The idea was to construct a 2-D code that could model multiple sources of contaminant, donor and acceptor, and thus be able to simulate pollution source and injection of materials for bioremediation, and their interactions through the biological matrix. The source and biology terms are explicitly dependent upon currrent timestep quantities. The equation for the microbes, X, will be solved separately as it is a simple ordinary differential equation. The problem is to find a stable method for solution of the combined diffusion and advection equation. Although a number of methods exist for the heat equation, addition of the advection terms make the problem more difficult.
Explicit methods are stable but generally set unacceptable limits on the time stepsize.
The new values obtained for the half step are then used in the evaluation of an implicit y, explicit x set. The advantage of this is that we are left with a number of tridiagonal systems to solve instead of a full NxN system. It should be noted that this system must be constructed and solved for each of the j columns of the grid. In our current model configuration, the boundary conditions are fixed. The 'tridag' routine is indexed from 1 to n where the arrays in our code are indexed 0 to n-1.