Self -adaptive hierarchic finite element solution of multiphase/multicomponent transport with microbial growth and degradation.

Abstract

Many problems of environmental significance require the solution of coupled differential equations on a large domain. Often these equations predict the displacement of various fronts with time. When solving such problems numerically, methods providing greater resolution at the fronts, where one or more of the state variables are changing rapidly, are computationally desirable. By enriching the approximation, based on feedback from previous solutions, these 'self adaptive' models can produce improved solutions, in terms of both efficiency and accuracy. This dissertation presents a two dimensional self adaptive finite element model for multiphase, multicomponent reactive transport. First, a comprehensive model for the simulation of two related remediation techniques known as soil vapor extraction and bioventing is developed and demonstrated. In soil vapor extraction, volatile non-aqueous phase liquids are removed from the unsaturated zone with an externally imposed advective gas flux. In bioventing, microbial degradation of organic contaminants is enhanced by the injection of air. Illustrative simulations examining the interplay of flow rate, mass transfer parameters, and biokinetic parameters reveal aspects of system performance that cannot be predicted by previous, less comprehensive models. Contaminant fluxes to the atmosphere are shown to depend strongly on the coupling of interphase mass exchange, flow, and microbial transformation rates. Next, two adaptive techniques are applied to a modified form of the comprehensive transport simulator. Enhanced spatial resolution is achieved by increasing the order of hierarchic basis functions in selected areas of the global domain in a technique known as the p-version finite element method. Temporal adaptation is explored by solving the transport equations more frequently over a selected portion of the spatial domain, otherwise known as 'subcycling'. This is the first study to apply these techniques in combination to a set of strongly coupled non-linear transport equations of environmental significance. The adaptive model is shown to provide more accurate simulations than the non-adaptive model for a given number of degrees of freedom in simple flow domains. Comparisons of more complex two dimensional bioventing simulations reveals that the adaptive model requires 23 to 72% less computational effort than the non-adaptive model for systems with comparable degrees of freedom.