Numerical errors of explicit finite difference approximation for two-dimensional solute transport equation with linear sorption |
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| Affiliation: | 1. College of Engineering, Peking University, Beijing 100871, China;2. NAAM Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China;1. School of Architecture and Civil Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212003, China;2. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, 210098, China;3. Institute of Geotechnical Engineering, Yangzhou University, Yangzhou, 225127, China;1. Graduate Institute of Applied Geology, National Central University, Taoyuan City 320, Taiwan;2. Department of Nursing, Fooyin University, Kaohsiung City 831, Taiwan;3. Sinotech Environmental Technology, Ltd, Taipei City 105, Taiwan;4. Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei City 106, Taiwan;1. University of Central Florida, Civil, Environmental, and Construction Engineering, 12800 Pegasus Drive, ENG I Room 340, Orlando, FL 32816, United States;2. University of Central Florida, Office of Research and Commercialization, 4365 Andromeda Loop N., MH 243, Orlando, FL 32816, United States |
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| Abstract: | The numerical errors associated with explicit upstream finite difference solutions of two-dimensional advection—Dispersion equation with linear sorption are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation. The numerical truncation errors are defined using Peclet and Courant numbers in the X and Y direction, a sink/source dimensionless number and new Peclet and Courant numbers in the XY plane. The effects of these truncation errors on the explicit solution of a two-dimensional advection–dispersion equation with a first-order reaction or degradation are demonstrated by comparison with an analytical solution in uniform flow field. The results show that these errors are not negligible and correcting the finite difference scheme for them results in a more accurate solution. |
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