Applied and Computational Mathematics
Main focus is on the study of partial differential equations (PDEs) that can be used to represent various dynamic phenomena, i.e. processes that involve changes in space and time.
Central classes are:
- multiphase flow models
- transport-reaction models
More specific reserach directions:
- development of mathematical models and comparison with experimental behavior
- development of suitable discrete versions of various PDEs
- mathematical analysis (existence, uniqueness, asymptotic behavior)
More specific applications of these models:
- chalk weakening effects
- brine-dependent oil recovery (chalk and sandstone)
- well and pipe flow
- coupled well-reservoir flow
S. Evje,"Global weak solutions for a compressible gas-liquid model with well-formation interaction", accepted in J. Diff. Eqs., 2011
S. Evje,"Weak solutions for a gas-liquid model relevant for describing gas-kick in oil wells", accepted in SIAM J. Math. Anal., 2011.
H.A. Friis and S. Evje, "Global weak solutions for a gas-liquid model with external forces and general pressure law", SIAM J. Appl. Math., Vol 71 (2), pp. 409-442, 2011.
H.A. Friis and S. Evje, "Numerical treatment of two-phase flow in capillary heterogeneous porous media by finite-volume approximations", Int. J. Num. Anal. Mod., to appear, 2011.
S. Evje and A. Hiorth, "A Mathematical Model for Dynamic Wettability Alteration Controlled by Water-Rock Chemistry", Networks and Heterogeneous Media, Vol 5 (2), pp. 217-256, 2010
S. Evje, A. Hiorth, M.V. Madland, R.I. Korsnes, "A mathematical model relevant for weakening of chalk reservoirs due to chemical reactions", Networks and Heterogeneous Media, Vol 4 (4), pp. 755-788, 2009.
S.T.Munkejord, S. Evje, T Flåtten, "A MUSTA scheme for a non-conservative two-fluid model", SIAM J. Sci. Comput. Vol 31, pp. 2587-2622, 2009
H.A.Friis, S.Evje and T.Flåtten, "A numerical study of characteristic slow-transient behavior of a compressible 2D gas-liquid two-fluid model", Adv. Appl. Math. Mech., Vol 1 (2), pp 166-200, 2009.
S. Evje and K.H. Karlsen "Global weak solutions for a viscous liquid-gas model with singular pressure law", Comm. Pure Appl. Anal, Vol 8 (6), pp 1867-1894, 2009.
S.Evje, T. Flåtten and H.A. Friis, "Global weak solutions for a viscous liquid-gas model with transition to single-phase gas flow and vacuum", Nonlinear Analysis TMA, Vol 70, pp. 3864--3886, 2009
S.Evje and K.H.Karlsen, "Global existence of weak solutions for a viscous two-phase model", J. Diff. Equations, Vol 245, Issue 9, 2008, pp. 2660--2703.
Yu, Evje, Fjelde, Kleppe et al, "Spontaneous Imbibition of Seawater into Preferentially Oil-Wet Chalk Cores - Experiments and Simulations", J. Pet. Sci. Eng., Vol 66, pp. 171-179, 2009.
Yu, Evje, Fjelde, Kleppe et al, "Modelling of wettability alteration processes in carbonate oil reservoirs", Networks and Heterogeneous Media, Vol 3 (1), 149-183, 2008.
S.Evje, T.Flåtten and H.A. Friis, "On a relation between pressure-based schemes and central schemes for hyperbolic conservation laws", Num. Meth. Part. Diff. Eq., Vol 24, Issue 2, 2008, pp. 605-645.
S.Evje and K.H.Karlsen, "A hyperbolic-elliptic model for coupled well-porous media flow", In Eleventh International Conference on Hyperbolic Problems: Theory, Numerics, Applications (Lyon 2006). Edt: S. Benzoni-Gavage and D. Serre, Jan 28, 2008.
S.Evje and K.H.Karlsen, "Hyperbolic-elliptic models for well-reservoir flow", Networks and Heterogeneous Media, Vol. 4 (1), 639-673, 2006.
Munkejord S.T., Evje S., Flåtten T., "The multi-staged centred scheme approach applied to a drift-flux two-phase flow model", Int. J. Num. Meth. Fluids, Vol 52 (6), pp. 679-705, 2006.
Evje, S., Flåtten, T. "CFL-violating numerical schemes for a two-fluid model", J. Sci. Comput, Vol 29 (1), pp. 83-114, 2006.
Evje, S., Flåtten, T. "Hybrid central-upwind schemes for numerical resolution of two-phase flows", ESAIM: Math. Mod. Num. Anal., vol. 39, 2005, No. 2, pp. 253-273.
Evje, S., Flåtten, T. "Weakly implicit numerical schemes for a two-fluid model", SIAM J. Sci. Comput., Vol. 26, 2005, No. 5, pp. 1449--1484.
Evje, S., Flåtten, T. "Hybrid flux-splitting schemes for a common two-fluid model", J. Comput. Phys., Vol. 192, Issue 1, 2003, pp.175-210.