An adaptive local grid refinement and peak/valley capture algorithm to solve nonlinear transport problems with moving sharp-fronts
- 85 Downloads
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.
KeywordsNonlinear advection–dispersion-reaction equations Lagrangian-Eulerian decoupling method with an adaptive ZOOMing and Peak/valley Capture (LEZOOMPC) Burger equation Multiphase flow Peak/valley capturing Adaptive local grid refinement
Unable to display preview. Download preview PDF.
- Allen, M.B.: Collocation techniques for modeling compositional flows in porous media. Ph.D. Dissertation. Dept. Of Civil Eng., Princeton University, Princeton, New Jersey (1983)Google Scholar
- Baptista, A.M.: Solution of advection-dominated transport by Eulerian-Lagrangian methods using the backward methods of characteristics. Ph.D. Dissertation. Dept. of Civil Eng., MIT (1987)Google Scholar
- Chilakapati, A.: Nonlinear reactions and nonlinear flows. In: Yabusaki, S. (ed.) Workshop on Subsurface Reactive Transport Modeling. Pacific Northwest National Laboratory, Richland, Washington, October 29–November 1 (1997)Google Scholar
- Huang, C.-P., Yeh, H.-D., Yang, S.-Y.: Applications of accelerate methods on the evaluation of two types of drawdown solutions. Proceedings of the 11th Hydraulic Engineering Conference. Taipei, Taiwan. 2000, July 5th–6th, D-147-D-152 (2000)Google Scholar
- Toda, K.: Numerical modeling of advection phenomena. Ph.D. Dissertation. Dept. Of Civil and Environ. Eng., The University of Iowa, Iowa City, Iowa, 118 pp (1986)Google Scholar
- Yang, S.-Y., Yeh, H.-D.: On the Formulas for Flux around the well under the Constanthead Condition. Proceedings of the 11th Hydraulic Engineering Conference. Taipei, Taiwan, July 5th–6th, D-169–D-173 (2000)Google Scholar
- Yeh, G.T.: Issues in modeling reactive chemical transport. In: Yabusaki, S. (ed.) Workshop on Subsurface Reactive Transport Modeling. Pacific Northwest National Laboratory, Richland, Washington, October 29–November 1 (1997)Google Scholar