Finite Difference Method of Modelling Groundwater Flow

ABSTRACT

In this study, finite difference method is used to solve the equations that govern groundwater flow to obtain flow rates, flow direction and hydraulic heads through an aquifer. The aim therefore is to discuss the principles of Finite Difference Method and its applications in groundwater modelling. To achieve this, a rectangular grid is overlain an aquifer in order to obtain an exact solution. Initial and boundary conditions are then determined. By discretizing the system into grids and cells that are small compared to the entire aquifer, exact solutions are obtained. A flow chart of the computational algorithm for particle tracking is also developed. Results show that under a steady-state flow with no recharge, pathlines coincide with streamlines. It is also found that the accuracy of the numerical solution by Finite Difference Method is largely dependent on initial particle distribution and number of particles assigned to a cell. It is therefore concluded that Finite Difference Method can be used to predict the future direction of flow and particle location within a simulation domain.

In this study, finite difference method is used to solve the equations that govern groundwater flow to obtain flow rates, flow direction and hydraulic heads through an aquifer. The aim therefore is to discuss the principles of Finite Difference Method and its applications in groundwater modelling. To achieve this, a rectangular grid is overlain an aquifer in order to obtain an exact solution. Initial and boundary conditions are then determined. By discretizing the system into grids and cells that are small compared to the entire aquifer, exact solutions are obtained. A flow chart of the computational algorithm for particle tracking is also developed. Results show that under a steady-state flow with no recharge, pathlines coincide with streamlines. It is also found that the accuracy of the numerical solution by Finite Difference Method is largely dependent on initial particle distribution and number of particles assigned to a cell. It is therefore concluded that Finite Difference Method can be used to predict the future direction of flow and particle location within a simulation domain.

KEYWORDS

Finite Difference Method, Groundwater Modelling, Particle Tracking, Algorithm, Discretization, Flow Rates, Hydraulic Heads

Finite Difference Method, Groundwater Modelling, Particle Tracking, Algorithm, Discretization, Flow Rates, Hydraulic Heads

Cite this paper

nullM. Igboekwe and N. Achi, "Finite Difference Method of Modelling Groundwater Flow,"*Journal of Water Resource and Protection*, Vol. 3 No. 3, 2011, pp. 192-198. doi: 10.4236/jwarp.2011.33025.

nullM. Igboekwe and N. Achi, "Finite Difference Method of Modelling Groundwater Flow,"

References

[1] R. A. Freeze, “Three Dimensional Transient Saturated– Unsaturated Flow in a Groundwater Basin,” Water resources Research, 1979, pp. 347-366.

[2] L. F. Konikow and J. D. Bredehoeft, “Computer Model of Two Dimensional Solute Transport and Dispersion in Groundwater,” U.S. Geological Survey, Techniques of Water Resources Investigation Book 7, Chapter C2, 1992, p. 90.

[3] V. Vu.Hung and Ramin S. Estandiari, “Dynamic Systems: Modelling and Analysis,” McGraw-Hill, New York, 1997 p. 612.

[4] J. M. McDonald and A. W. Harbaugh, “A Modular Thr- ee-Dimensional Finite-Difference Groundwater Flow M- ode,” Techniques of Water Resources Investigations of the U. S. Geological Survey Book.6, 1988, p. 586.

[5] T. Narasimha Reddy and V. V. S. Gurunadha Rao, “Water Balance Model and Groundwater Flow Model of Dulapally Basin,” Granitic Terrain, A.P., Research Series No. 9, 1991.

[6] M. P. Anderson and W. W. Woessner, “Applied Gro- undwater Modeling, Simulation of Flow and Advective Transport,” Academic Press, San Diego, C. A, 1992.

[7] M. U. Igboekwe, V. V. S. Gurunadha Rao and E. E. Okwueze, “Groundwater Flow Modelling of Kwa Ibo River Watershed Southeastern Nigeria,” Hydrological Processes, Vol. 22, No. 10, 2008, pp. 1523-1531. doi:10.1002/hyp.6530

[8] M. K. Hubbert, “Darcy’s Law and Field Equations of Flow of Underground Fluids Transaction,” American Institute of Mining and Metallurgical engineers, 1956, pp. 22-239.

[9] T. A. Prickette and C. G. Longuist, “Selected Digital Co- mputer Techniques for Groundwater Resource Evaluation,” Bull.55, Illinois State Water Survey, Urbana, 1981. p. 62.

[10] W. J. Gray and J. L. Hoffman, “A Numerical Model Stu- dy of Ground-Water Contamination from Price's Landfill, New Jersey — I. Data Base and Flow Simulation,” Groundwater, Vol. 21, No. 1, 1983, pp. 7-14. doi:10.1111/j.1745-6584.1983.tb00699.x

[11] D. K. Todd, “Groundwater Hydrology,” 2nd Edition, John Wiley and Sons, New York, 2001.

[12] Peter. C. Trescott and S. P. Larson, “Finite Difference Model for Aquifer Simulation in Two-Dimensions with Results of Numerical Experiments,” U.S. Geological Survey Techniques at Water-Resources Investigations, Book 7, Chapter C1, 1976, p. 116.

[13] C. W. Fetter, “Applied Hydrogeology: Finite Difference Model,” CBS Publishers and Distributors, New Delhi, India, 2000, p. 592.

[14] M. U. Igboekwe, “Geoelectrical Exploration for GroundWater Potentials in Abia State, Nigeria,” An Unpublished PhD dissertation. Michael Okpara University of Agriculture, Umudike, 2005, p. 131.

[15] R. T. Peter, “Numerical Analysis: Runger–Kutta Meth- od,” ISBN 0. 333 -58665- 4, 1994, pp. 214-217.

[1] R. A. Freeze, “Three Dimensional Transient Saturated– Unsaturated Flow in a Groundwater Basin,” Water resources Research, 1979, pp. 347-366.

[2] L. F. Konikow and J. D. Bredehoeft, “Computer Model of Two Dimensional Solute Transport and Dispersion in Groundwater,” U.S. Geological Survey, Techniques of Water Resources Investigation Book 7, Chapter C2, 1992, p. 90.

[3] V. Vu.Hung and Ramin S. Estandiari, “Dynamic Systems: Modelling and Analysis,” McGraw-Hill, New York, 1997 p. 612.

[4] J. M. McDonald and A. W. Harbaugh, “A Modular Thr- ee-Dimensional Finite-Difference Groundwater Flow M- ode,” Techniques of Water Resources Investigations of the U. S. Geological Survey Book.6, 1988, p. 586.

[5] T. Narasimha Reddy and V. V. S. Gurunadha Rao, “Water Balance Model and Groundwater Flow Model of Dulapally Basin,” Granitic Terrain, A.P., Research Series No. 9, 1991.

[6] M. P. Anderson and W. W. Woessner, “Applied Gro- undwater Modeling, Simulation of Flow and Advective Transport,” Academic Press, San Diego, C. A, 1992.

[7] M. U. Igboekwe, V. V. S. Gurunadha Rao and E. E. Okwueze, “Groundwater Flow Modelling of Kwa Ibo River Watershed Southeastern Nigeria,” Hydrological Processes, Vol. 22, No. 10, 2008, pp. 1523-1531. doi:10.1002/hyp.6530

[8] M. K. Hubbert, “Darcy’s Law and Field Equations of Flow of Underground Fluids Transaction,” American Institute of Mining and Metallurgical engineers, 1956, pp. 22-239.

[9] T. A. Prickette and C. G. Longuist, “Selected Digital Co- mputer Techniques for Groundwater Resource Evaluation,” Bull.55, Illinois State Water Survey, Urbana, 1981. p. 62.

[10] W. J. Gray and J. L. Hoffman, “A Numerical Model Stu- dy of Ground-Water Contamination from Price's Landfill, New Jersey — I. Data Base and Flow Simulation,” Groundwater, Vol. 21, No. 1, 1983, pp. 7-14. doi:10.1111/j.1745-6584.1983.tb00699.x

[11] D. K. Todd, “Groundwater Hydrology,” 2nd Edition, John Wiley and Sons, New York, 2001.

[12] Peter. C. Trescott and S. P. Larson, “Finite Difference Model for Aquifer Simulation in Two-Dimensions with Results of Numerical Experiments,” U.S. Geological Survey Techniques at Water-Resources Investigations, Book 7, Chapter C1, 1976, p. 116.

[13] C. W. Fetter, “Applied Hydrogeology: Finite Difference Model,” CBS Publishers and Distributors, New Delhi, India, 2000, p. 592.

[14] M. U. Igboekwe, “Geoelectrical Exploration for GroundWater Potentials in Abia State, Nigeria,” An Unpublished PhD dissertation. Michael Okpara University of Agriculture, Umudike, 2005, p. 131.

[15] R. T. Peter, “Numerical Analysis: Runger–Kutta Meth- od,” ISBN 0. 333 -58665- 4, 1994, pp. 214-217.