A method of alternating characteristics with application to advection-dominated environmental systems.
Scientists at Lawrence Berkeley National Lab (LBNL) propose a numerical integration method, termed the method of alternating characteristics (MAC), to efficiently and accurately solve systems of partial differential equations that arise in modeling environmental processes. They highlight the advantages of the MAC with emphasis on advection-dominated environmental systems with biogeochemical reactions.
The proposed method is uniquely suited for solving depth-resolved models of advection-dominated environmental systems with biogeochemical reactions and offers advantages in performance over other numerical integration schemes that often require considerable computational resources.
Here, LBNL scientists present a numerical integration method for solving systems of partial differential equations (PDEs) that arise 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 proposed method, termed the method of alternating characteristics (MAC), 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.
Contacts (BER PM)
Terrestrial Ecosystem Science, SC-23.1
William J. Riley
Lawrence Berkeley National Laboratory
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, Terrestrial Ecosystem Science Program, under contract number DE-AC02-05CH11231. K.G. acknowledges support from 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.
Georgiou, K., J. Harte, A. Mesbah, and W. J. Riley. "A method of alternating characteristics with application to advection-dominated environmental systems." Computational Geosciences, (2018). [DOI:10.1007/s10596-018-9729-5]
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