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@ARTICLE{Asmouh:1052309,
      author       = {Asmouh, Ilham and Ouardghi, Abdelouahed},
      title        = {{A} {BDF}2 characteristic-{G}alerkin isogeometric analysis
                      for the miscible displacement of incompressible fluids in
                      porous media},
      journal      = {Computers $\&$ fluids},
      volume       = {298},
      issn         = {0045-7930},
      address      = {Amsterdam [u.a.]},
      publisher    = {Elsevier Science},
      reportid     = {FZJ-2026-00919},
      pages        = {106675},
      year         = {2025},
      abstract     = {Incompressible-miscible problems arise in many fields of
                      application where the main objective is to describe the
                      change of the pressure and the velocity during displacement.
                      These problems are usually subject to some complicated
                      features related to the dominance of convection. Therefore,
                      the multiphysical scales in these problems represent a
                      challenging endeavor. In this study, we propose a
                      NURBS-based isogeometric analysis (IgA) combined with an
                      $L^2$-projection characteristic Galerkin method to deal with
                      this class of equations. The advection part is treated in a
                      characteristic Galerkin framework where high-order
                      nonuniform rational B-spline functions are used to
                      interpolate the solution. The resulting semi-discrete
                      equation is solved using an efficient backward
                      differentiation time-stepping algorithm. The accuracy of the
                      method is analyzed through several Darcy’s flow problems
                      with analytical solutions on differently shaped
                      computational domains, including a miscible displacement of
                      an incompressible fluid, and a real problem with a viscous
                      fingering in porous media. The numerical results presented
                      in this study demonstrate the potential of the proposed IgA
                      characteristic Galerkin method to allow for large time steps
                      in the computations without deteriorating the accuracy of
                      the obtained solutions, and to accurately maintain the shape
                      of the solution in the presence of complex patterns on
                      complex geometries.},
      cin          = {JSC},
      ddc          = {004},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511) / SDLFSE - SDL Fluids $\&$
                      Solids Engineering (SDLFSE)},
      pid          = {G:(DE-HGF)POF4-5112 / G:(DE-Juel-1)SDLFSE},
      typ          = {PUB:(DE-HGF)16},
      doi          = {10.1016/j.compfluid.2025.106675},
      url          = {https://juser.fz-juelich.de/record/1052309},
}