Coupling surface flow and subsurface flow in complex soil structures using mimetic finite differences

Ethan T. Coon, J. David Moulton, Evgeny Kikinzon, Markus Berndt, Gianmarco Manzini, Rao Garimella, Konstantin Lipnikov, Scott L. Painter

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

We explore the coupling of surface and subsurface flows on fully unstructured meshes that conform to complex soil structures. To accommodate the distorted meshes that inevitably result from explicit representation of complex soil structures, we leverage the structure of the Mimetic Finite Difference (MFD) spatial discretization scheme to couple surface and subsurface flows. The MFD method achieves second-order accuracy and maintains local mass conservation on distorted meshes. We couple the diffusion wave approximation for surface flows to the Richards equation for subsurface flow, ensuring continuity of both pressure and flux between the surface and subsurface. The MFD method is particularly convenient for this coupling because it uses face-based constraints in the subsurface system that can be expressed as face-pressure unknowns. Those unknowns are coincident with surface cell-based unknowns, thus allowing the discrete surface system to be directly substituted into the subsurface system and solved implicitly as a global system. Robust representation of the transition between wet and dry surface conditions requires upwinding of the relative permeability and is facilitated by globalization in the nonlinear solver. The approach and its implementation in the Advanced Terrestrial Simulator (ATS) are evaluated by comparison to previously published benchmarks. Using runoff from soils with patchy groundcover (duff) as an example, we show that the new method converges significantly faster in mesh convergence tests than the commonly used two-point flux approximation.

Original languageEnglish
Article number103701
JournalAdvances in Water Resources
Volume144
DOIs
StatePublished - Oct 2020

Funding

The authors would like to especially thank Reed Maxwell and the participants of the first intercomparison of integrated hydrology codes for developing test problems and sharing their solutions; these efforts take a lot of work but provide a true community service. The ATS software is open source and may be downloaded from https://github/amanzi/ats. Input and output files are available by contacting the corresponding author. This work was supported by ORNL LDRD-8872 , LANL LDRD-20150397DR and LDRD201200068DR , the Interoperable Design of Extreme-scale Application Software (IDEAS) project, and the Next Generation Ecosystem Experiment (NGEE-Arctic) project. IDEAS and NGEE-Arctic are supported by the Office of Biological and Environmental Research in the DOE Office of Science.

Keywords

  • Complex stratigraphy
  • Integrated hydrology
  • Mimetic finite differences

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