Introduction to MODFLOW

1 / 27

# Introduction to MODFLOW - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Introduction to MODFLOW' - enye

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

i-1 i i+1

xi-1/2

xi+1/2

General 3D equation used in MODFLOW

Block centered grid

xi

K values in the space between nodes

is calculated using the harmonic mean

No flow boundary

Imaginary

nodes

K=0

(i+1)

(i,j,k)

K=0

K=0

= 0

Conductance

Darcy’s law

In general, conductance

= KA/L

Also:

leakance = Kv/thickness

resistance = thickness/Kv

(resistance is an analytic element term)

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”

Vertical conductance is defined using leakance, or

VCONT in MODFLOW language.

We also have horizontal conductance along rows

and along columns.

See MODFLOW manual (p. 2-19)

or 2nd ed. of textbook

by Domenico & Schwartz (Eqn. 7.15)

for MODFLOW’s FD equation

Types of Layers (LAYCON array)

Confined

Unconfined

Convertible

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

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)

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.)

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.

Examples of solution techniques that combine

matrix solution with iteration:

IADI (see chapter 5 of W&A)

SSOR*

SIP*

PCG2*

*Used in MODFLOW

m+1

Note: m is time level and

n is iteration level.

t

m

m-1

Schematic

of solution

procedure

The 3D eqn. with

an implicit approximation

generates a

coefficient matrix

with 7 diagonals

Matrix is sparse and symmetric.

SSOR

The coefficient matrix has 5 diagonals

Coefficient matrix is

Symmetric and banded

MODFLOW88/96

Packages

required

required