As an applied mathematician, my main research interest is to facilitate enhanced understanding of nature by the development mathematical models for physical phenomena, analysis of the resulting equations, and the construction of numerical solution algorithms for the problems. My main focus is on porous media, as this contains problems of high societal importance such as subsurface processes (energy extraction and waste disposal) and biological flow, and also lead to interesting and challenging mathematical problems. However, my research interest also includes elasticity, geo- and hydro-mechanics.
Specific research fields that I am involved in include:
- Geothermal energy, including both fluid flow and coupling of flow and geo-mechanics.
- Multiscale approaches to porous media flow, including both modeling and numerical methods.
- Design of linear and non-linear solvers, with focus on exploiting physical properties of the underlying equations to improve the numerical methods.
- 2018. Dual virtual element method for discrete fractures networks. SIAM Journal on Scientific Computing. 40: B228-B258. doi: 10.1137/16M1098231
- 2018. Finite-volume discretisations for flow in fractured porous media. Transport in Porous Media. 124: 439-462. doi: 10.1007/s11242-018-1077-3
- 2018. Three-Dimensional Numerical Modeling of Shear Stimulation of Fractured Reservoirs. Journal of Geophysical Research - Solid Earth. 123: 3891-3908. doi: 10.1029/2017JB015241
- 2018. A finite-volume discretization for deformation of fractured media. Computational Geosciences. 22: 993-1007. doi: 10.1007/s10596-018-9734-8
- 2017. Fractal structures in freezing brine. Journal of Fluid Mechanics. 826: 975-995. doi: 10.1017/jfm.2017.472
- 2017. Finite volume methods for elasticity with weak symmetry. International Journal for Numerical Methods in Engineering. 112: 939-962. doi: 10.1002/nme.5538
- 2017. Heterogeneity preserving upscaling for heat transport in fractured geothermal reservoirs. Computational Geosciences. 22: 451-467. doi: 10.1007/s10596-017-9704-6
- 2017. High-accuracy phase-field models for brittle fracture based on a new family of degradation functions. Journal of the mechanics and physics of solids. 111: 458-489. doi: 10.1016/j.jmps.2017.10.015
- 2017. Postinjection normal closure of fractures as a mechanism for induced seismicity. Geophysical Research Letters. 44: 9598-9606. doi: 10.1002/2017GL074282
- 2016. A multiscale multilayer vertically integrated model with vertical dynamics for CO2 sequestration in layered geological formations. Water resources research. 52: 6490-6505. doi: 10.1002/2016WR018714
- 2016. The effect of deformation bands on simulated fluid flow within fault-propagation fold trap types: Lessons from the San Rafael monocline, Utah. American Association of Petroleum Geologists Bulletin. 100: 1523-1540. doi: 10.1306/04151614153
- 2015. Hvordan håndtere usikkerhet ved CO2-lagring. Bergens Tidende. Published 2015-04-20.
- 2015. Inexact linear solvers for control volume discretizations in porous media. Computational Geosciences. 19: 159-176. doi: 10.1007/s10596-014-9453-8
- 2015. Two-scale preconditioning for two-phase nonlinear flows in porous media. Transport in Porous Media. 114: 485-503. doi: 10.1007/s11242-015-0587-5
- 2014. Analysis of control volume heterogeneous multiscale methods for single phase flow in porous media. Multiscale Modeling & simulation. 12: 335-363. doi: 10.1137/120885541
- 2014. Application of Vertically-Integrated Models with Subscale Vertical Dynamics to Field Sites for CO2 Sequestration. Energy Procedia. 63: 3523-3531. doi: 10.1016/j.egypro.2014.11.381
- 2014. Sprekker er nøkkelen til dyp jordvarme. Bergens Tidende.
- 2014. Conservative inexact solvers for porous media flow. Lecture Notes in Computational Science and Engineering. 98: 333-340. doi: 10.1007/978-3-319-05789-7_30
- 2014. Physics-based preconditioners for flow in fractured porous media. Water resources research. 50: 1357-1373. doi: 10.1002/2012WR013034
- 2013. Deformation bands and their impact on fluid flow in sandstone reservoirs: the role of natural thickness variations. Geofluids. 13: 359-371. doi: 10.1111/gfl.12030
- 2013. Auxiliary variables for 3D multiscale simulations in heterogeneous porous media. Journal of Computational Physics. 238: 141-153. doi: 10.1016/j.jcp.2012.12.016
- 2013. Domain decomposition strategies for nonlinear flow problems in porous media. Journal of Computational Physics. 234: 439-451. doi: 10.1016/j.jcp.2012.10.001
- 2012. Multidimensional upstream weighting for multiphase transport on general grids. Computational Geosciences. 16: 1021-1042. doi: 10.1007/s10596-012-9301-7
- 2012. Tensor relative permeabilities: Origin, modeling and numerical discretization. International Journal of Numerical Analysis & Modeling. 9: 701-724.
- 2010. Simulation of anisotropic heterogeneous near-well flow using MPFA methods on flexible grids. Computational Geosciences. 14: 509-525. doi: 10.1007/s10596-009-9167-5
- 2010. Robust Control Volume Methods for Reservoir Simulation on Challenging Grids. 200 pages.
- 2018. Three-dimensional numerical modelling of fracture reactivation due to fluid injection in geothermal reservoirs. artikkel. In:
- 2018. 52nd US Rock Mechanics / Geomechanics Symposium, 17-20 June 2018, Seattle, Washington. American Rock Mechanics Association (ARMA). ISBN: 978-0-9794975-3-7.
- 2016. Modelling of the Shear Dilation Based Hydraulic Stimulation in Enhanced Geothermal Systems Considering Fractures in Different Scales. Geophysics (methodology, general). In:
- 2016. EGC2016 proceedings. 500 pages. ISBN: 978-2-9601946-0-9.
- 2015. Simulation of Slip-Induced Permeability Enhancement Accounting For Multiscale Fractures. Enhanced Geothermal Systems. In:
- 2015. 40th Workshop on Geothermal Reservoir Engineering 2015. Curran Associates, Inc.. 1254 pages. ISBN: 978-1-5108-0274-2.
- 2013. Multiscale simulation of flow and heat transport in fractured geothermal reservoirs: inexact solvers and improved transport upscaling. Modeling. In:
- 2013. Proceedings of the 38th Workshop on Geothermal Reservoir Engineering 2013. 1741 pages. ISBN: 9781627485708.
- 2012. MULTISCALE SIMULATION OF NON-DARCY FLOWS. MULTISCALE SIMULATION OF NON-DARCY FLOWS, pages . In:
- 2006. Proceedings - CMWR XVI - Computational Methods in Water Resources.
- 2012. Mass conservative domain decomposition for porous media flow. Chapter 11, pages . In:
- 2012. Finite Volume Method. INTECH. 370 pages. ISBN: 978-953-51-0445-2.
- 2012. Mass Conservative Domain Decomposition for Fractured Porous Media. -. In:
- 2000. 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. The XIII international conference on computational methods in water resources, Calgary, Alberta, Canada. 700 pages.
- 2010. Monotone Multi-dimensional Upstream Weighting on General Grids. Artikkel. In:
- 2010. Conference Proceedings ECMOR XII. European Association of Geoscientists and Engineers. 1000 pages. ISBN: 9789073781894.
- 2010. A Multiscale Framework for Simulating Multi-phase Flow on Flexible Grids. Artikkel. In:
- 2008. Monotonicity for control volume methods on unstructured grids. artikkel, pages . In:
- 2008. Proceedings of the 11th European Conference on the Mathematics of Oil Recovery. European Association of Geoscientists and Engineers. 1050 pages. ISBN: 9789073781559.
- 2008. Discretization schemes for anisotropic heterogeneous problems on near-well grids. artikkel, pages . In:
- B. Gou, K.W. Bandilla, F. Doster, E. Keilegavlen, M.A. Celia: A Vertically-integrated Model with Vertical Dynamics for CO2 Storage, Water Resources Research, submitted.
- T.H. Sande, I. Berre, E. Keilegavlen, J.M. Nordbotten: An automated MINC method for simulation of heat transport in fractured geothermal reservoirs, Mathematical Geosciences, submitted.
Peer reviewed publications:
- E. Keilegavlen, J.M. Nordbotten: Inexact linear solvers for control volume discretizations in porous media, Computational Geosciences, in press.
- T.H. Sandve, E. Keilegavlen, J.M. Nordbotten (2014): Physics-based preconditioners for flow in fractured porous media, Water Resources Research,, 50(2), 1357-1373.
- S. Alyaev, E. Keilegavlen, J. M. Nordbotten (2014): Analysis of control volume heterogeneous multiscale methods for single phase flow in porous media, SIAM Multiscale Modeling and Simulation, 12(1) 335-363. Preprint.
- A. Rotevatn, T.H. Sandve, E. Keilegavlen, D. Kolyukhin, H. Fossen (2013): Deformation bands and their impact on fluid flow in sandstone aquifers: the role of natural thickness variations, GeoFluids, 13 (3), 359-373.
- A. Sandvin, E. Keilegavlen, J. M. Nordbotten (2013): Auxiliary variables in multiscale simualtions, Journal of Computational Physics, 238, 141-153. Preprint.
- J.O. Skogestad, E. Keilegavlen, J. M. Nordbotten (2013): Domain Decomposition Strategies for Non-linear Flow Problems in Porous Media, Journal of Computational Physics, 234, 439-451. Preprint.
- E. Keilegavlen, J. Kozdon and B. Mallison (2012): Multi-dimensional upstream weighting for multi-phase flow on general grids, Computational Geosciences 16(4) 1021-1042. Preprint.
- E. Keilegavlen, J.M. Nordbotten, A. Stephansen (2012): Tensorial Relative Permeabilities: Origin, Modelling and Discretization, International Journal of Numerical Analysis and Modeling 9 (3), 701-724. Preprint.
- E. Keilegavlen and I. Aavatsmark (2011): Monotonicity for MPFA methods on triangular grids, Computational Geosciences 15 (1), 3-16.
- S. Mundal, E. Keilegavlen and I. Aavatsmark (2010): Simulation of Anisotropic Heterogeneous Near-well Flow using MPFA Methods on Flexible Grids, Computational Geosciences 14 (4), 509-525.
- E. Keilegavlen, J. M. Nordbotten and I. Aavatsmark. (2009): Sufficient monotonicity criteria are necessary for control volume methods, Applied Mathematical Letters 22 (8), 1178-1180. Preprint.
- E. Keilegavlen and J. Berntsen (2009): Non-hydrostatic pressure in sigma-coordinate ocean models, Ocean Modelling 28(4), 240-249. Preprint.
Peer reviewed book chapters:
- F. Doster, E. Keilegavlen, J.M. Nordbotten: A robust implicit pressure explicit mass method for multi-phase multi-component flow including capillary pressure and buoyancy. In Computational Methods for CO2 Geo-sequestration & Compressed Air Storage, Edited by Rafid Al-Khoury, Jochen BundSchuh, ISBN: 9781138015203, CRC Press.
- E. Keilegavlen, J.M. Nordbotten: Conservative inexact solvers for porous media flow, Proceedings of the 21st International Conference on Domain Decomposition Methods, to be published in Springer Lecture Notes in Computational Science and Engineering.
- J.M. Nordbotten, E. Keilegavlen, A. Sandvin (2011): Mass conservative domain decomposition for porous media flow, In: Finite Volume Method - Powerful Means of Engineering Design, Edited by PhD. Radostina Petrova, ISBN: 978-953-51-0445-2, InTech.
- E. Keilegavlen, J.O. Skogestad, J.M. Nordbotten (2014): Domain decomposition preconditioning for non-linear elasticity problems, Proceedings of 11th Word Congress of Computational Mechanics, Barcelona.
- T.H. Sandve, I. Berre, E. Keilegavlen, J.M. Nordbotten (2013): Multiscale simulation of flow and heat transport in fractured geothermal reservoirs: Inexact solvers and improved transport upscaling, Proceedings of the thirty-eight workshop on geothermal reservoir engineering, Stanford University.
- T.H. Sandve, E. Keilegavlen, J.M. Nordbotten (2012): Mass conservative domain decomposition for fractured porous media, Proceedings of the XIX International Conference on Water Resources (CMWR).
- S. Alyaev, E. Keilegavlen, J.M. Nordbotten (2012): Multiscale simulations of non-Darcy flows, Proceedings of CMWR XIX.
- E. Keilegavlen, J.M. Nordbotten, A. Stephansen (2011): Simulating two-phase flow in porous media with anisotropic relative permeabilities, Proceedings of SPE Reservoir Simulation Symposium, SPE 141552.
- E. Keilegavlen, J. Kozdon and B.T. Mallison (2010): Monotone Multi-dimensional Upstream Weighting on General Grids, Proceeding of the 12th European Conference on the Mathematics of Oil Recovery (ECMOR XII).
- A. Sandvin , J.O. Skogestad, E. Keilegavlen and J.M. Nordbotten (2010): A Multiscale Framework for Simulating Multi-phase Flow on Flexible Grids, Proceedings of ECMOR XII.
- H.M. Nilsen, P.A. Herrera, M. Ashraf, I. Ligaarden, M. Iding, C. Hermanrud, K.-A. Lie, J.M. Nordbotten, H.K. Dahle and E. Keilegavlen (2010): Field-case simulation of CO2-plume migration using vertical-equilibrium models, Proceedings of GHGT 10.
- P.A. Herrera , J.M. Nordbotten B.F. El-Faour, E. Keilegavlen and H.K. Dahle (2010): The impact of natural heterogeneity on CO2 migration in deep saline aquifers, Proceedings of British Hydrological Society International Symposium 2010.
- E. Keilegavlen and I. Aavatsmark (2008): Monotonicity for control volume methods on triangular grids, Proceedings of ECMOR XI.
- S. Mundal, E. Keilegavlen and I. Aavatsmark (2008): Discretisation schemes for anisotropic heterogeneous problems on near-well grids, Proceedings of ECMOR XI.
Stimulation of fracture networks via shear dilation: The project considers the coupling of porous media flow with geo-mechanics to investigate the opening of fractures during fluid injection. See the GeoStim project for more information.
Dynamic reconstruction models for the simulation of CO2 injection: The goal of this work is to extend the applicability of a popular class of methods that is tailored for simulating CO2 injection. This is joint work with researchers at Princeton University.
Inexact linear solvers and physics-based preconditioners for porous media flow: This has been a long ongoing effort which aims to design a holistic framework for solvers, upscaling and discretization based on control volume disrcetizations of porous media flow. Recent work considers the adaption of the framework to account for stochastic parameter fields.
Preconditioners for non-linear elasticity problems: The project considers the construction of non-linear preconditioning of Newton's method for the solution of problems in elasticity. Special attention is paid to the treatment of spatial scales.