Method of lines solution of Richards' equation with spatially and temporally adaptive discretization techniques
Public Deposited- Last Modified
- February 27, 2019
- Creator
-
Abhishek, Chandra
- Affiliation: Gillings School of Global Public Health, Department of Environmental Sciences and Engineering
- Abstract
- Efficient, robust simulation of groundwater flow in the unsaturated zone remains difficult for problems characterized by sharp fronts in both space and time. Employing uniform spatial and temporal discretizations for the numerical solution of these problems can lead to inefficient and expensive simulations. In this work, we solve Richards' equation using the method of lines with both temporally and spatially adaptive approximations. The time discretization adapts both the approximation order and step-size based on formal error control to satisfy user-specified error tolerances. For the spatial discretization, we use h-refinement with a Lagrangian prediction of the fluid front location to determine when and where to refine. We evaluate our method in comparison with uniform spatial discretizations for several test problems. The numerical results demonstrate that this method provides a robust and efficient alternative to standard approaches for simulating variably saturated flow.
- Date of publication
- August 2002
- DOI
- Resource type
- Rights statement
- In Copyright
- Advisor
- DiGiano, Francis A.
- Miller, Cass T.
- Farthing, Matthew W.
- Degree
- Master of Science in Environmental Engineering
- Academic concentration
- Environmental Engineering
- Degree granting institution
- University of North Carolina at Chapel Hill
- Graduation year
- 2002
- Language
- Deposit record
- 8daa46ae-58bd-4ddf-8097-0c44062f7d48
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