dc.contributor.advisor Holden, Helge nb_NO dc.contributor.advisor Lie, Knut-Andreas nb_NO dc.contributor.advisor Krogstad, Stein nb_NO dc.contributor.author Haugland, Christine Marie Øvrebø nb_NO dc.date.accessioned 2014-12-19T13:59:51Z dc.date.available 2014-12-19T13:59:51Z dc.date.created 2012-11-08 nb_NO dc.date.issued 2012 nb_NO dc.identifier 566279 nb_NO dc.identifier ntnudaim:7359 nb_NO dc.identifier.uri http://hdl.handle.net/11250/259037 dc.description.abstract In this thesis we present the theoretical background for the two-point flux-approximation method; (TPFA), mimetic discretisation methods, and the multipoint flux approximation method; (MPFA). Theoretical arguments concerning monotonicity and the fact that loss of monotonicity may lead to oscillations and nonphysical cycles in the flux field are also discussed. TPFA is only consistent for $mathbf{K}$-orthogonal grids. Multipoint flux approximation methods and mimetic discretisation methods are consistent, even for grids that are not K-orthogonal, but sometimes they lead to solutions containing cycles in the flux field. These cycles may cause problems for some transport solvers and diminish the efficiency of others, and to try to cure this problem, we present two hybrid methods. The first is a hybrid mimetic method applying TPFA in the vertical direction and mimetic discretisation in the plane. The second hybrid method is the hybrid MPFA method applying TPFA in the vertical direction and MPFA in the plane. We present results comparing the accuracy of the methods and the number of cycles obtained by the different methods. The results obtained shows that the hybrid methods are more accurate than TPFA, and for specific cases they have less cycles than the original full methods. nb_NO dc.language eng nb_NO dc.publisher Institutt for matematiske fag nb_NO dc.subject ntnudaim:7359 no_NO dc.subject MTFYMA fysikk og matematikk no_NO dc.subject Industriell matematikk no_NO dc.title Applying hybrid methods to reduce nonphysical cycles in the flux field nb_NO dc.type Master thesis nb_NO dc.source.pagenumber 71 nb_NO dc.contributor.department Norges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fag nb_NO
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