American Society of Civil Engineers

Dynamic Subtiming-Based Implicit Nonoscillating Scheme for Contaminant Transport Modeling

by Chaitali Misra, (Graduate Student, Dept. of Civil Engineering, IIT Madras, Chennai 600036, India), S. T. Manikandan, (Chief Scientist, Miyav Learning, Saibaba Colony, Coimbatore 641011, India), S. Murty Bhallamudi, (Professor, Dept. of Civil Eng., IIT Madras, Chennai 600036, India), and Sorab Panday, (corresponding author), (AMEC Geomatrix, Herndon, VA 20170 E-mail:

Journal of Hydrologic Engineering, Vol. 17, No. 6, June 2012, pp. 694-703, (doi:

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Document type: Journal Paper
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.

ASCE Subject Headings:
Subsurface flow
Numerical models
Water pollution

Author Keywords:
Dynamic subtime-stepping
Subsurface flow
Numerical models