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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

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Toth Problem (2D, steady state)

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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.


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