In Journals
- J. Li, L. Zhao, O. Møyner, K.-A. Lie. A new near-wellbore
modeling method for deviated wells in corner-point grid. Advances in Geo-Energy
Research, 2025, 15(2):
112-128. DOI: 10.46690/ager.2025.02.04.
- B. Aslam, B. Yan, K.-A. Lie, S. Krogstad, O. Møyner, and X. He.
A novel hybrid physics/data-driven model for fractured reservoir simulation.
SPE Journal, 2024. DOI: 10.2118/219110-PA
- L. Salo-Salgado, O. Møyner, K.-A. Lie, and R. Juanes. Three-dimensional
simulation of geologic carbon dioxide sequestration using MRST. Advances in Geo-Energy Research,
2024. DOI: 10.46690/ager.2024.10.06.
- W. Xiong, L.-H. Zhang, Y.-L. Zhao, S.-M. Wen, K. Bao, O. Møyner,
and K.-A. Lie. Compositional simulation for carbon storage in porous media using
an electrolyte association equation of state. SPE Journal,
2024. DOI: 10.2118/219734-PA.
- J M. Nordbotten, M. A. Fernø, B. Flemisch, A. R. Kovscek, and K.-A. Lie.
The 11th Society of Petroleum Engineers Comparative Solution Project: Problem definition.
SPE Journal, 2024. DOI: 10.2118/218015-PA.
- K.-A. Lie and S. Krogstad. Data-driven modelling with coarse-grid
network models. Computational Geosciences, 2023.
DOI: 10.1007/s10596-023-10237-y.
- O. Møyner, A. F. Rasmussen, Ø. Klemetsdal, H. M. Nilsen,
A. Moncorgé, and K.-A. Lie. Nonlinear domain-decomposition preconditioning for
robust and efficient field-scale simulation of subsurface flow. Computational
Geosciences,
2023. DOI: 10.1007/s10596-023-10215-4
- K.-A. Lie and S. Krogstad. Comparison of two different types of
reduced graph-based reservoir models: Interwell networks (GPSNet) versus
aggregated coarse-grid networks (CGNet). Geoenergy Science and Engineering
Volume 221, February 2023, 111266. DOI:
10.1016/j.petrol.2022.111266.
- G. P. Oliveira, T. N. E. Rodrigues, and K.-A. Lie. GAWPS: A
MRST-based module for wellbore profiling and graphical analysis of flow
units. Advances in Geo-Energy Research, 2021, 6(1):
38-53. DOI: 10.46690/ager.2022.01.04.
- F. Watson, S. Krogstad, and K.-A. Lie. The use of flow diagnostics
to rank model ensembles. Computational Geosciences, 2021. In
press. DOI: 10.1007/s10596-021-10087-6.
- Ø. S. Klemetsdal, A. Moncorgé, H. M. Nilsen, O. Møyner, and
K.-A. Lie. An adaptive sequential fully implicit domain-decomposition
solver. SPE Journal,
2021. DOI: 10.2118/203991-PA
- S. Ma, B. Ju, L. Zhao, K.-A. Lie, Y. Dong, Q. Zhang, and
Y. Tian. Embedded discrete fracture modelling: flow diagnostics, non-Darcy flow,
and well placement optimization. Journal of Petroleum Science and Engineering,
Vol. 208, Part C, January 2022, 109477.
DOI: 10.1016/j.petrol.2021.109477.
Springer Share Link.
- Ø. S. Klemetsdal, A. Moncorgé, O. Møyner, and K-A. Lie. A numerical
study of the additive Schwarz preconditioned exact Newton method (ASPEN) as a
nonlinear preconditioner for immiscible and compositional porous media flow.
Computational Geosciences,
2021. DOI: 10.1007/s10596-021-10090-x
- Ø. S. Klemetsdal, O. Møyner, A. Moncorgé, H. M. Nilsen, and
K.-A. Lie. High-resolution compositional reservoir simulation with dynamic
coarsening and local timestepping for unstructured grids. SPE Journal, Vol. 26,
Issue 06, pp. 4157-4173, 2021. DOI:
10.2118/203982-PA
- X. Raynaud, A. Pizzolato, A. Johansson, F. Caresani, A. Ferrari,
O. Møyner, H. M. Nilsen, A. Cominelli, and K.-A. Lie. Toward accurate
reservoir simulations on unstructured grids: design of simple error estimators and
critical benchmarking of consistent discretization methods for practical
implementation. SPE Journal, , Vol. 26, Issue 06, pp. 4109-4127,2021. DOI:
10.2118/203920-PA.
- A. F. Rasmussen, T. H. Sandve, K. Bao, A. Lauser, J. Hove,
B. Skaflestad, R. Klöfkorn, M. Blatt, A. B. Rustad, O. Sævareid, K.-A. Lie,
A. Thune. The Open Porous Media Flow Reservoir Simulator. Computers and
Mathematics with Applications, Vol. 81, pp. 159-185, 2021.
DOI: 10.1016/j.camwa.2020.05.014.
- Ø. S. Klemetsdal and K.-A. Lie. Dynamic coarsening and local
reordered nonlinear solvers for simulating transport in porous media. SPE
Journal. Vol. 25, No. 4, pp. 2021-2040,
2021. DOI: 10.2118/201089-PA.
- G. Linga, O. Møyner, H.M. Nilsen, A. Moncorgé, and K.-A. Lie. An
implicit local time-stepping method based on cell reordering for multiphase flow
in porous media. Journal of Computational Physics: X, Vol. 6, March 2020, 100051. DOI:
10.1016/j.jcpx.2020.100051
- Ø. S. Klemetsdal, A. F. Rasmussen, O. Møyner, and K.-A. Lie.
Efficient reordered nonlinear Gauss-Seidel solvers with higher order
for black-oil models. Comput. Geosci., Vol. 24, pp. 593-607, 2020. DOI:
10.1007/s10596-019-09844-5,
Springer Nature SharedIt
- K.-A. Lie, T. S. Mykkeltvedt, and
O. Møyner. A fully implicit WENO scheme on
stratigraphic and unstructured polyhedral grids. Comput. Geosci., Vol. 24,
pp. 405-423, 2020. DOI:
10.1007/s10596-019-9829-x,
Springer Nature SharedIt
- Ø. S. Klemetsdal, O. Møyner, and K.-A. Lie.
Accelerating multiscale simulation of complex
geomodels by use of dynamically adapted basis functions. Comput. Geosci.,
Vol. 24, pp. 459-476, 2020. DOI:
10.1007/s10596-019-9827-z,
Springer Nature SharedIt
- Ø. S. Klemetsdal, O. Møyner, and
K.-A. Lie. Robust nonlinear Newton solver with
adaptive interface-localized trust regions. SPE Journal, Vol. 24, Issue 04,
pp. 1576-1594, 2019. DOI:
10.2118/195682-PA
- H. A. Marefat, M. A. Ashjari Aghdam, and K.-A. Lie. Preserving vorticity improves
the accuracy of multiscale solvers. J. Petrol. Sci. Eng., Vol. 182, 2019, 106231. DOI:
10.1016/j.petrol.2019.106231
- R. L. Berge, Ø. S. Klemetsdal, and
K.-A. Lie. Unstructured Voronoi grids conforming to
lower-dimensional objects. Comput. Geosci., Vol. 23, Issue 1, pp 169-188
2019. DOI:
10.1007/s10596-018-9790-0. Springer
Nature SharedIt
- M. G. Zefreh, H. M. Nilsen, K.-A. Lie, X. Raynaud, and F. Doster.
Streamline simulation of a reactive advective flow with discontinuous flux
function. Comput. Geosci., Volume 23, Issue 2, pp 255-271,
2019. DOI:
10.1007/s10596-018-9771-3.
- R. Allen, H. M. Nilsen, K.-A. Lie, O. Møyner, and
O. Andersen. Using simplified methods to explore the impact of parameter
uncertainty on CO2 storage estimates with application to the Norwegian
Continental Shelf. International Journal of Greenhouse Gas Control, Vol. 75,
pp. 198-213, 2018. DOI:
10.1016/j.ijggc.2018.05.017
- R. Allen, H. M. Nilsen, O. Andersen, and K.-A. Lie.
Ranking and categorizing large-scale saline aquifer
formations based on optimized CO2 storage potentials and economic
factors. International Journal of Greenhouse Gas Control, Vol. 65,
pp. 182-194, 2017. DOI:
10.1016/j.ijggc.2017.07.023
- K.-A. Lie, O. Møyner, and J. R. Natvig.
Use of multiple multiscale operators to accelerate
simulation of complex geomodels. SPE Journal, Vol. 22, Issue 6,
pp. 1929-1945, 2017. DOI:
10.2118/182701-PA
- H. M. Nilsen, S. Krogstad, O. Andersen, R. Allen,
K.-A. Lie. Using sensitivities and
vertical-equilibrium models for parameter estimation of CO2 injection models
with application to the Sleipner injection to measured data. Energy
Procedia, Vol. 114, pp. 3476-3495, 2017. DOI:
10.1016/j.egypro.2017.03.1478
- R. Allen, H. M. Nilsen, O. Andersen, K.-A. Lie. Categorization of
Norwegian Continental Shelf formations in terms of geological CO2 storage
potentials. Energy Procedia, Vol. 114, pp. 4583-4594, 2017. DOI:
10.1016/j.egypro.2017.03.1579
Revised version in which
we have corrected inaccuracies in the calculation of pressure values that
determine whether an aquifer is constrained by leakage or pressure
buildup
- T. S. Mykkeltvedt, X. Raynaud, and
K.-A. Lie. Fully implicit higher-order schemes
applied to polymer flooding. Comput. Geosci., Vol. 21, Issue 5-6,
pp. 1245-1266, 2017. DOI:
10.1007/s10596-017-9676-6. Springer
Nature SharedIt
- S. Krogstad, K.-A. Lie, H. M. Nilsen, C. F. Berg, and
V. Kippe. Efficient flow diagnostics proxies for
polymer flooding. Comput. Geosci., Vol. 21, Issue 5-6, pp. 1203-1218,
2017. DOI:
10.1007/s10596-017-9681-9
- R. Allen, H. M. Nilsen, O. Andersen, and
K.-A. Lie. On obtaining optimal well rates and
placement for CO2 storage. Comput. Geosci., Vol. 21, Issue 5-6,
pp. 1403-1422, 2017. DOI:
10.1007/s10596-017-9631-6. Springer
Nature SharedIt
- K.-A. Lie, O. Møyner, J. R. Natvig, A. Kozlova, K. Bratvedt,
S. Watanabe, and Z. Li. Successful application of
multiscale methods in a real reservoir simulator environment.
Comput. Geosci., Vol. 21, Issue 5-6, pp. 981-998, 2017. DOI:
10.1007/s10596-017-9627-2
- K. Bao, K.-A. Lie, O. Møyner, and
M. Liu. Fully implicit simulation of polymer
flooding with MRST. Comput. Geosci., Vol. 21, Issue 5-6, pp. 1219-1244,
2017. DOI:
10.1007/s10596-017-9624-5. Springer Nature
SharedIt
- O. Møyner and K.-A. Lie. A
multiscale restriction-smoothed basis method for compressible black-oil
models. SPE Journal, Vol. 21, No. 06, pp. 2079-2096,
2016. DOI: 10.2118/173265-PA
- S. Shah, O. Møyner, M. Tene, K.-A. Lie, and
H. Hajibeygi. The multiscale restriction smoothed basis
method for fractured porous media (F-MsRSB). J. Comput. Phys., Vol. 318,
pp. 36-57, 2016. DOI:
10.1016/j.jcp.2016.05.001
- S. T. Hilden, O. Møyner, K.-A. Lie, and
K. Bao. Multiscale simulation of polymer flooding with
shear effects. Transport in Porous Media, Vol. 113, Issue 1, pp. 111-135,
2016. DOI:
10.1007/s11242-016-0682-2
- X. Raynaud, K.-A. Lie, H. M. Nilsen, and A. Rasmussen.
The single-cell transport problem for two-phase flow
with polymer. Comput. Geosci., Vol. 20, Issue 3, pp. 495-507, 2016.
DOI:
10.1007/s10596-015-9502-y Springer
Nature SharedIt
- K.-A. Lie, H. M. Nilsen, O. Andersen, and
O. Møyner. A simulation workflow for
large-scale CO2 storage in the Norwegian North Sea. Comput. Geosci.,
Vol. 20, Issue 3, pp. 607-622, 2016. DOI:
10.1007/s10596-015-9487-6 Springer
Nature SharedIt
- H. M. Nilsen, K.-A. Lie, and O. Andersen.
Robust simulation of sharp-interface models for fast
estimation of CO2 trapping capacity in large-scale aquifer
systems. Comput. Geosci., Vol. 20, Issue 1, pp. 93-113, 2016. DOI:
10.1007/s10596-015-9549-9
- H. M. Nilsen, K.-A. Lie, and O. Andersen.
Fully-implicit simulation of vertical-equilibrium models
with hysteresis and capillary fringe. Comput. Geosci., Vol. 20, Issue 1,
pp. 49-67, 2016. DOI:
10.1007/s10596-015-9547-y
- O. Andersen, K.-A. Lie, and
H. M. Nilsen. An open-source toolchain for
simulation and optimization of aquifer-wide CO2 storage. Energy Procedia,
Vol. 86, pp. 324-333,
2016. DOI:
10.1016/j.egypro.2016.01.033
- O. Møyner and K.-A. Lie. A
multiscale restriction-smoothed basis method for high contrast porous media
represented on unstructured grids. J. Comput. Phys, Vol. 304, pp. 46-71,
2016. DOI:
10.1016/j.jcp.2015.10.010
- H. M. Nilsen, K.-A. Lie, and
O. Andersen. Analysis of CO2 trapping capacities and
long-term migration for geological formations in the Norwegian North Sea using
MRST-co2lab. Computers & Geoscience, Vol. 79, pp. 15-26, 2015. DOI:
10.1016/j.cageo.2015.03.001
- H. M. Nilsen, K.-A. Lie, O. Møyner, and
O. Andersen. Spill-point analysis and structural trapping
capacity in saline aquifers using MRST-co2lab. Computers & Geoscience,
Vol. 75, pp. 33-43, 2015. DOI:
10.1016/j.cageo.2014.11.002
- M. Pal, S. Lamine, K.-A. Lie, and
S. Krogstad. Validation of the multiscale mixed
finite-element method. Int. J. Numer. Meth. Fluids, Vol. 77, Issue 4,
pp. 206-223, 2015. DOI:
10.1002/fld.3978
- S. Kaulmann, B. Flemisch, B. Haasdonk, K.-A. Lie, and M. Ohlberger.
The localized reduced basis multiscale method for two-phase flows in porous
media. Int. J. Numer. Meth. Engng., Vol. 102, No. 5, pp. 1018-1040, 2015.
DOI: 10.1002/nme.4773
- M. L. Sætra, A. R. Brodtkorb, and
K.-A. Lie. Efficient GPU-implementation of adaptive mesh
refinement for the shallow-water equations. J. Sci. Comp., Vol. 63, No. 1,
pp. 23-48, 2015.
DOI:
10.1007/s10915-014-9883-4
- O. Møyner, S. Krogstad, and
K.-A. Lie. The application of flow diagnostics for
reservoir management. SPE J., Vol. 20, No. 2, pp. 306-323, 2015. DOI:
10.2118/171557-PA
- K.-A. Lie, H. M. Nilsen, A. F. Rasmussen, and
X. Raynaud. Fast simulation of polymer injection in
heavy-oil reservoirs based on topological sorting and sequential
splitting. SPE J., Vol. 19, No. 6, pp. 991-1004,
2014. DOI: 10.2118/163599-PA.
|
- O. Møyner and K.-A. Lie. The
multiscale finite-volume method on stratigraphic grids. SPE J., Vol. 19,
No. 5, pp. 816-831, 2014.
DOI: 10.2118/163649-PA.
- O. Møyner and K.-A. Lie. A
multiscale two-point flux-approximation method. J. Comput. Phys., Vol. 275,
pp. 273-293, 2014. DOI:
10.1016/j.jcp.2014.07.003.
- K.-A. Lie, J. R. Natvig, S. Krogstad, Y. Yang, and
X.-H. Wu. Grid adaptation for the Dirichlet-Neumann
representation method and the multiscale mixed finite-element method.
Comput. Geosci., Vol. 18, No. 3, pp. 357-372, 2014.
DOI:
10.1007/s10596-013-9397-4
- F. O. Alpak, M. Pal, and K.-A. Lie.
A multiscale method for modeling flow in stratigraphically complex
reservoirs. SPE J., Vol. 17, No. 4, pp. 1056-1070,
2012. DOI: 10.2118/140403-PA
- H. M. Nilsen, A. R. Syversveen, K.-A. Lie, J. Tveranger, and
J. M. Nordbotten. Impact of top-surface morphology on
CO2 storage capacity. Int. J. Greenhouse Gas Control, Vol. 11, pp. 221-235,
2012. DOI:
10.1016/j.ijggc.2012.08.012
- H. M. Nilsen, K.-A. Lie, and J. R. Natvig.
Accurate modelling of faults by multipoint,
mimetic, and mixed methods. SPE J., Vol. 17, No. 2, pp. 568-579, June
2012. DOI: 10.2118/149690-PA.
- K.-A. Lie, J. R. Natvig, and H. M. Nilsen.
Discussion of dynamics and operator splitting
techniques for two-phase flow with gravity. Int. J
Numer. Anal. Mod. (Special issue in memory of Magne Espedal), Vol. 9, No. 3,
pp. 684-700, 2012.
- K.-A. Lie, S. Krogstad, I. S. Ligaarden, J. R. Natvig,
H. M. Nilsen, and B. Skaflestad. Open source MATLAB
implementation of consistent discretisations on complex
grids. Comput. Geosci., Vol. 16, No. 2, pp. 297-322, 2012. DOI:
10.1007/s10596-011-9244-4
- V. L. Hauge, K.-A. Lie, and
J. R. Natvig. Flow-based coarsening for multiscale
simulation of transport in porous media. Comput. Geosci., Vol. 16, No. 2,
pp. 391-408, 2012. DOI:
10.1007/s10596-011-9230-x.
- J. R. Natvig, B. Skaflestad, F. Bratvedt, K. Bratvedt, K.-A. Lie,
V. Laptev, and S. K. Khataniar. Multiscale mimetic
solvers for efficient streamline simulation of fractured reservoirs. SPE J.,
Vol. 16, No. 4, pp. 880-880, 2011.
DOI: 10.2018/119132-PA
- M. Krotkiewski, I. Ligaarden, K.-A. Lie,
D. W. Schmid. On the importance of the Stokes-Brinkman
equations for computing effective permeability in carbonate karst reservoirs.
Comm. Comput. Phys, Vol. 10, No. 5, pp. 1315-1332,
2011. DOI:
10.4208/cicp.290610.020211a
- H. M. Nilsen, P. A. Herrera, M. Ashraf, I. S. Ligaarden, M. Iding,
C. Hermanrud, K.-A. Lie, J. M. Nordbotten, H. K. Dahle, and E. Keilegavlen. Field-case simulation of CO2-plume migration using
vertical-equilibrium models. Energi Procedia, Vol. 4, pp. 3801-3808,
2011. DOI:
10.1016/j.egypro.2011.02.315
- A. R. Brodtkorb, T. R. Hagen, K.-A. Lie, and
J. R. Natvig. Simulation and visualization of the Saint-Venant
system using GPUs. Comput. Visual. Sci. (Special issue on Hot Topics in
Computational Engineering), Vol. 13, No. 7, pp. 341--353, 2010.
DOI:
10.1007/s00791-010-0149-x
- A. F. Gulbransen, V. L. Hauge, and
K.-A. Lie. A multiscale mixed finite-element method
for vuggy and naturally-fractured reservoirs. SPE J., Vol. 15, No. 12,
pp. 395-403, 2010.
DOI: 10.2118/119104-PA
- B. Eikemo, K.-A. Lie, G.T. Eigestad, and
H.K. Dahle. Discontinuous Galerkin methods for advective
transport in single-continuum models of fractured media. Adv. Water
Resour. Vol. 32, Issue 4, pp. 493-506. 2009. DOI:
10.1016/j.advwatres.2008.12.010.
- V. R. Stenerud, K.-A. Lie, and V. Kippe. Generalized travel-time inversion on unstructured
grids. J. Pet. Sci. Eng. Vol. 65, Issues 3-4, pp. 175-187, 2009. doi: 10.1016/j.petrol.2008.12.030
- J. R. Natvig and K.-A. Lie. Fast computation of
multiphase flow in porous media by implicit discontinuous Galerkin schemes with
optimal ordering of elements. J. Comput. Phys, Vol. 227, Issue 24,
pp. 10108-10124, 2008. doi:10.1016/j.jcp.2008.08.024.
- V. R. Stenerud, V. Kippe, K.-A. Lie, and A. Datta-Gupta. Adaptive multiscale streamline simulation and inversion for
high-resolution geomodels. SPE J., Vol. 13, No. 1, pp. 99--111, March
2008. DOI: 10.2118/106228-PA
- V. Kippe, J. E. Aarnes, and K.-A. Lie. A comparison
of multiscale methods for elliptic problems in porous media flow.
Comput. Geosci., Special issue on multiscale methods. Vol. 12, No. 3, pp. 377-398,
2008. DOI: 10.1007/s10596-007-9074-6
- J. E. Aarnes, S. Krogstad, and K.-A. Lie. Multiscale
mixed/mimetic methods on corner-point grids. Comput. Geosci., Special issue on
multiscale methods. Vol. 12, No. 3, pp. 297-315, 2008. DOI: 10.1007/s10596-007-9072-8
- R. Juanes and K.-A. Lie. Numerical modeling of
multiphase first-contact miscible flows. Part 2. Front-tracking and streamline
simulation. Transp. Porous Media, Vol. 72, No. 1/March, pp. 97-120, 2008.
DOI: 10.1007/s11242-007-9139-y
- J. R. Natvig, K.-A. Lie, B. Eikemo, and
I. Berre. An efficient discontinuous Galerkin method for
advective transport in porous media. Adv. Water Resour, Vol. 30, Issue 12,
pp. 2424-2438, 2007. DOI:
10.1016/j.advwatres.2007.05.015
- H. Hægland, H. K. Dahle, G. T. Eigestad, K.-A. Lie, and I. Aavatsmark.
Improved streamlines and time-of-flight for streamline
simulation on irregular grids. Adv. Water Resour. Vol. 30, Issue 4,
pp. 1027-1045, 2007. DOI:
10.1016/j.advwatres.2006.09.00.
- R. Juanes and K.-A. Lie. Numerical modeling of
multiphase first-contact miscible flows. Part 1. Analytical Riemann solver.
Transp. Porous Media, Vol. 67, No. 3 / April, pp. 375-393, 2007. DOI: 10.1007/s11242-006-9031-1.
- V. R. Stenerud and K.-A. Lie. A multiscale streamline
method for inversion of production data. J. Pet. Sci. Eng., Vol. 54,
pp. 79-92, 2006. DOI:
10.1016/j.petrol.2006.08.003.
- J. E. Aarnes, S. Krogstad and
K.-A. Lie. A hierarchical multiscale method for
two-phase flow based upon mixed finite elements and nonuniform coarse
grids. Multiscale Model. Simul., Vol. 5, No. 2, pp. 337-363,
2006. DOI: 10.1137/050634566
- I. Berre, K. H. Karlsen, K.-A. Lie, and J. R. Natvig. Fast computation of arrival times in heterogeneous
media. Comput. Geosci., Vol. 9, No. 4, pp. 179-201, 2005. DOI
10.1007/s10596-005-9002-6
- T. R. Hagen, J. M. Hjelmervik, K.-A. Lie, J. R. Natvig, M. Ofstad Henriksen.
Visual simulation of shallow-water
waves. Simul.
Model. Pract. Theory, Vol. 13, Issue 8 (Special Issue on Programmable Graphics
Hardware), pp.716-726, November 2005. DOI:
10.1016/j.simpat.2005.08.006
- K.-A. Lie and R. Juanes. A front-tracking method
for the simulation of three-phase flow in porous media.
Comput. Geosci., Vol. 9, No. 1, pp. 29-59, March 2005. DOI: 10.1007/s10596-005-5663-4
- J. E. Aarnes, V. Kippe, and K.-A. Lie. Mixed
multiscale finite elements and streamline methods for reservoir simulation of
large geomodels. Adv. Water Resour., Vol. 28, Issue 3, pp. 257-271,
2005. DOI:
10.1016/j.advwatres.2004.10.007
- K.-A. Lie and S. Noelle. On the artificial
compression method for second-order nonoscillatory central difference schemes for
systems of conservation laws. SIAM J. Sci. Comp., Vol. 24, No. 4,
pp. 1157-1174, 2003. DOI:
10.1137/S1064827501392880
- K.-A. Lie and S. Noelle. An improved
quadrature rule for the flux-computation in staggered central difference schemes
in multidimensions. J. Sci. Comp., Vol. 18, No. 1, pp. 69-81, February
2003. DOI:
10.1023/A:1020386111898
- K. Hvistendahl Karlsen, K.-A. Lie, J. R. Natvig, H. F. Nordhaug,
and H. K. Dahle. Operator splitting methods for systems of
convection-diffusion equations: nonlinear error mechanisms and correction
strategies. J. Comput. Phys., Vol. 173, Issue 2, pp. 636-663,
2001. DOI: 10.1006/jcph.2001.6901
- V. Haugse, K. H. Karlsen, K.-A. Lie, and J. R. Natvig.
Numerical solution of the polymer system by front
tracking. Transp. Porous Media, Vol 44, No 1, pp. 63-83,
2001. DOI:
10.1023/A:1010740024800
- H. Holden, K. Hvistendahl Karlsen, and K.-A. Lie.
Operator splitting
methods for degenerate convection-diffusion equations II: numerical examples
with emphasis on reservoir simulation and sedimentation.
Comput. Geosci., Vol. 4, No. 4, pp. 287-322, 2000. DOI:
10.1023/A:1011582819188
- H. Holden, K. Hvistendahl Karlsen, and K.-A. Lie.
Operator splitting methods for
degenerate convection-diffusion equations I: convergence and entropy
estimates.
CMS Conf. Proc., Vol. 129, pp. 293-316, 2000.
- K. Hvistendahl Karlsen, K.-A. Lie, and N. H. Risebro.
A fast marching method for reservoir simulation.
Comput. Geosci., Vol. 4, No. 2, pp. 185-206,
2000. DOI:
10.1023/A:1011564017218
- K.-A. Lie.
Front tracking for one-dimensional
quasilinear hyperbolic equations with variable coefficients.
Numer. Algorithms, Vol. 24, No. 3, pp. 275-298, 2000.
- R. Bürger, S. Evje, K. Hvistendahl Karlsen, and K.-A. Lie.
Numerical methods for the simulation of the
settling of flocculated suspensions.
Chem. Eng. J., Vol. 80, pp. 91-104, 2000.
- S. Evje, K. Hvistendahl Karlsen, K.-A. Lie, and N. H. Risebro.
Front tracking and operator splitting
for nonlinear degenerate convection-diffusion equations.
In "Parallel solution of partial differential
equations", Eds., P. Bjørstad and M. Luskin,
IMA Vol. Math. Appl., Vol. 120, pp. 209-227, Springer Verlag, 2000.
- K.-A. Lie.
A dimensional splitting method for
quasilinear hyperbolic equations with variable coefficients.
BIT, Vol. 39, No. 4, pp. 683-700, 1999.
Awarded the Carl-Erik
Fröberg Prize for young nordic authors.
- R. Holdahl, H. Holden, and K.-A. Lie.
Unconditionally stable splitting
methods for the shallow water equations.
BIT, Vol. 39, No. 3, pp. 451-472, 1999.
- K. Hvistendahl Karlsen and K.-A. Lie.
An unconditionally stable splitting
scheme for a class of nonlinear parabolic equations.
IMA J. Num. Anal., Vol. 19, No. 4, pp. 609-635, 1999.
- H. Holden, K.-A. Lie, and N. H. Risebro.
An unconditionally stable
method for the Euler equations. J. Comput. Phys.
Vol. 150, no. 1, pp. 76-96, 1999.
- K. Hvistendahl Karlsen, K.-A. Lie, N. H. Risebro, and J. Frøyen.
A front-tracking approach to a two-phase
fluid-flow model with capillary forces.
In Situ (A Special Issue on Reservoir Simulation), Vol. 22, Issue No. 1,
pp. 59-89, 1998.
- K. Hvistendahl Karlsen, K. Brusdal, H. K. Dahle, S. Evje,
and K.-A. Lie.
The corrected operator splitting
approach applied to an advection-diffusion problem.
Comput. Methods Appl. Mech. Engrg., Vol. 167, Issue 3-4, pp. 239-260, 1998.
- K.-A. Lie, V. Haugse, and K. Hvistendahl Karlsen.
Dimensional splitting with front
tracking and adaptive local grid refinement.
Numer. Methods Partial Differential Equations, Vol. 14, No. 5, pp. 627-648,
1998.
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