## Unsteady pipe-flow using the Petrov-Galerkin finite element method

Thesis (MScEng)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: Presented here is an Eulerian scheme for solving the unsteady pipe-flow equations. It
is called the Characteristic Dissipative Petrov-Galerkin finite element algorithm. It is
based on Hicks and Steffler's open-channel finite element algorithm [5]. The algorithm
features a highly selective dissipative interface, which damps out spurious oscillations in
the pressure field while leaving the rest of the field almost unaffected. The dissipative
interface is obtained through upwinding of the test shape functions, which is controlled
by the characteristic directions of the flow field at a node. The algorithm can be applied
to variable grids, since the dissipative interface is locally controlled. The algorithm was
applied to waterhammer problems, which included reservoir, deadend, valve and pump
boundary conditions. Satisfactory results were obtained using a simple one-dimensional
element with linear shape functions. / AFRIKAANSE OPSOMMING: 'n Euleriese skema word hier beskryf om die onbestendige pypvloei differensiaal vergelykings
op te los. Dit word die Karakteristieke Dissiperende Petrov-Galerkin eindige element
algoritme genoem. Die algoritme is gebaseer op Hicks en Steffler se oop-kanaal eindige
element algoritme [5]. In hierdie algoritme word onrealistiese ossilasies in die drukveld
selektief gedissipeer, sonder om die res van die veld te beinvloed. Die dissiperende koppelvlak
word verkry deur stroomop weegfunksies, wat beheer word deur die karakteristieke
rigtings in die vloeiveld, by 'n node. Die algoritme kan dus gebruik word op veranderbare
roosters, omdat die dissiperende koppelvlak lokaal beheer word. Die algoritme was
toegepas op waterslag probleme waarvan die grenskondisies reservoirs, entpunte, kleppe
en pompe ingesluit het. Bevredigende resultate was verkry vir hierdie probleme, al was
die geimplementeerde element een-dimensioneel met lineere vormfunksies.

 Identifer oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/50214 Date 04 1900 Creators Gerber, George Contributors Maincon, Philippe, Stellenbosch University. Faculty of Engineering. Dept. of Civil Engineering. Publisher Stellenbosch : Stellenbosch University Source Sets South African National ETD Portal Language en_ZA Detected Language English Type Thesis Format 120 p. : ill. Rights Stellenbosch University

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