations continuously over the whole spherical surface, which is not possible with only two coordinates. The symmetric equations are applied to one-layer shallow water models on cubed-sphere and icosahedral grids, the latter being computationally simple and applicable to an ocean domain.Model results are presented for three different initial conditions and five different resolutions.

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Performance modeling for SPMD message-passing programs

Brehm

Worley

Madhukar

1998

Concurrency: Pract. Exper.

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Today's massively parallel machines are typically message-passing systems consisting of hundreds or thousands of processors. Implementing parallel applications efficiently in this environment is a challenging task, and poor parallel design decisions can be expensive to correct. Tools and techniques that allow the fast and accurate evaluation of different parallelization strategies would significantly improve the productivity of application developers and increase throughput on pardel architectures. This paper investigates one of the major issues in building tools to compare parallelization strategies: determining what type of performance models of the application code and of the computer system are sufficient for a fast and accurate comparison of different strategies. The paper is built around a case study employing the Performance Prediction Tool (PerPreT) to predict performance of the Parallel Spectral Transform Shallow Water Model code (PSTSWM) on the Intel Paragon.PSTSWM is a parallel application code that was designed to evaluate different pard e l strategies for the spectral transform method as it is used in climate modeling and weather forecasting. Multiple parallel algorithms and algorithm variants are embedded in the code. PerPreT uses a relatively simple algebraic model to predict execution time for SPMD (Single Program Multiple Data) parallel applications. Applications are modeled through parameterized formulae for communication and computation, where the parameters include the problem size, the number of processors used to execute the program, and system characteristics (e+, setup times for communication, link bandwidth, and sustained computing performance per processor).In this paper we describe performance models that predict the performance of the different algorithms in PSTSWM accurately enough to allow them to be compared, establishing the feasibility of such a demanding application of performance modeling. We also discuss issues in generating and validating the performance models, emphasizing the practical importance of tools such as PerPreT in such studies.

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A standard test set for numerical approximations to the shallow water equations in spherical geometry

Cited by 779 publications

References 17 publications

A comparative study of the performance of high resolution advection schemes in the context of data assimilation

A comparative study of the performance of high resolution advection schemes in the context of data assimilation

Symmetric Equations on the Surface of a Sphere as Used by Model GISS:IB

Performance modeling for SPMD message-passing programs

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