Automatic Time Stepping with Global Error Control for Groundwater Flow Models
Publication: Journal of Hydrologic Engineering
Volume 13, Issue 9
Abstract
Automatic time stepping with global error control is proposed for the time integration of the diffusion equation to simulate groundwater flow in confined aquifers. The scheme is based on an a posteriori error estimate for the discontinuous Galerkin finite-element methods. A stability factor is involved in the error estimate and it is used to adapt the time step and control the global temporal error for the backward Euler method. The stability factor can be estimated by solving a dual problem. The stability factor is not sensitive to the accuracy of the dual solution and the overhead computational cost can be minimized by solving the dual problem using large time steps. Numerical experiments are conducted to show the application and the performance of the automatic time stepping scheme. Implementation of the scheme can lead to improvements in accuracy and efficiency of groundwater flow models.
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Acknowledgments
This material is based upon work supported by the National Science Foundation under Grant No. NSFCMS-0093752 (CAREER program) and by the U.S. Department of Energy’s Office of Science Biological and Environmental Research, Environmental Remediation Sciences Program (ERSP). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the writers and do not necessarily reflect the views of the National Science Foundation. Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for the U.S. Department of Energy under Contract No. DOEDE-AC05-00OR22725.DOE
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Information
Published In
Journal of Hydrologic Engineering
Volume 13 • Issue 9 • September 2008
Pages: 803 - 810
Copyright
© 2008 ASCE.
History
Received: Oct 23, 2006
Accepted: Jun 4, 2007
Published online: Sep 1, 2008
Published in print: Sep 2008
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