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@ARTICLE{Kuppe:894425,
      author       = {Kuppe, Christian W. and Huber, Gregor and Postma, Johannes
                      A.},
      title        = {{C}omparison of numerical methods for radial solute
                      transport to simulate uptake by plant roots},
      journal      = {Rhizosphere},
      volume       = {18},
      issn         = {2452-2198},
      address      = {Amsterdam},
      publisher    = {Elsevier},
      reportid     = {FZJ-2021-03217},
      pages        = {100352},
      year         = {2021},
      abstract     = {The 1D radial solute transport model with non-linear inner
                      boundary condition is widely used for simulating nutrient
                      uptake by plant roots. When included into an architectural
                      root model, this local model has to be solved for a high
                      number of root segments, e. g. – segments for large root
                      systems. Each root segment comes with its own local
                      parameter set in heterogeneous root architectural models.
                      Depending on the soil and solute, the effective diffusion
                      coefficient spans over more than six orders (e. g. for N, K,
                      and P). Thus a numerical implementation of this rhizosphere
                      transport model is required to be fast, accurate and stable
                      for a large parameter space. We apply 13 methods to this
                      rhizosphere model with root hairs and compare their
                      accuracy, computational speed, and applicability. In
                      particular, the Crank-Nicolson method is compared to
                      higher-order explicit adaptive methods and some stiff
                      solvers. The Crank-Nicolson method sometimes oscillated and
                      was up to a hundred times slower than an explicit adaptive
                      scheme with similar accuracy. For a given spatial
                      resolution, Crank-Nicolson had about one order lower
                      accuracy as other tested methods. The maximum spatial time
                      step can be estimated from root radius, solute diffusion,
                      advection, and soil buffer power. Although Crank-Nicolson is
                      a viable method and often used as de-facto standard method
                      for rhizosphere models, it was not the best performer in our
                      comparison. While the best method remains problem specific,
                      for general use in root architectural models we recommend
                      adaptive Runge-Kutta with cubic or quadratic upwind for
                      advection.},
      cin          = {IBG-2},
      ddc          = {580},
      cid          = {I:(DE-Juel1)IBG-2-20101118},
      pnm          = {2171 - Biological and environmental resources for
                      sustainable use (POF4-217)},
      pid          = {G:(DE-HGF)POF4-2171},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000663433400001},
      doi          = {10.1016/j.rhisph.2021.100352},
      url          = {https://juser.fz-juelich.de/record/894425},
}