Dynamic Subtiming-Based Implicit Nonoscillating Scheme for Contaminant Transport Modeling
Publication: Journal of Hydrologic Engineering
Volume 17, Issue 6
Abstract
A dynamic subtime-stepping method is described for solving contaminant transport problems that utilize higher-order implicit time-marching procedures with higher-accuracy nonoscillating spatial-discretization methods to resolve sharp-plume fronts in advection-dominated systems. Nonoscillating spatial-discretization methods for the advective term prevent unphysical oscillations and minimize numerical diffusion. Second-order temporal accuracy is achieved by using the Crank-Nicholson implicit scheme, however nonoscillating properties may be violated for Courant Numbers larger than one, leading to spurious oscillations. The proposed subtiming method allows use of small time-step sizes in critical portions of a domain, with larger time-step sizes in other locations. This locally limits the Courant number where required and still keeps the general solution free of time-step size restrictions. This technique makes it possible to apply higher-order nonoscillating schemes with higher-order temporal weighting for advection-dominated flows, even when the Courant number is much greater than one. Feasibility and applicability of the dynamic implicit subtiming method are demonstrated through three proof-of-concept example problems.
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Published In
Journal of Hydrologic Engineering
Volume 17 • Issue 6 • June 2012
Pages: 694 - 703
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Dec 26, 2010
Accepted: Sep 13, 2011
Published online: Sep 15, 2011
Published in print: Jun 1, 2012
Published ahead of production: Jun 15, 2012
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