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@ARTICLE{Bhler:828051,
      author       = {Bühler, Jonas and Huber, Gregor and von Lieres, Eric},
      title        = {{F}inite volume schemes for the numerical simulation of
                      tracer transport in plants},
      journal      = {Mathematical biosciences},
      volume       = {288},
      issn         = {0025-5564},
      address      = {New York, NY},
      publisher    = {American Elsevier},
      reportid     = {FZJ-2017-02065},
      pages        = {14 - 20},
      year         = {2017},
      abstract     = {Compartmental models can be used for inverse modeling of
                      long distance tracer transport experiments in plants. Such
                      transport models describe axial convection and diffusion as
                      well as exchange between compartments, and are defined by
                      partial differential equations (PDEs). Since for inverse
                      modeling, the forward simulation needs to be evaluated
                      frequently, a fast PDE solver is required. Here, we compare
                      several different finite volumes schemes up to fifth order
                      for spatial discretization with respect to ac- curacy,
                      computation time and numerical oscillations. The comparison
                      has been performed using initial conditions with varying
                      steepness, and periodic boundary conditions. For time
                      discretization, standard fifth order Runge–Kutta methods
                      are used. For smooth initial conditions, fifth order upwind
                      schemes for spatial discretization yield the most precise
                      and fast solutions. For higher steepness of the initial
                      condi- tion, higher order upwind schemes produce spurious
                      oscillations while flux limiter schemes as well as weighted
                      essentially non-oscillating (WENO) schemes can suppress
                      these oscillations, at the expense of comparably slower
                      convergence rates and higher computation times.},
      cin          = {IBG-2 / IBG-1},
      ddc          = {570},
      cid          = {I:(DE-Juel1)IBG-2-20101118 / I:(DE-Juel1)IBG-1-20101118},
      pnm          = {583 - Innovative Synergisms (POF3-583)},
      pid          = {G:(DE-HGF)POF3-583},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000401386600002},
      doi          = {10.1016/j.mbs.2017.02.009},
      url          = {https://juser.fz-juelich.de/record/828051},
}