The solution of steady-state free surface problems by the finite element method

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dc.contributor.advisorReddy, B Dayaen_ZA
dc.contributor.authorChandrasiri, L H G Sen_ZA
dc.date.accessioned2016-02-29T12:00:54Z
dc.date.available2016-02-29T12:00:54Z
dc.date.issued1992en_ZA
dc.descriptionBibliography: pages 64-68.en_ZA
dc.description.abstractThis thesis is concerned with the development of a variational formulation for the problem of viscous incompressible free surface flows, and with the development and implementation of algorithms for the solution of this problem by finite elements. The study is restricted to two-dimensional steady problems. The approach differs from those in current use, in that it is based on a two-stage strategy suggested by theoretical (existence) studies of the problem. In the first stage the free surface is kept fixed and the resulting so-called auxiliary problem is solved. In the second stage the equation for the normal stress on the free surface is used to update the free surface. Both the auxiliary problem and the normal stress equation are formulated variationally; in the case of the latter problem the unknown variable is actually the slope of the free surface. Finite element approximations are used in both problems. Algorithms are developed for determining solutions at the two stages, and for the overall problem. The key example treated is the dieswell problem, for the plane and axisymmetric cases. Solutions obtained by the present method are presented, and compared with the solutions of others where available.en_ZA
dc.identifier.apacitationChandrasiri, L. H. G. S. (1992). <i>The solution of steady-state free surface problems by the finite element method</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/17333en_ZA
dc.identifier.chicagocitationChandrasiri, L H G S. <i>"The solution of steady-state free surface problems by the finite element method."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1992. http://hdl.handle.net/11427/17333en_ZA
dc.identifier.citationChandrasiri, L. 1992. The solution of steady-state free surface problems by the finite element method. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Chandrasiri, L H G S AB - This thesis is concerned with the development of a variational formulation for the problem of viscous incompressible free surface flows, and with the development and implementation of algorithms for the solution of this problem by finite elements. The study is restricted to two-dimensional steady problems. The approach differs from those in current use, in that it is based on a two-stage strategy suggested by theoretical (existence) studies of the problem. In the first stage the free surface is kept fixed and the resulting so-called auxiliary problem is solved. In the second stage the equation for the normal stress on the free surface is used to update the free surface. Both the auxiliary problem and the normal stress equation are formulated variationally; in the case of the latter problem the unknown variable is actually the slope of the free surface. Finite element approximations are used in both problems. Algorithms are developed for determining solutions at the two stages, and for the overall problem. The key example treated is the dieswell problem, for the plane and axisymmetric cases. Solutions obtained by the present method are presented, and compared with the solutions of others where available. DA - 1992 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1992 T1 - The solution of steady-state free surface problems by the finite element method TI - The solution of steady-state free surface problems by the finite element method UR - http://hdl.handle.net/11427/17333 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/17333
dc.identifier.vancouvercitationChandrasiri LHGS. The solution of steady-state free surface problems by the finite element method. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1992 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/17333en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherApplied Mathematicsen_ZA
dc.titleThe solution of steady-state free surface problems by the finite element methoden_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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