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Application of the GRP scheme to open channel flow equations

Birman, A; Falcovitz, J.

Description

The GRP (generalized Riemann problem) scheme, originally conceived for gasdynamics, is reformulated for the numerical integration of the shallow water equations in channels of rectangular cross-section, variable width and bed profile, including a friction model for the fluid-channel shear stress. This scheme is a second-order analytic extension of the first-order Godunov-scheme, based on time-derivatives of flow variables at cell-interfaces resulting from piecewise-linear data reconstruction in...[Show more]

dc.contributor.authorBirman, A
dc.contributor.authorFalcovitz, J.
dc.date.accessioned2015-12-10T21:56:25Z
dc.identifier.issn0021-9991
dc.identifier.urihttp://hdl.handle.net/1885/39419
dc.description.abstractThe GRP (generalized Riemann problem) scheme, originally conceived for gasdynamics, is reformulated for the numerical integration of the shallow water equations in channels of rectangular cross-section, variable width and bed profile, including a friction model for the fluid-channel shear stress. This scheme is a second-order analytic extension of the first-order Godunov-scheme, based on time-derivatives of flow variables at cell-interfaces resulting from piecewise-linear data reconstruction in cells. The second-order time-integration is based on solutions to generalized Riemann problems at cell-interfaces, thus accounting for the full governing equations, including source terms. The source term due to variable bed elevation is treated in a well-balanced way so that quiescent flow is exactly replicated; this is done by adopting the Surface Gradient Method (SGM). Several problems of steady or unsteady open channel flow are considered, including the terms corresponding to variable channel width and bed elevation, as well as to shear stress at the fluid-channel interface (using the Manning friction model). In all these examples remarkable agreement is obtained between the numerical integration and the exact or accurate solutions.
dc.publisherAcademic Press
dc.sourceJournal of Computational Physics
dc.subjectKeywords: Generalized Riemann problem (GRP); Hydraulic jump; Hyperbolic conservation laws; Open channel; Quasi-1D flow; Second-order scheme; Shallow water
dc.titleApplication of the GRP scheme to open channel flow equations
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume222
dc.date.issued2007
local.identifier.absfor010399 - Numerical and Computational Mathematics not elsewhere classified
local.identifier.ariespublicationU1408929xPUB177
local.type.statusPublished Version
local.contributor.affiliationBirman, A, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationFalcovitz, J., Hebrew University of Jerusalem
local.description.embargo2037-12-31
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage131
local.bibliographicCitation.lastpage54
local.identifier.doi10.1016/j.jcp.2006.07.008
dc.date.updated2015-12-09T07:37:24Z
local.identifier.scopusID2-s2.0-33846842247
CollectionsANU Research Publications

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