DEVELOPMENT OF SPLIT-OPERATOR, PETROV-GALERKIN METHODS TO SIMULATE TRANSPORT AND DIFFUSION-PROBLEMS

The rate at which contaminants in groundwater undergo sorption and des orption is routinely described using diffusion models. Such approaches , when incorporated into transport models, lead to large systems of co upled equations, often nonlinear. This has restricted applications of coupled transport and diffusion models to one-dimensional systems. Fur ther, numerical difficulties inherent in many common solution formulat ions to coupled transport and diffusion problems result in inaccurate and unreliable solutions to problems of common interest. The objective of this work was to develop methods that provide accurate and robust solutions to coupled transport and diffusion problems for single and m ulticomponent solute systems in both one and two spatial dimensions. P roblems involving pore, surface, and combined pore and surface diffusi on into spherical particles are considered. A split-operator formulati on is proposed in which the reaction operator is separated from the tr ansport operator and solved independently. Models derived from such sp lit-operator formulations to selected coupled transport and diffusion problems are shown to be robust, accurate, and computationally efficie nt. The developed split-operator approaches are also amenable to solut ion using parallel, or for some problems massively parallel, processin g methods.