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dc.contributor.authorBerthelsen, Petter Andreasnb_NO
dc.date.accessioned2014-12-19T11:43:44Z
dc.date.available2014-12-19T11:43:44Z
dc.date.created2004-11-19nb_NO
dc.date.issued2004nb_NO
dc.identifier124946nb_NO
dc.identifier.isbn82-471-6503-1nb_NO
dc.identifier.urihttp://hdl.handle.net/11250/233379
dc.description.abstractThis thesis deals with the construction of a numerical method for solving two-dimensional elliptic interface problems, such as fully developed stratified flow in pipes. Interface problems are characterized by its non-smooth and often discontinuous behaviour along a sharp boundary separating the fluids or other materials. Classical numerical schemes are not suitable for these problems due to the irregular geometry of the interface. Standard finite difference discretization across the interface violates the interfacial boundary conditions; therefore special care must be taken at irregular grid nodes. In this thesis a decomposed immersed interface method is presented. The immersed interface method is a numerical technique formulated to solve partial differential equations in the presence of an interface where the solution and its derivatives may be discontinuous and non-smooth. Componentwise corrections terms are added to the finite difference stencil in order to make the discretization well-defined across the interface. A method that approximates the correction terms is also proposed. Results from numerical experiments show that the rate of convergence is approximately of second order. Moreover, the immersed interface method is applied to stratified multiphase flow in pipes. The flow is assumed to be fully developed and in steady-state. For turbulent flow, both a low Reynolds number turbulence model and a two-layer turbulence model are adopted in order to imitate turbulence in the flow field and in the vicinity of the boundaries. The latter turbulence model is modified accordingly to account for the effects of a wavy interface. In this case, the concept of interfacial roughness is used to model the wavy nature of the interface. Numerical results are compared with analytical solutions for laminar flow and experimental data for turbulent flow. It is also demonstrated that the current numerical method offers more flexibility in simulating stratified pipe flow problems with complex shaped interfaces, including three-phase flow, than seen in any previous approach.nb_NO
dc.languageengnb_NO
dc.publisherFakultet for ingeniørvitenskap og teknologinb_NO
dc.relation.ispartofseriesDoktoravhandlinger ved NTNU, 1503-8181; 2004:139nb_NO
dc.relation.haspartBerthelsen, PA. A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions. Journal of Computational Physics. 197(1): 364-386, 2004.nb_NO
dc.relation.haspartBerthelsen, PA; Ytrehus, T. Stratified smooth two-phase flow using the immersed interface method. Computers & Fluids, 2004.nb_NO
dc.relation.haspartBerthelsen, PA; Ytrehus, T. Numerical modelling of stratified turbulent two- and three-phase pipe flow with arbitrary shaped interfaces, Presented at The 5th International Conference on Multiphase Flow, ICMF’04, Yokohama, Japan, May 30–June 4. .nb_NO
dc.relation.haspartBerthelsen, PA; Ytrehus, T. Calculations of stratified wavy two-phase flow in pipes. International Journal of Multiphase Flow, 2004.nb_NO
dc.subjectEnergy- and processengineeringen_GB
dc.titleAn immersed interface method for two-dimensional modelling of stratified flow in pipesnb_NO
dc.typeDoctoral thesisnb_NO
dc.source.pagenumber108nb_NO
dc.contributor.departmentNorges teknisk-naturvitenskapelige universitet, Fakultet for ingeniørvitenskap og teknologi, Institutt for energi- og prosessteknikknb_NO
dc.description.degreePhD i energi- og prosessteknikknb_NO
dc.description.degreePhD in Energy and Process Engineeringen_GB


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