Page 280 - Process Modelling and Simulation With Finite Element Methods

Coupling Vuriables Revisited 261

(7.12)

Let M be the total concentration dose in the domain

(7.13)

Then these projection coupling variables can be treated as normalized
conditional probability density functions, with moments, in the case of projI:

(7.14)

For c=cO(x,y), the initial Gaussian, one can show that the first moment locates
the x-coordinate, mx,l=xo. The second moment permits the computation of the
standard deviation according to

(7.15)

Both conclusions obviously hold for x-projections onto the y-axis. So
projections can locate and size a cloud of Gaussian shape. For non-Gaussian
clouds, they provide at least a notion of centrality and degree of spread.
Now we demonstrate this example in action in FEMLAB. Launch FEMLAB and
in the Model Navigator do the following:

Select 2-D dimension
Select ChE=K!artesian*Mass Balance, Convection and
Diffusion, time-dependent (cd mode)>>
1 dependent variable c