An adaptive local grid refinement and peak/valley capture algorithm to solve nonlinear transport problems with moving sharp-fronts

Highly nonlinear advection–dispersion-reaction equations govern numerous transport phenomena. Robust, accurate, and efficient algorithms to solve these equations hold the key to the success of applying numerical models to field problems. This paper presents the development and verification of a comp...

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Bibliographic Details
Published in:Transport in porous media 2008-03, Vol.72 (1), p.53-69
Main Authors: Zhang, F., Jiang, L., Yeh, G. T., Parker, J. C.
Format: Article
Language:English
Subjects:
Algorithms
Burgers equation
Civil Engineering
Classical and Continuum Physics
Contaminants
Convergence
Decoupling method
Earth and Environmental Science
Earth Sciences
Earth, ocean, space
Exact sciences and technology
Geotechnical Engineering & Applied Earth Sciences
Grid refinement (mathematics)
Hydrogeology
Hydrology. Hydrogeology
Hydrology/Water Resources
Industrial Chemistry/Chemical Engineering
Multiphase flow
Nonlinear equations
Organic chemistry
Program verification (computers)
Robustness (mathematics)
Tracking
Transport phenomena
Zooming
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Summary:Highly nonlinear advection–dispersion-reaction equations govern numerous transport phenomena. Robust, accurate, and efficient algorithms to solve these equations hold the key to the success of applying numerical models to field problems. This paper presents the development and verification of a computational algorithm to approximate the highly nonlinear transport equations of reactive chemical transport and multiphase flow. The algorithm was developed based on the L agrangian- E ulerian decoupling method with an adaptive ZOOM ing and P eak/valley C apture (LEZOOMPC) scheme. It consists of both backward and forward node tracking, rough element determination, peak/valley capturing, and adaptive local grid refinement. A second-order tracking was implemented to accurately and efficiently track all fictitious particles. Shanks’ method was introduced to deal with slowly converging case. The accuracy and efficiency of the algorithm were verified with the Burger equation for a variety of cases. The robustness of the algorithm to achieve convergent solutions was demonstrated by highly nonlinear reactive contaminant transport and multiphase flow problems.
ISSN:0169-3913
1573-1634
DOI:10.1007/s11242-007-9135-2