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.