Time-Centered Split Method for Implicit Discretization of Unsteady Advection Problems
Publication: Journal of Engineering Mechanics
Volume 135, Issue 4
Abstract
A new method for implicit solution of unsteady nonlinear advection equations is presented. This time-centered split (TCS) method uses a nested application of the midpoint rule to computationally decouple advection terms in a temporally second-order accurate time-marching discretization. The method requires solution of only two sets of linear equations without an outer iteration, and is theoretically applicable to quadratically nonlinear coupled equations for any number of variables. The TCS algorithm is compared to other nonlinear solution methods (local linearization, Picard iteration, and Newton iteration) and applied to the Crank-Nicolson discretization of the one-dimensional Burgers’ equation. The temporal accuracy and practical stability of the method is confirmed using an unsteady flow test case with an analytical solution. The method is shown to require computational effort similar to local linearization, but does not require discrete computation of a functional Jacobian for solution.
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Acknowledgments
The writers would like to thank Dr. Spyros Kinnas and Dr. Graham Carey as well as Yi-Hsiang Yu, Vimal Vinayan, and Paula Kulis for insightful discussions and suggestions. The writers also appreciate all the valuable comments from the anonymous reviewers. This research was partially supported by NSF Earth Science Hydrology Grant No. NSFEAR-0710901 and Texas Water Development Board Research and Planning Grant Nos. UNSPECIFIED2003-469 and UNSPECIFIED2004-483. Additional support was provided by the Center for Research in Water Resources at the University of Texas at Austin.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 4 • April 2009
Pages: 256 - 264
Copyright
© 2009 ASCE.
History
Received: May 8, 2007
Accepted: Nov 25, 2008
Published online: Apr 1, 2009
Published in print: Apr 2009
Notes
Note. Associate Editor: Brett F. Sanders
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