the model the chamber values are shifted back one chamber per time step and the

mixing process repeated. This procedure results in memory of the history of

concentrations crossing the boundary, delays full specification of the nominal

boundary concentration Cb, and generally provides more realistic boundary

conditions. Furthermore, the buffering also provides a buffer for the changes that

any plan alternatives to be tested may have on the boundary conditions.

The governing equation (1) is then cast into the Galerkin finite element form using

quadratic shape functions, N ,

∂C ⎤

⎡

∂N j

∂C ∂N j

^

^

^

^

⎧

^⎫ +

∂C

∂C

∑1 ∫∫ ⎢ N j ⎨*Q *+ *u *∂x + *v *∂y -α 1 C ⎬ ∂x

⎥

⎩

⎭

⎦

⎣

+∑∫*N*

=0

⎛ ∧⎞

⎜∂*C *⎟

⎜ ∂*t *⎟ + α 2 for the transient problem

Where Q=

⎜

⎟

⎝

⎠

where

=

total number of elements

=

the quadratic shape(or basis) functions

Q

=

See above

^

=

the approximate concentration in an element as evaluated from

shape functions and nodal point values of C

=

total number of boundary segments

ζ

=

the local coordinate

=

flux from source on boundary i

The transient equation is expressed as

[T ]∂ {C} + [K ]{C}- {F } = 0

∂t

where each element in the computation mesh contributes the following terms to the

global matrix

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