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Ivar Aavatsmarks oversikt

• Vitenskapelige beregninger
• Reservoarsimulering
• Strømning i porøse media
• Diskretisering av partielle differensialligninger
• Gitring

Anmeldelser i Zentralblatt MATH
SPE-artikler
ECMOR-artikler

• S. Tveit, I. Aavatsmark:
  Errors in the upstream mobility scheme for countercurrent two-phase flow in heterogeneous porous media.
  Computational Geosciences, 16:809-825, 2012.
• A. Sandvin, J. M. Nordbotten, I. Aavatsmark:
  Multiscale mass conservative domain decomposition preconditioners for elliptic problems on irregular grids.
  Computational Geosciences, 15:587-602, 2011.
• E. Keilegavlen, I. Aavatsmark:
  Monotonicity for MPFA methods on triangular grids.
  Computational Geosciences, 15:3-16, 2011.
• I. Aavatsmark, G.T. Eigestad, B.-O. Heimsund, B.T. Mallison, J.M. Nordbotten, E. Øian:
  A new finite volume approach to efficient discretization on challenging grids.
  SPE Journal, 15:658-669, 2010.
• S.S. Mundal, E. Keilegavlen, I. Aavatsmark:
  Simulation of anisotropic heterogeneous near-well flow using MPFA methods on flexible grids.
  Computational Geosciences, 14:509-525, 2010.
• E. Keilegavlen, J.M. Nordbotten, I. Aavatsmark:
  Sufficient criteria are necessary for monotone control volume methods.
  Applied Mathematics Letters, 22:1178-1180, 2009.
• I. Aavatsmark, G.T. Eigestad, B.T. Mallison, J.M. Nordbotten:
  A compact multipoint flux approximation method with improved robustness.
  Numerical Methods for Partial Differential Equations, 24:1329-1360, 2008.
• I. Aavatsmark:
  Comparison of monotonicity for some multipoint flux approximation methods.
  In: R. Eymard, J.-M. Hérard (editors), Finite Volumes for Complex Applications, 5:19-34, Wiley-ISTE, 2008.
• D. Eydinov, S.I. Aanonsen, J. Haukås, I. Aavatsmark:
  A method for automatic history matching of a compositional reservoir simulator with multipoint flux approximation.
  Computational Geosciences, 12:209-225, 2008.
• S.K. Khattri, I. Aavatsmark:
  Numerical convergence on adaptive grids for control volume methods.
  Numerical Methods for Partial Differential Equations, 24:465-475, 2008.
• I. Aavatsmark, G.T. Eigestad, R.A. Klausen, M.F. Wheeler, I. Yotov:
  Convergence of a symmetric MPFA method on quadrilateral grids.
  Computational Geosciences, 11:333-345, 2007.
• I. Aavatsmark:
  Interpretation of a two-point flux stencil for skew parallelogram grids.
  Computational Geosciences, 11:199-206, 2007.
• J.M. Nordbotten, I. Aavatsmark, G.T. Eigestad:
  Monotonicity of control volume methods.
  Numerische Mathematik, 106:255-288, 2007.
• J. Haukås, I. Aavatsmark, M. Espedal, E. Reiso:
  A comparison of two different IMPSAT models in compositional simulation.
  SPE Journal, 12:145-151, 2007.
• H. Hægland, H.K. Dahle, G.T. Eigestad, K.-A. Lie, I. Aavatsmark:
  Improved streamlines and time-of-flight for streamline simulation on irregular grids.
  Advances in Water Resources, 30:1027-1045, 2007.
• I. Aavatsmark, G.T. Eigestad:
  Numerical convergence of the MPFA O-method and U-method for general quadrilateral grids.
  International Journal for Numerical Methods in Fluids, 51:939-961, 2006.
• I. Aavatsmark, G.T. Eigestad, R.A. Klausen:
  Numerical convergence of the MPFA O-method for general quadrilateral grids in two and three dimensions.
  In: D.N. Arnold, P.B. Bochev, R.B. Lehoucq, R.A. Nicolaides, M. Shashkov (editors),
  Compatible spatial discretizations, The IMA Volumes in Mathematics and its Applications, 142:1-21, Springer, 2006.
• J.M. Nordbotten, I. Aavatsmark:
  Monotonicity conditions for control volume methods on uniform parallelogram grids in homogeneous media.
  Computational Geosciences, 9:61-72, 2005.
• T. Aadland, I. Aavatsmark, H.K. Dahle:
  Performance of a flux splitting scheme when solving the single-phase pressure equation discretized by MPFA.
  Computational Geosciences, 8:325-340, 2004.
• A.-A. Grimstad, T. Mannseth, S.I. Aanonsen, I. Aavatsmark, A. Cominelli, S. Mantica:
  Identification of unknown permeability trends from history matching of production data.
  SPE Journal, 9:419-428, 2004.
• I. Aavatsmark, R.A. Klausen:
  Well index in reservoir simulation for slanted and slightly curved wells in 3D grids.
  SPE Journal, 8:41-48, 2003.
• I. Aavatsmark:
  An introduction to multipoint flux approximations for quadrilateral grids.
  Computational Geosciences, 6:405-432, 2002.
• G.T. Eigestad, I. Aavatsmark, M. Espedal:
  Symmetry and M-matrix issues for the O-method on an unstructured grid.
  Computational Geosciences, 6:381-404, 2002.
• I. Aavatsmark, E. Reiso, R. Teigland:
  Control-volume discretization method for quadrilateral grids with faults and local refinements.
  Computational Geosciences, 5:1-23, 2001.
• I. Aavatsmark, T. Barkve, Ø. Bøe, T. Mannseth:
  Discretization on unstructured grids for inhomogeneous, anisotropic media. Part I: Derivation of the methods.
  SIAM Journal on Scientific Computing, 19:1700-1716, 1998.
• I. Aavatsmark, T. Barkve, Ø. Bøe, T. Mannseth:
  Discretization on unstructured grids for inhomogeneous, anisotropic media. Part II: Discussion and numerical results.
  SIAM Journal on Scientific Computing, 19:1717-1736, 1998.
• I. Aavatsmark, T. Barkve, T. Mannseth:
  Control-volume discretization methods for 3D quadrilateral grids in inhomogeneous, anisotropic reservoirs.
  SPE Journal, 3:146-154, 1998.
• I. Aavatsmark, T. Barkve, Ø. Bøe, T. Mannseth:
  Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media.
  Journal of Computational Physics, 127:2-14, 1996.
• K. Seines, I. Aavatsmark, S.C. Lien, P. Rushworth:
  Considering well bore friction effects in planning horizontal wells.
  Journal of Petroleum Technology, 45:994-1000, 1993, and 46:620-620, 1994.
• I. Aavatsmark:
  Modellierung von Verdrängungsvorgängen in Laborversuchen.
  Zeitschrift für angewandte Mathematik und Mechanik, 71:341-354, 1991.
• I. Aavatsmark:
  Kapillarenergie als Entropiefunktion.
  Zeitschrift für angewandte Mathematik und Mechanik, 69:319-327, 1989.

• I. Aavatsmark:
  Mathematische Einführung in die Thermodynamik der Gemische.
  Akademie Verlag, Berlin 1995, 171 s.

• I. Aavatsmark:
  Multipoint flux approximation methods for quadrilateral grids.
  9th International Forum on Reservoir Simulation, Abu Dhabi, December 2007, 44 s.
• I. Aavatsmark:
  Mehrpunktflussverfahren.
  Vorlesungen an der Universität Stuttgart, 2004, 49 s.
• I. Aavatsmark:
  Bevarelsesmetoder for hyperbolske differensialligninger.
  Forelesninger ved Universitetet i Bergen, 2003, 140 s.
• I. Aavatsmark:
  Bevarelsesmetoder for elliptiske differensialligninger.
  Forelesninger ved Universitetet i Bergen, 2002, 175 s.

Medlem av den vitenskapelige komité for European Conference on the Mathematics of Oil Recovery (ECMOR). Formann for ECMOR XI, Bergen, 2008.

Studiepoeng: 10

Innhold: Kurset gir en innføring i egenskaper til hyperbolske bevarelseslover og numeriske metoder for løsning av ligningene. I den analytiske delen behandles for både skalare ligninger og systemer av ligninger emner som bølgetyper, entropibetingelse og løsning av Riemann-problemet. I den numeriske delen drøftes begreper som bevarelse, monotoni, stabilitet og nøyaktighet for metodene.

Forelesningene bygger ikke på en enkelt lærebok, men er satt sammen av stoff fra flere lærebøker. Forelesningsnotatene er tilgjengelige her.

Anbefalte forkunnskaper: MAT234, MAT263 eller tilsvarende kunnskaper.

Studiepoeng: 10

Innhold: Kurset behandler tre ekvivalente formuleringer for elliptiske ligninger: integralformulering, variasjonsformulering og sadelpunktformulering. Med utgangspunkt i disse formuleringene utledes ulike numeriske metoder, og metodenes egenskaper drøftes. Det fokuseres på metoder som kan anvendes på koblede ikkelineære differensialligninger, slik som i reservoarsimulering. Følgende metoder behandles:

• Differensmetoden
• Elementmetoden
• Metoden med blandede elementer
• Kontrollvolummetoden

Forelesningene bygger ikke på en enkelt lærebok, men er satt sammen av stoff fra flere lærebøker. Forelesningsnotatene er tilgjengelige her.

Anbefalte forkunnskaper: MAT234, MAT263 eller tilsvarende kunnskaper.

• Pål Sævik, UiB, 2011.
• Svenn Tveit, UiB, 2011.
• Steffi Hundorf, Universität München, 2007.
• Sissel Mundal, UiB, 2005.
• Håkon Hægland, UiB, 2003.
• Jarle Haukås, UiB, 2003.
• Torbjørn Aadland, UiB, 2003.
• Bente Camilla Günther, NTNU, 2002.
• Geir Terje Eigestad, UiB, 1999.
• Stian Frøiland, NTNU, 1999.
• Aina Beate Furnes, NTNU, 1998.
• Carl Frederik Eek-Jensen, NTNU, 1998.

• Faiza Muneer, Universitetet i Bergen, start 2012.
  
• Trine Mykkeltvedt, Universitetet i Bergen, start 2010.
  
• Benjamin Faigle, Universität Stuttgart, start 2010.
  
• Andreas Sandvin, Universitetet i Bergen, 2012:
  Robust multiscale control-volume methods for reservoir simulation.
• Eirik Keilegavlen, Universitetet i Bergen, 2010:
  Robust control volume methods for reservoir simulation on challenging grids.
• Sissel Mundal, Universitetet i Bergen, 2009:
  Conservative numerical methods for elliptic problems with applications to simulation of near-well flow.
• Håkon Hægland, Universitetet i Bergen, 2009:
  Streamline methods with application to flow and transport in fractured media.
• Jarle Haukås, Universitetet i Bergen, 2006:
  Compositional reservoir simulation with emphasis on the IMPSAT formulation.
• Runhild Aae Klausen, Universitetet i Oslo, 2003:
  On locally conservative numerical methods for elliptic problems; Application to reservoir simulation.
• Geir Terje Eigestad, Universitetet i Bergen, 2003:
  Reservoir simulation on heterogeneous and anisotropic media with imposed flux continuity conditions for general geometries, and the inclusion of hysteresis in forward modeling.
• Ole Vignes, Norges tekniske høgskole, 1993:
  Application of optimization methods in oil recovery problems.

Sist endret: Mars 2012