title: Non-standard numerical methods applied to subsurface biobarrier formation models in porous media.
abstract: Biofilm forming microbes have complex effects on the flow properties of natural porous media. Subsurface biofilms have the potential for the formation of biobarriers to inhibit contaminant migration in groundwater. Another example of beneficial microbial effects is the biotransformation of organic contaminants to less harmful forms, thereby providing an in situ method for treatment of contaminated groundwater supplies. Mathematical models that describe contaminant transport with biodegradation involve a set of coupled convection-dispersion equations with non-linear reactions. The reactive solute transport equation is one for which numerical solution procedures continue to exhibit significant limitations for certain problems of groundwater hydrology interest. Accurate numerical simulations are crucial to the development of contaminant remediation strategies. A new numerical method is developed for simulation of reactive bacterial transport in porous media. The non-standard numerical approach is based on the ideas of the 'exact' time-stepping scheme. It leads to solutions free from the numerical instabilities that arise from incorrect modeling of derivatives and reaction terms. Applications to different biofilm models are examined and numerical results are presented to demonstrate the performance of the proposed new method.
authors: Department of Mathematics, University of Wyoming, PO Box 3036, Laramie, WY 82071-3036, USA. chen@cuervo.uwyo.edu
authors: B M
authors: BM
authors: Chen
authors: H V
authors: HV
authors: Kojouharov
mesh_terms: D018407:Bacterial Physiological Phenomena; D001673:Biodegradation, Environmental; D018441:Biofilms / Q000254:growth & development*; D008433:Mathematics; D008954:Models, Biological; D017711:Nonlinear Dynamics; D014874:Water Pollutants, Chemical / Q000378:metabolism
chemical_list: D014874:Water Pollutants, Chemical