(3)
Solving the Model
The existence of the stochastic components in the model equations makes it difficult to solve them. If we integrate (1) , the velocity equation, we get:
|
|
(3) |
The last term in (3) must be replaced by 
which is given by:
|
|
NEEDS CHECKING (4) |
where
|
dt |
represents the integration step length |
|
N(0,1) |
represents a standard normal variate |
|
e |
is the eigenvalue of the matrix which models the space correlation which occurs due to the Wiener process W |
|
s |
represents the size of the random component |
The scheme for the solute flux equation (2) is similar. See (Kulasiri ,1997) for further information on the solution of the equations.
