2013
DOI: 10.1002/qj.2226
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Abstract: This article provides an intercomparison of the dispersive and diffusive properties of several standard numerical methods applied to the 1D linearized shallow‐water equations without the Coriolis term, including upwind and central finite‐volume, spectral finite‐volume, discontinuous Galerkin, spectral element, and staggered finite‐volume. All methods are studied up to tenth‐order accuracy, where possible. A consistent framework is developed which allows for direct intercomparison of the ability of these method… Show more

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Cited by 27 publications
(21 citation statements)
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“…In the context of the geophysical flows, several previous works have conducted linearized analyses of high-order numerical schemes in 1-D and 2-D (Eldred & Le Roux, 2018;Giraldo, 2014;Kent et al, 2014;Lauritzen, 2007;Randall, 1994;Skamarock, 2008;Staniforth et al, 2013;Ullrich, 2014). Historically, in numerical weather prediction and climate simulation, the unstaggered grid is considered a poor choice because it is believed to have significant dispersion errors for short wavelength modes.…”
Section: Introductionmentioning
confidence: 99%
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“…In the context of the geophysical flows, several previous works have conducted linearized analyses of high-order numerical schemes in 1-D and 2-D (Eldred & Le Roux, 2018;Giraldo, 2014;Kent et al, 2014;Lauritzen, 2007;Randall, 1994;Skamarock, 2008;Staniforth et al, 2013;Ullrich, 2014). Historically, in numerical weather prediction and climate simulation, the unstaggered grid is considered a poor choice because it is believed to have significant dispersion errors for short wavelength modes.…”
Section: Introductionmentioning
confidence: 99%
“…Traditional linearized analysis shows the unstaggered schemes have the worst performance in resolving the grid-scale processes because such waves are almost stationary. This work follows the numerical analyses of Ullrich (2014) and of Kent et al (2014) and focuses on the role of the grid staggering choices to both dispersion and dissipation properties of high-order schemes and how the diffusion mechanisms alter them. Therefore, it is natural to perform the Von Neumann analysis on high-order LMARS to examine if any adverse dispersion property suggested by the traditional perception exists.…”
Section: Introductionmentioning
confidence: 99%
“…Second, as observed by Thuburn and Woollings (2005), Thuburn (2006), and Toy and Randall (2007), the choice of vertical coordinate (whether height based, mass based or entropy based) implies an optimal vertical staggering of prognostic variables for maintaining correct behavior for wave motions relevant to the atmosphere. Third, unstaggered discretizations (that is, discretizations where all prognostic variables are stored on model levels) possess stationary computational modes, which represent gross errors in the dispersion properties of the solution (Melvin et al, 2012;Ullrich, 2014b). As in the horizontal, unstaggered Finite Element Method (FEM) leads to waves with zero phase speed in the limit as the wavelength tends to 2 x, where x is the average grid spacing between degrees of freedom.…”
Section: Introductionmentioning
confidence: 99%
“…A thorough investigation of different values of n p would greatly extend the length of the manuscript, so n p was chosen in accordance with the Community Atmosphere Model spectral element dynamical core. As argued by Ullrich (2013), this choice is also optimal when considering the accurate treatment of linear waves.…”
Section: Resultsmentioning
confidence: 99%