Alternative split-operator approach for solving chemical reaction/groundwater transport models |
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| Institution: | 1. Environment Research Institute, Shandong University, Jinan, 250100, PR China;2. College of Environment and Safety Engineering, Qingdao University of Science and Technology, Qingdao, 266042, PR China;1. University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands;2. Dutch Polymer Institute DPI, PO Box 902, 5600 AX Eindhoven, The Netherlands;1. Faculty of Engineering, China University of Geosciences (Wuhan), Wuhan 430074, China;2. State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230027, China;3. Jiangsu Key Laboratory of Urban and Industrial Safety, College of Safety Science and Engineering, Nanjing Tech University, Nanjing 210009, China;4. School of Civil Engineering, Hefei University of Technology, Hefei 230009, China;1. Van ’t Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands;2. Dutch Polymer Institute DPI, PO Box 902, 5600 AX Eindhoven, The Netherlands;1. Beijing Training Institute of Aviation Equipment, Beijing 100076, China;2. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China;3. Beijing Institute of Tracking and Telecommunications Technology, Beijing 100094, China |
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| Abstract: | Various schemes are available to solve coupled transport/reaction mathematical models, one of the most efficient and easy to apply being the two-step split-operator method in which the transport and reaction steps are performed separately. Operator splitting, however, does not solve exactly the fully coupled numerical model derived from the governing partial differential and algebraic equations describing the transport and reaction processes. An error, proportional to Δt (the time step used in the numerical solution) is introduced. Thus, small time steps must be used to ensure that accurate solutions result. An alternative scheme is presented, which iterates to the exact solution of the fully coupled numerical model. The new scheme enables accurate solutions to be calculated more efficiently than the two-step method, while maintaining separation of the transport and reaction steps in the calculations. As in the two-step method, the reaction calculations are performed node-wise throughout the computation grid. However, because the scheme relies on LU factorisation of the coefficient matrix in the transport equation solution, the reaction calculations must be performed in sequence, the sequence order being determined by the ordering of the nodes in the grid. Also, because LU factorisation is used, the scheme is limited to solute transport problems for which LU factorisation is a practical solution method. |
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