http://hdl.handle.net/1956/920 Search the Channel search http://bora.uib.no/simple-search http://hdl.handle.net/1956/2324 Title: Total Variation Regularization of Matrix-Valued Images <br/> <br/>Authors: Christiansen, Oddvar; Lee, Tin-Man; Lie, Johan; Sinha, Usha; Chan, Tony F. <br/> <br/>Abstract: We generalize the total variation restoration model, introduced by Rudin, Osher, and Fatemi in 1992, to matrix-valued data, in particular, to diffusion tensor images (DTIs). Our model is a natural extension of the color total variation model proposed by Blomgren and Chan in 1998. We treat the diffusion matrix D implicitly as the product D = LLT , and work with the elements of L as variables, instead of working directly on the elements of D. This ensures positive definiteness of the tensor during the regularization flow, which is essential when regularizing DTI.We perform numerical experiments on both synthetical data and 3D human brain DTI, and measure the quantitative behavior of the proposed model. Mon, 12 Mar 2007 22:58:59 GMT http://hdl.handle.net/1956/2289 Title: Thickness and weak integrability & approximation and u-ideals <br/> <br/>Authors: Abrahmsen, Trond Arnold Thu, 14 Jun 2007 22:58:59 GMT http://hdl.handle.net/1956/2232 Title: Two phase flow including interfacial area as a variable <br/> <br/>Authors: Nordhaug, Hans Fredrik; Dahle, Helge K.; Espedal, Magne S.; Gray, William G.; Celia, Michael A. <br/> <br/>Abstract: Based on the procedure of (Gray & Hassanizadeh 1998) we state macroscale conservation equations for multi phase flow in porous media including interfacial area as a variable. The phases we consider are a solid phase, a wetting phase and a non-wetting phase. Some modeling work is done to decide the functionality of the coefficients in the equations. In particular we construct constitutive relationships for the interfacial area as a function of saturation and capillary pressure, and the resistance terms. The final set of equations is reduced to a 2 x 2 system with the saturation and the interfacial area as independent variables. Some preliminary numerical experiments are reported. <br/> <br/>Description: In: Computational methods in water resources XIII : proceedings of the XIII International Conference on Computational Methods in Water Resources, Calgary, Alberta, Canada, 25-29 June 2000 / Laurence R Bentley (editor). pp: 231-238 Fri, 29 Oct 1999 22:58:59 GMT http://hdl.handle.net/1956/2231 Title: A Local Streamline Eulerian-Lagrangian Method for Two-Phase Flow <br/> <br/>Authors: Ask, A. K.; Dahle, Henrik K.; Karlsen, Kenneth Hvistendahl; Nordhaug, Hans Fredrik <br/> <br/>Abstract: A method for solving the saturation equation for two-phase now is presented. The method may be viewed as an operator splitting method or as an Eulerian-Lagrangian backtracking procedure or as a modi£ed method of characteristics. For each time step, the method consists of an advection step and a diffusion step. The advection step requires the tracking of streamlines locally around certain integration points. On each streamline we have to solve a nonlinear hyperbolic equation. This is done using a front tracking method. The solution from the tracking step is projected back onto a fixed grid, and we finally have to solve a parabolic heat-type equation. <br/> <br/>Description: In: Computational methods in water resources XIII : proceedings of the XIII International Conference on Computational Methods in Water Resources, Calgary, Alberta, Canada, 25-29 June 2000 / Laurence R Bentley (editor). pp:645-650 Fri, 29 Oct 1999 22:58:59 GMT http://hdl.handle.net/1956/2230 Title: Operator splitting methods for systems of convection-diffusion equations : nonlinear error mechanisms and correction strategies <br/> <br/>Authors: Karlsen, Kenneth Hvistendahl; Lie, K. A.; Natvig, J. R.; Nordhaug, Hans Fredrik; Dahle, Helge K. <br/> <br/>Abstract: Many numerical methods for systems of convection-diffusion equations are based upon an operator splitting formulation, where convective and diffusive forces are accounted for in separate substeps. We describe the nonlinear mechanism of the splitting error in such numerical methods in the onedimensional case, a mechanism that is intimately linked to the local linearizations introduced implicitly in the (hyperbolic) convection steps by the use of an entropy condition. For convection-dominated flows, we demonstrate that operator splitting methods typically generate a numerical widening of viscous fronts, unless the splitting step is of the same magnitude as the diffusion scale. To compensate for the potentially damaging splitting error, we propose a corrected operator splitting (COS) method for general systems of convection-diffusion equations with the ability of correctly resolving the nonlinear balance between the convective and diffusive forces. In particular, COS produces viscous shocks with correct structure also when the splitting step is large. A front tracking method for systems of conservation laws, which in turn relies heavily on a Riemann solver, constitutes an important part of our COS strategy. The proposed COS method is successfully applied to a system modelling two-phase, multicomponent flow in porous media and a triangular system modelling three-phase flow. <br/> <br/>Description: Authors final draft post-refereeing. Sun, 29 Oct 2000 22:58:59 GMT http://hdl.handle.net/1956/2201 Title: A pore network model for calculation of interfacial velocities <br/> <br/>Authors: Nordhaug, Hans Fredrik; Celia, Michael; Dahle, Helge K. <br/> <br/>Abstract: Two-phase flow in porous media is characterized by fluid-fluid interfaces that separate the fluid phases at the pore scale. These interfaces support pressure differences between phases, and their dynamics allow for saturation changes within the porous medium. Dynamic porescale network models allow interface dynamics to be modeled explicitly, such that each fluid-fluid interface within a network of pores is tracked explicitly in space and time. Because these models produce a detailed description of both phase and interface dynamics, results from these models can be averaged to provide values for many upscaled variables. These include nontraditional variables such as amounts of interfacial area, and volumeaveraged interfacial velocities. While these upscaled variables provide insights into the underlying dynamics of two-phase flow systems, they also allow new theories involving interfacial area to be tested directly. Results from a test of one such theory reveals that proposed constitutive equations involving interfacial velocities fail to match results from the network model for most cases considered. Therefore the macroscopic equations require additional development before they can be used for macro-scale simulations. <br/> <br/>Description: The authors final, peer-reviewed postprint version of the article. Tue, 29 Oct 2002 22:58:59 GMT http://hdl.handle.net/1956/2200 Title: A streamline front tracking method for two- and three-phase flow including capillary forces <br/> <br/>Authors: Berre, Inga; Dahle, Helge K.; Karlsen, Kenneth Hvistendahl; Nordhaug, Hans Fredrik <br/> <br/>Description: In: Contemporary Mathematics: Fluid flow and transport in porous media: mathematical and numerical treatment 295, Zhangxin Chen and Richard E. Ewing (Eds.), pp. 49-61. Mon, 29 Oct 2001 22:58:59 GMT http://hdl.handle.net/1956/2199 Title: Modeling of Multi Phase Flow in Porous Media : Operator Splitting, Front Tracking, Interfacial Area and Network Models <br/> <br/>Authors: Nordhaug, Hans Fredrik <br/> <br/>Abstract: In this work several new numerical methods and a new mathematical model related to multi phase flow in oil reservoirs have been developed, implemented and tested. The numerical difficulties in multi phase flow stem from the highly nonlinear nature of the equations. The solution can develop sharp fronts that travel through the reservoir. We have used front tracking to capture these fronts in our numerical methods. In addition corrected operator splitting for systems has been used and developed because of the advection dominated nature of the equations. The new mathematical model was developed to improve short comings of existing models and to include interfacial area as a new independent variable. Wed, 19 Dec 2001 22:58:59 GMT