Grid Refinement in Cartesian Coordinates for Groundwater Flow Models Using the Divergence Theorem and Taylor's Series
Article first published online: 12 MAR 2012
© 2012, British Geological Survey © NERC 2012. Ground Water © 2012, National GroundWater Association.
Volume 51, Issue 1, pages 66–75, January/February 2013
How to Cite
Mansour, M.M. and Spink, A.E.F. (2013), Grid Refinement in Cartesian Coordinates for Groundwater Flow Models Using the Divergence Theorem and Taylor's Series. Groundwater, 51: 66–75. doi: 10.1111/j.1745-6584.2012.00924.x
- Issue published online: 2 JAN 2013
- Article first published online: 12 MAR 2012
- Received January 2011, accepted February 2012.
Grid refinement is introduced in a numerical groundwater model to increase the accuracy of the solution over local areas without compromising the run time of the model. Numerical methods developed for grid refinement suffered certain drawbacks, for example, deficiencies in the implemented interpolation technique; the non-reciprocity in head calculations or flow calculations; lack of accuracy resulting from high truncation errors, and numerical problems resulting from the construction of elongated meshes. A refinement scheme based on the divergence theorem and Taylor's expansions is presented in this article. This scheme is based on the work of De Marsily (1986) but includes more terms of the Taylor's series to improve the numerical solution. In this scheme, flow reciprocity is maintained and high order of refinement was achievable. The new numerical method is applied to simulate groundwater flows in homogeneous and heterogeneous confined aquifers. It produced results with acceptable degrees of accuracy. This method shows the potential for its application to solving groundwater heads over nested meshes with irregular shapes.