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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

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slide1
Toth Problem(2D, steady state)

z

water table

Governing Equation:

Groundwater

divide

Groundwater

divide

Impermeable Rock

x

slide2
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)
slide4

z

h = c x + zo

Groundwater

divide

Groundwater

divide

Impermeable Rock

x

slide5
Toth Problem

h = c x + zo

2D, steady state

slide6
Block Centered

Boundary

How to handle

flux boundary conditions

Imaginary

Node

Mesh Centered

Boundary

slide7
Imaginary

Node

Mesh Centered

Boundary

slide8
Mesh Centered Boundary

At RHS boundary:

i+1,j

i,j

i-1,j

slide9
Mesh Centered Boundary

At LHS boundary:

i,j

i-1,j

i+1,j

slide10
Block Centered

Boundary

i,j

i+1,j

Imaginary

Node

slide11
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

slide12
109.5

100.5

100

110

100 ft

200 ft

Toth Problem

mesh vs block centered grids – another view

x = y = a = 20 ft

slide13
109.5

100.5

100

110

Toth Problem:

mesh centered has 11 columns and 6 rows block centered has 10 columns and 5 rows

slide14
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

slide15
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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