Paul Hsieh provides a sample random walk program on his web page from Stanford University. This is a nice tool that exhibits the character of a random walk simulation.

Open the web page, Sample Random Walk Simulation read the brief directions, then follow these steps

Start:

Grid Spacing 50

Columns 20

Rows 40

Average gradient 0.001

OK

Properties

Check Randomize

OK

Head

20

Compute

Flow

Check Particle Movement

Initial Particle Spacing 20

OK

Place the Cursor near the left side of the flow field

Click the left mouse button 4 times forming a square, and holding the shift key while clicking the 4th time

Animation

1 sec 30 days

Longitudinal Dispersivity 10

Transverse Dispersivity 5

Check Show Center of Mass

OK

Click on the flow field to start the particle movement

Click again to stop/start particles

Notice the particles "jump" in a forward advective step, but then the random movement of the dispersive step make the particles move backwards at times as well as sideways.

Notice the net effect of the plume with time

You can lay any size grid over this and compute concentration as the number of particles times their mass divided by the volume represented by the grid

A coarse grid causes averaging of the concentration

A fine grid provides a more accurate reflection as long as it is not so fine such that many of the grid cells contain no particles.

The local velocity controls the advective step, so if the time step is long you will miss the twists and turns of the flow lines as they adjust to the heterogeneity

Recall that dispersivity is a construct of the hydrology profession to cope with variable advection at a scale that is too small to represent with flow models

You can experiment with comparing random walks through homogeneous materials with various values of dispersivity to heterogeneous models with ZERO dispersivities

CLOSE the RANDOM WALK MODEL

CLOSE the external WEB PAGE

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