Toth Problem (2D, steady state)

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

Types of Boundary Conditions • 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)

water table

 z h = c x + zo Groundwater divide Groundwater divide Impermeable Rock x

Toth Problem h = c x + zo 2D, steady state

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

Imaginary Node Mesh Centered Boundary

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

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

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

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

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

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

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

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.

Toth Problem (2D, steady state)