dc.contributor.author | Lervåg, Karl Yngve | nb_NO |
dc.date.accessioned | 2014-12-19T11:50:48Z | |
dc.date.available | 2014-12-19T11:50:48Z | |
dc.date.created | 2013-09-17 | nb_NO |
dc.date.issued | 2013 | nb_NO |
dc.identifier | 649166 | nb_NO |
dc.identifier.isbn | 978-82-471-4544-9 (printed version) | nb_NO |
dc.identifier.isbn | 978-82-471-4545-6 (electronic version) | nb_NO |
dc.identifier.uri | http://hdl.handle.net/11250/235170 | |
dc.description.abstract | This thesis considers in the first part the mathematical modelling of incompressible two-phase flow, in particular the calculation of interface curvatures and normal vectors with the level-set method. The main contribution is the development of two new numerical methods that enable a more robust calculation of the curvature and normal vectors in areas where the gradient of the level-set method is discontinuous.
Incompressible two-phase flow is in this thesis modelled by the Navier- Stokes equations with a singular source term at the interface between the phases. The singular source term leads to a set of interface jump conditions. These jump conditions are used in the ghost-fluid method to solve two-phase flow in a sharp manner. The interface position is captured and evolved in time with the level-set method. The Navier- Stokes equations for two-phase flow are solved with projection methods and discretized by finite differences in space and Runge-Kutta methods in time. The advective terms in the governing equations are discretized by a weighted essentially non-oscillatory scheme.
In the second part, the thesis considers the more general problem of solving partial-differential equations (PDEs) in complex geometries. An extension of a diffuse-domain method is presented, where the accuracy is improved by adding a correction term. The extension is derived for elliptic problems with Neumann and Robin boundary conditions. One of the advantages of the diffuse-domain methods is that they allow the use of standard tools and methods because they are based on solving PDEs reformulated in larger and regular domains. | nb_NO |
dc.language | eng | nb_NO |
dc.publisher | Norges teknisk-naturvitenskapelige universitet, Fakultet for ingeniørvitenskap og teknologi, Institutt for energi- og prosessteknikk | nb_NO |
dc.relation.ispartofseries | Doktoravhandlinger ved NTNU, 1503-8181; 2013:214 | nb_NO |
dc.relation.haspart | Lervåg, Karl Yngve. Calculation of interface curvature with the level-set method. MekIT’11: 171-187, 2011. | nb_NO |
dc.relation.haspart | Lervåg, Karl Yngve; Ervik, Åsmund. Curvature calculations for the level-set method. Proceedings of ENUMATH 2011: 209-217, 2013. <a href='http://dx.doi.org/10.1007/978-3-642-33134-3_23'>10.1007/978-3-642-33134-3_23</a>. | nb_NO |
dc.relation.haspart | Lervag, Karl Yngve; Mueller, Bernhard; Munkejord, Svend Tollak. Calculation of the interface curvature and normal vector with the level-set method. Computers & Fluids. (ISSN 0045-7930). 84: 218-230, 2013. <a href='http://dx.doi.org/10.1016/j.compfluid.2013.06.004'>10.1016/j.compfluid.2013.06.004</a>. | nb_NO |
dc.relation.haspart | Ervik, Å.; Lervåg, K. Y.; Munkejord, S. T.. A robust method for calculating interface curvature and normal vectors using an extracted local level set. . | nb_NO |
dc.relation.haspart | Lervåg, K. Y.; Lowengrub, J.. TOWARDS A SECOND-ORDER DIFFUSE-DOMAIN METHOD FOR SOLVING PDES IN COMPLEX GEOMETRIES. . | nb_NO |
dc.title | Calculation of interface curvatures with the level-set method for two-phase flow simulations and a second-order diffuse-domain method for elliptic problems in complex geometries | nb_NO |
dc.type | Doctoral thesis | nb_NO |
dc.contributor.department | Norges teknisk-naturvitenskapelige universitet, Fakultet for ingeniørvitenskap og teknologi, Institutt for energi- og prosessteknikk | nb_NO |
dc.description.degree | PhD i energi- og prosessteknikk | nb_NO |
dc.description.degree | PhD in Energy and Process Engineering | en_GB |