An Adaptive Local Grid Refinement and Peak/Valley Capture Algorithm to Solve Nonlinear Transport Problems with Moving Sharp-Fronts

Journal Article · Tue Jan 01 04:00:00 EST 2008 · Transport in Porous Media

DOI:https://doi.org/10.1007/s11242-007-9135-2· OSTI ID:930880

Zhang, Fan ^[1]; Jiang, L. ^[2]; Yeh, Gour-Tsyh ^[3]; Parker, Jack C ^[1]

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1. ORNL
2. University of Texas, Arlington
3. University of Central Florida, Orlando

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 Lagrangian-Eulerian decoupling method with an adaptive ZOOMing and Peak/valley Capture (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.

• Research Organization: Oak Ridge National Laboratory (ORNL)
• Sponsoring Organization: ORNL work for others
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 930880
• Journal Information: Transport in Porous Media, Journal Name: Transport in Porous Media Journal Issue: 1 Vol. 72; ISSN TPMEEI
• Country of Publication: United States
• Language: English

Related Subjects

54 ENVIRONMENTAL SCIENCES
97 MATHEMATICS AND COMPUTING
ALGORITHMS
CALCULATION METHODS
CHEMICAL REACTIONS
ENVIRONMENTAL TRANSPORT
MULTIPHASE FLOW
NONLINEAR PROBLEMS
POLLUTANTS