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Peer methods for the one-dimensional shallow-water equations with CWENO space discretization

  • For many practical problems an efficient solution of the one-dimensional shallow-water equations (Saint–Venant equations) is important, especially when large networks of rivers, channels or pipes are considered. In order to test and develop numerical methods four test problems are formulated. These tests include the well-known dam break and hydraulic jump problems and two steady state problems with varying channel bottom, channel width and friction. The space discretization of the partial differential equations is based on a finite volume approach with central WENO interpolation and local Lax–Friedrich fluxes (Kurganov and Levy, 2000) [7]. For time-integration new linearly-implicit two-step peer methods of orders three and four are developed. These methods are especially adapted to the usage within the method of lines framework. They show a good performance compared to the well-established methods like ode15s, radau5 or rodasp.

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Metadaten
Document Type:Article
Language:English
Parent Title (English):Applied Numerical Mathematics
Volume:62
Issue:10
First Page:1567
Last Page:1578
ISSN:0168-9274
DOI:https://doi.org/10.1016/j.apnum.2012.06.009
Publisher:Elsevier
Date of first publication:2012/06/06
Tag:Method of lines; Peer methods; Shallow-water equations; WENO schemes
Departments, institutes and facilities:Fachbereich Elektrotechnik, Maschinenbau, Technikjournalismus
Institut für Technik, Ressourcenschonung und Energieeffizienz (TREE)
Dewey Decimal Classification (DDC):5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Entry in this database:2015/04/02