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Introduction to MODFLOW. i-1 i i+1. x i-1/2. x i+1/2. General 3D equation used in MODFLOW. Block centered grid. x i. K values in the space between nodes is calculated using the harmonic mean. The default boundary condition is no flow.

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slide2

i-1 i i+1

xi-1/2

xi+1/2

General 3D equation used in MODFLOW

Block centered grid

xi

slide4

K values in the space between nodes

is calculated using the harmonic mean

slide6

No flow boundary

Imaginary

nodes

K=0

(i+1)

(i,j,k)

K=0

K=0

= 0

slide9

Conductance

Darcy’s law

slide10

In general, conductance

= KA/L

Also:

leakance = Kv/thickness

resistance = thickness/Kv

(resistance is an analytic element term)

slide11

Vertical Conductance Terms

MODFLOW uses special terms (VCONT) for

vertical conductance, which is required in

3D problems. Modflow.exe requires the user

to supply values for the VCONT arrays.

GW Vistas computes the values in the VCONT

arrays for you.

VCONT = Kv/z

= Conductance/(xy)

= “leakance”

slide12

Vertical conductance is defined using leakance, or

VCONT in MODFLOW language.

We also have horizontal conductance along rows

and along columns.

slide13

See MODFLOW manual (p. 2-19)

or 2nd ed. of textbook

by Domenico & Schwartz (Eqn. 7.15)

for MODFLOW’s FD equation

slide14

Types of Layers (LAYCON array)

Confined

Unconfined

Convertible

(Useful to think in terms of a layer transmissivity.)

slide15

h

layer 1

bot

layer 2

datum

Conductance

Confined layer transmissivity = (KRi,j-1/2,k)(vk)

Unconfined layer transmissivity = (KRi,j-1/2,k)(hi,j,k-BOTi,j,k)

slide16

TOP

BOT

Input of Grid Spacing

  • MODFLOW asks for values of horizontal grid spacing
  • (i.e., r and c) but not vertical grid spacing (v).
  • Vertical grid spacing (v) is calculated by MODFLOW
  • from user supplied values of the bottom (BOT)
  • of each layer. (GwVistas asks for both top and bottom of
  • each layer.)
slide17

Note that a top unconfined layer actually has no top.

The head value in the top layer could potentially

rise to infinity.

Land surface elevation is not used in MODFLOW,

except in the ET package.

slide18

Examples of solution techniques that combine

matrix solution with iteration:

IADI (see chapter 5 of W&A)

SSOR*

SIP*

PCG2*

*Used in MODFLOW

slide19

m+1

Note: m is time level and

n is iteration level.

t

m

m-1

Schematic

of solution

procedure

slide20

The 3D eqn. with

an implicit approximation

generates a

coefficient matrix

with 7 diagonals

slide21

Coefficient Matrix for a model with 2 rows, 3 columns, 2 layers.

Matrix is sparse and symmetric.

slide23

SSOR

The coefficient matrix has 5 diagonals

Coefficient matrix is

Symmetric and banded

slide25

MODFLOW88/96

Packages

required

required

head

dependent

BCs

1 is required

& PCG2

slide26

Input assembly

for the BAS Package