Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/26924

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Title
Adaptive time stepping and error control in a mass conservative numerical solution of the mixed form of Richards equation
Author/Creator
Kavetski, D.;  Binning, P.;  Sloan, S. W.
Description
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.
Relation
Advances in Water Resources Vol. 24, Issue 6, p. 595-605
Publisher Link
http://dx.doi.org/10.1016/S0309-1708(00)00076-2
Date
2001
Publisher
Elseview Science
Keyword(s)
Richards equation;  adaptive time stepping;  conservation of mass
Resource Type
journal article
Identifier
http://hdl.handle.net/1959.13/26924
Identifier
ISSN:0309-1708
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Subject
"Advances in Water Resources"
 
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