1. Toth Problem (2D, steady state) Impermeable Rock Groundwater divide Groundwater divide z x water table Governing Equation:

2. Types of Boundary Conditions 1.Specified head (also called a Dirichlet or Type 1 boundary) 2. Specified flux (also called a Neumann or Type 2 boundary) 3. Head dependent flux (also called a Cauchy or Type 3 boundary)

3. water table

4. Impermeable Rock Groundwater divide Groundwater divide z x h = c x + z o 

5. Toth Problem 2D, steady state h = c x + z o

6. Mesh Centered Boundary Block Centered Boundary Imaginary Node How to handle flux boundary conditions

7. Mesh Centered Boundary Imaginary Node

8. At RHS boundary: i,j i+1,j i-1,j Mesh Centered Boundary

9. At LHS boundary: i,j i-1,ji+1,j Mesh Centered Boundary

10. Block Centered Boundary Imaginary Node i,j i+1,j

11. For Problem Set 1: The mesh centered grid has 11 columns and 6 rows. One option is to set up the block centered grid with 11 columns and 6 rows

12.  x =  y = a = 20 ft 100 110 Toth Problem mesh vs block centered grids – another view 100.5 109.5 100 ft 200 ft

13. 100 110 Toth Problem: mesh centered has 11 columns and 6 rows block centered has 10 columns and 5 rows 100.5 109.5

14. 100 110 Toth Problem: mesh centered has 11 columns and 6 rows block centered has 10 columns and 5 rows 100.5 109.5 90 ft

15. Now we can set up a spreadsheet to solve the Toth Problem. The next step is to compute the water budget and the error in the water budget.