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

Gerber, George (2004-04)

Thesis (MScEng)--University of Stellenbosch, 2004.

Thesis

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.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/50214

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