A Lagrangian particle/panel method for the barotropic vorticity equations on a rotating sphere

Bosler, Peter Andrew; Wang, Lei; Jablonowski, Christiane; Krasny, Robert

doi:10.1088/0169-5983/46/3/031406

Cited by 15 publications

(13 citation statements)

References 36 publications

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“…Using this procedure he concluded that the emergent noise in his model was due to a small but significant divergence field missing from the initial fields. Even though the solutions of the non-divergent barotropic vorticity equation are not solutions of the shallow-water equations (SWEs), Phillips' procedure was adopted by Williamson et al (1992) as a standard test case for shallow-water models and has been extensively used ever since (Jablonowski et al, 2009;Mohammadian and Marshall, 2010;Bosler et al, 2014;Ullrich, 2014;Li et al, 2015, are only five recent examples).…”

Section: Introductionmentioning

confidence: 99%

The Matsuno baroclinic wave test case

et al. 2019

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Abstract. The analytic wave solutions obtained by Matsuno (1966) in his seminal work on equatorial waves provide a simple and informative way of assessing the performance of atmospheric models by measuring the accuracy with which they simulate these waves. These solutions approximate the solutions of the shallow-water equations on the sphere for low gravity-wave speeds such as those of the baroclinic modes in the atmosphere. This is in contrast to the solutions of the non-divergent barotropic vorticity equation, used in the Rossby–Haurwitz test case, which are only accurate for high gravity-wave speeds such as those of the barotropic mode. The proposed test case assigns specific values to the wave parameters (gravity-wave speed, zonal wave number, meridional wave mode and wave amplitude) for both planetary and inertia-gravity waves, and suggests simple assessment criteria suitable for zonally propagating wave solutions. The test is successfully applied to a spherical shallow-water model in an equatorial channel and to a global-scale model. By adding a small perturbation to the initial fields it is demonstrated that the chosen initial waves remain stable for at least 100 wave periods. The proposed test case can also be used as a resolution convergence test.

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Section: Introductionmentioning

confidence: 99%

The Matsuno baroclinic wave test case

et al. 2019

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“…It has been introduced by [25] with a forward (explicit) and a backward (implicit) version, the latter being widely used in geosciences for global computations [94,64,80,86,84] and also in plasma dynamics [30,20,85,52]. Advection dominated problems, such as passive scalar transport, are good candidates for forward semi-Lagrangian approaches; e.g., methods have been recently proposed for weather or climate forecasts [22,14]. In the context of a disperse phase of droplets or particles, semi-Lagrangian methods are attractive because they are naturally compatible with the weakly-coupled nature of the material elements that are transported; i.e., weak diffusion and collisions, and slow or zero-velocity waves allow the characteristics to remain fairly independent of each other.…”

Section: Introductionmentioning

confidence: 99%

“…These N p trivial linear extrapolations exactly solve the transport part of the kinetic equation in the context of operator splitting. 2a) Gather (projection) according to the mapping of Eq (14)…”

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confidence: 99%

A semi-Lagrangian transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows

Doisneau

Arienti

Oefelein

2017

Journal of Computational Physics

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For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier-Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the Eulerian formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-Lagrangian schemes, developed for Gas Dynamics. We show how semi-Lagrangian formulations are relevant for a disperse phase far from equilibrium and where the particle-particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of Eulerian fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.

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“…Instead he only examined qualitatively the spatial and temporal smoothness of his results and concluded that the emergent noise (manifested in the form of inertia-gravity (IG) waves) resulted from a small but significant divergence field that was missing from the initial conditions. Phillips' procedure was adopted by Williamson et al as part of their suite of test cases for numerical approximations of the SWEs and have been frequently used since (Jablonowski et al, 2009;Mohammadian and Marshall, 2010;Bosler et al, 2014;Ullrich, 2014;Li et al, 2015, are only five recent examples).…”

Section: Introductionmentioning

confidence: 99%

A quantitative test case for global‐scale dynamical cores based on analytic wave solutions of the shallow‐water equations

Shamir

Paldor

2016

Quart J Royal Meteoro Soc

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Recently derived analytic wave solutions of the shallow‐water equations (SWEs) on the rotating spherical Earth are employed to construct a test case for hydrostatic dynamical cores of global‐scale general circulation models (GCMs). The proposed test case is more relevant to the SWEs than the frequently used Rossby–Haurwitz test case which is based on wave solutions of the non‐divergent barotropic vorticity equation and not the SWEs. The applicability of the proposed test case to operational GCMs is demonstrated by using the spectral Eulerian dynamical core of the atmospheric component of NCAR's Community Earth System Model to simulate the analytic solutions. An initial slowly propagating Rossby wave and a fast eastward propagating inertia–gravity wave are both accurately simulated for 100 wave periods. In order to quantify the accuracy of the simulations, two error‐measures are suggested which complement the conservation of global energy and, unlike the frequently used L2 error‐measure, provide independent assessments of the errors in the phase speeds and the meridional structures of the simulated waves and are therefore more relevant to periodic wave solutions.

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A Lagrangian particle/panel method for the barotropic vorticity equations on a rotating sphere

Cited by 15 publications

References 36 publications

The Matsuno baroclinic wave test case

The Matsuno baroclinic wave test case

A semi-Lagrangian transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows

A quantitative test case for global‐scale dynamical cores based on analytic wave solutions of the shallow‐water equations

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