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A method of alternating characteristics with application to advection-dominated environmental systems

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Abstract

We present a numerical method for solving a class of systems of partial differential equations (PDEs) that arises in modeling environmental processes undergoing advection and biogeochemical reactions. The salient feature of these PDEs is that all partial derivatives appear in linear expressions. As a result, the system can be viewed as a set of ordinary differential equations (ODEs), albeit each one along a different characteristic. The method then consists of alternating between equations and integrating each one step-wise along its own characteristic, thus creating a customized grid on which solutions are computed. Since the solutions of such PDEs are generally smoother along their characteristics, the method offers the potential of using larger time steps while maintaining accuracy and reducing numerical dispersion. The advantages in efficiency and accuracy of the proposed method are demonstrated in two illustrative examples that simulate depth-resolved reactive transport and soil carbon cycling.

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Acknowledgments

We thank the two anonymous reviewers for their constructive input, which greatly improved this manuscript. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, as part of the Terrestrial Ecosystem Science Program under Contract No. DE-AC02-05CH11231.

Funding

K.G. acknowledges support from the National Science Foundation Graduate Research Fellowship under Grant No. DGE 1106400 and the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists, Office of Science Graduate Student Research (SCGSR) program. The SCGSR program is administered by the Oak Ridge Institute for Science and Education (ORISE) for the DOE. ORISE is managed by ORAU under contract number DE-SC0014664.

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Authors and Affiliations

  1. Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA, 94720, USA

    Katerina Georgiou & Ali Mesbah

  2. Earth and Environmental Sciences, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., 74R316C, Berkeley, CA, 94720, USA

    Katerina Georgiou & William J. Riley

  3. Energy and Resources Group, University of California, Berkeley, CA, 94720, USA

    John Harte

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  1. Katerina Georgiou
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Correspondence to Katerina Georgiou.

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Georgiou, K., Harte, J., Mesbah, A. et al. A method of alternating characteristics with application to advection-dominated environmental systems. Comput Geosci 22, 851–865 (2018). https://doi.org/10.1007/s10596-018-9729-5

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  • DOI: https://doi.org/10.1007/s10596-018-9729-5

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