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Spectral methods for limited area models

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dc.contributor.authorFulton, Scott R., author
dc.date.accessioned2022-05-27T21:21:00Z
dc.date.available2022-05-27T21:21:00Z
dc.date.issued1984-11
dc.descriptionNovember 1984.
dc.descriptionAlso issued as author's dissertation (Ph.D.) -- Colorado State University, 1984.
dc.description.abstractThis study investigates the usefulness of Chebyshev spectral methods in limited area atmospheric modeling. Basic concepts of spectral methods and properties of Chebyshev polynomials are reviewed. Chebyshev spectral methods are illustrated by applying them to the linear advection equation in one dimension. Numerical results demonstrate the high accuracy obtained compared to finite difference methods. The nonlinear shallow water equations on a bounded domain in two dimensions are then considered as a more realistic prototype model. Characteristic boundary conditions based on Reimann invariants are developed, and contrasted with wall conditions and boundary conditions based on the assumption of balanced flow. Chebyshev tau and collocation methods are developed for this model. Results from one-dimensional tests show the superiority of the characteristic conditions in most situations. Results from two-dimensional tests are also presented. Comparison of the tau and collocation methods shows that each has its own advantages and both are practical. Time differencing schemes for Chebyshev spectral methods are studied. The stability condition obtained with explicit time differencing, often thought to be "severe", is shown to be less severe than the corresponding condition for finite difference methods. Numerical results and asymptotic estimates show that time steps may in fact be limited by accuracy rather than stability, in which case simple explicit time differencing is practical and efficient. ยท,Two modified explicit schemes are reviewed, and implicit time differencing is also discussed. The results of this study indicate that Chebyshev spectral methods are a practical alternative to finite difference methods for limited area modeling, especially when high accuracy is desired. Spectral methods require less storage than finite difference methods, are more efficient when high enough accuracy is desired, and are at least as easy to program.
dc.description.sponsorshipSponsored by the National Science Foundation under grant ATM-8207563, and the Office of Naval Research under grant N00014-84-C-0591.
dc.format.mediumreports
dc.identifier.urihttps://hdl.handle.net/10217/235139
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartofAtmospheric Science Papers (Blue Books)
dc.relation.ispartofAtmospheric science paper, no. 384
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subject.lcshMeteorology -- Mathematical models
dc.subject.lcshNumerical weather forecasting
dc.subject.lcshChebyshev polynomials
dc.titleSpectral methods for limited area models
dc.typeText
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