Simulation and parameter optimization

The system described above is an oversimplification of the actual biofilm processes in nature. However, the example serves to illustrate how complex the solution for such a simplified version could be. In the old days before fast and efficient computers, solving such problems manually was unthink­able. Lately, computer speed has increased exponentially and memory is no longer a limiting factor. Innovative tools for simulation of the PDE system and heuristic approaches for estimating parameters are now available. For example, Nkhalambayausi-Chirwa and Wang (2005) applied a custom PDE solver to solve the model equations for simultaneous Cr+6 reduction and phenol degradation in a dual species biofilm reactor. The PDE solver uti­lized the (fourth-order) Runge-Kutta method with spatial discretization using the (second-order) Crank-Nicholson and Backward Euler finite dif­ference methods for the biofilm spatial profiles. The solution of the biofilm PDE system of equations is shown as a solid line in the effluent from a biofilm reactor showing the prediction of the metal reduction process in the biofilm (Figs 15.12 and 15.13).

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