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Grid refinement in Cartesian coordinates for groundwater flow models using the divergence theorem and Taylor's series
1British Geological Survey, Kingsley Dunham Centre, Keyworth, Nottinghamshire, UK. majm@bgs.ac.uk
Ground Water
|March 14, 2012
Summary
A new numerical groundwater model uses grid refinement to enhance accuracy without slowing simulations. This method improves flow calculations and accuracy for complex aquifer simulations.
Area of Science:
- Hydrogeology
- Numerical Modeling
- Computational Methods
Background:
- Traditional numerical groundwater models face challenges with accuracy and computational efficiency.
- Existing grid refinement techniques exhibit drawbacks like interpolation deficiencies and non-reciprocal calculations.
- High truncation errors and mesh construction issues limit the precision of numerical solutions.
Purpose of the Study:
- To introduce an advanced grid refinement scheme for numerical groundwater modeling.
- To improve the accuracy of local solutions without increasing model run time.
- To address limitations of previous grid refinement methods.
Main Methods:
- Developed a novel grid refinement scheme based on the divergence theorem and Taylor's expansions.
- Incorporated additional terms from Taylor's series to enhance numerical solution precision.
- Ensured flow reciprocity and achieved high-order refinement capabilities.
Main Results:
- Applied the new numerical method to simulate groundwater flow in confined aquifers (homogeneous and heterogeneous).
- Achieved acceptable degrees of accuracy in the simulation results.
- Demonstrated the method's effectiveness in maintaining flow reciprocity.
Conclusions:
- The presented grid refinement scheme offers improved accuracy for numerical groundwater modeling.
- The method successfully simulates groundwater flow in various aquifer conditions.
- This approach shows potential for solving groundwater head problems on nested, irregular meshes.
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