Adaptive time stepping and error control in a mass conservative numerical solution of the mixed form of Richards equation

Publication: Research - peer-reviewJournal article – Annual report year: 2002

Without internal affiliation

  • Author: Kavetski, D.

    University of Newcastle, Department of Civil, Surveying and Environmental Engineering

  • Author: Binning, Philip John

    Unknown

  • Author: Sloan, S. W.

    Department of Civil, Surveying and Environmental Engineering

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Adaptive time stepping with embedded error control is applied to the mixed form of Richards equation. It is the first mathematically based adaptive scheme applied to this form of Richards equation. The key to the method is the approximation of the local truncation error of the scheme in terms of the pressure head, although, to enforce mass conservation, the principal time approximation is based on the moisture content. The time stepping scheme is closely related to an implicit Thomas-Gladwell approximation and is unconditionally stable and second-order accurate. Numerical trials demonstrate that the new algorithm fully automates stepsize selection and robustly constrains temporal discretisation errors given a user tolerance. The adaptive mechanism is shown to improve the performance of the non-linear solver, providing accurate initial solution estimates for the iterative process. Furthermore, the stepsize variation patterns reflect the adequacy of the spatial discretisation, here accomplished by linear finite elements. When sufficiently dense spatial grids are used, the time step varies smoothly, while excessively coarse grids induce stepsize oscillations. (C) 2001 Elsevier Science Ltd. All rights reserved.
Keyword: conservation of mass,adaptive time stepping,Richards equation
Original languageEnglish
JournalAdvances in Water Resources
Publication date2002
Volume24
Issue5
Pages595-605
ISSN0309-1708
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 43
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