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Numerical Simulation of Groundwater Pollution Problems Based on Convection Diffusion Equation
College of Mathematics and Statistics, Shandong Normal University, Jinan, China
College of Mathematics and Statistics, Shandong Normal University, Jinan, China
- 1 College of Mathematics and Statistics, Shandong Normal University, Jinan, China
- 2 College of Mathematics and Statistics, Shandong Normal University, Jinan, China
American Journal of Computational Mathematics·Volume 07 (2017)·Pages 350–370·Published 1 August 2017·DOI10.4236/ajcm.2017.73025
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Abstract
The analytical solution of the convection diffusion equation is considered by two-dimensional Fourier transform and the inverse Fourier transform. To get the numerical solution, the Crank-Nicolson finite difference method is constructed, which is second-order accurate in time and space. Numerical simulation shows excellent agreement with the analytical solution. The dynamic visualization of the simulating results is realized on ArcGIS platform. This work provides a quick and intuitive decision-making basis for water resources protection, especially in dealing with water pollution emergencies.
KeywordsGroundwater PollutionTwo-Dimensional Convection Diffusion EquationFinite Difference MethodVisualizationNumerical Simulation
- Ger, M., Baran, O.U. and Irfanoglu, B. (2004) Numerical Simulation of Groundwater Contamination. Building Partnerships, Building Partnerships, ASCE.
- Chen, J.D., Wang, Y., Song, M.L. and Zhao, R.C. (2017) Analyzing the Decoupling Relationship between Marine Economic Growth and Marine Pollution in China. Ocean Engineering, 137, 1-12.
- Hasnain, S. and Saqib, M. (2017) Numerical Study of One Dimensional Fishers KPP Equation with Finite Difference Schemes. American Journal of Computational Mathematics, 7, 70-83. https://doi.org/10.4236/ajcm.2017.71006
- Park, E. and Zhan, H. (2001) Analytical Solutions of Contaminant Transport from Finite One-, Two-, and Three-Dimensional Sources in a Finite-Thickness Aquifer. Journal of Contaminant Hydrology, 53, 41-61.
- Refsgaard, J.C., Thorsen, M., Jensen, J.B., Kleeschulte, S. and Hansen, S. (1999) Large Scale Modeling of Groundwater Contamination from Nitrate Leaching. Journal of Hydrodynamics, 221, 117-140.
- Dillon, P.J. (1989) An Analytical Model of Contaminant Transport from Diffuse Sources in Saturated Porous Media. Water Resources Research, 25, 1208-1218. https://doi.org/10.1029/WR025i006p01208
- Li, H. and Jiao, J.J. (2002) Analytical Solutions of Tidal Groundwater Flow in Coastal Two-Aquifer System. Advances in Water Resources, 25, 417-426.
- Sun, N.Z. (1989) Applications of Numerical Methods to Simulate the Movement of Contaminants in Groundwater. Environmental Health Perspectives, 83, 97-115. https://doi.org/10.1289/ehp.898397
- Lin, L., Yang, J.Z., Zhang, B., Zhang, B. and Zhu, Y. (2010) A Simplified Numerical Model of 3-D Groundwater and Solute Transport at Large Scale Area. Journal of Hydrodynamics, 22, 319-328.
- Zhu, Q., Wang, Q., Fu, J. and Zhang, Z. (2012) New Second-Order Finite Difference Scheme for the Problem of Contaminant in Groundwater Flow. Journal of Applied Mathematics, 2012, 129-154.
- Qin, R., Lin, L., Kuang, C., Su, T.C., Mao, X. and Zhou, Y. (2017) A GIS-Based Software for Forecasting Pollutant Drift on Coastal Water Surfaces Using Fractional Brownian Motion: A Case Study on Red Tide Drift. Environmental Modelling & Software, 92, 252-260.
- Valocchi, A.J. and Werth, C.J. (2004) Web-Based Interactive Simulation of Groundwater Pollutant Fate and Transport. Computer Applications in Engineering Education, 12, 75-83. https://doi.org/10.1002/cae.20000