Browsing by Author "Dawson, C.N."
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Item An Operator-Splitting Method for Advection-Diffusion-Reaction Problems(1987-05) Wheeler, M.F.; Dawson, C.N.Item Asymptotic Profiles with Finite Mass in One-Dimensional Contaminant Transport Through Porous Media: The Fast Reaction(1992-04) Grundy, R.; van Duijn, C.J.; Dawson, C.N.Item Characteristic-Galerkin Methods for Contaminant Transport with Non-Equilibrium Adsorption Kinetics(1992-08) Dawson, C.N.; van Duijn, C.J.; Wheeler, M.F.A procedure based on combining the method of characteristics with a Galerkin finite element method is analyzed for approximating reactive transport in groundwater. In particular, we consider equations modeling contaminant transport with nonlinear, non-equilibrium adsorption reactions. This phenomena gives rise to non-Lipschitz but monotone nonlinearities which complicate the analysis. A physical and mathematical description of the problem under consideration is given, then the numerical method is described and a priori error estimates are derived.Item Large Time Asymptotics in Contaminant Transport in Porous Media(1994-11) Dawson, C.N.; van Duijn, C.J.; Grundy, R.E.In this paper we derive large time solutions of the partial differential equations modelling contaminant transport in porous media for initial data with bounded support. While the main emphasis is on two space dimensions, for the sake of completeness we give a brief summary of the corresponding results for one space dimension. The philosophy behind the paper is to compare the results of a formal asymptotic analysis of the governing equations as t -> infinity with numerical solutions of the complete initial value problem. the analytic results are obtained using the method of "asymptotic balancing" which identifies the dominant terms in the model equations determining the behaviour of the solution in the large time limit. These are found in terms of time scaled space similarity variables and the procedure results in a reduction of the number of independent variables in the original partial differential equation. This generates what we call a reduced equation the solution of which depends crucially on the value of a parameter appearing in the problem. In some cases the reduced equation can be solved explicitly while in others they have a particularly intractable structure which inhibits any analytic or numerical progress. However we can extract a number of global and local properties of the solution which enables us to form a reasonably complete picture of what the profiles look like. Extensive comparison with numerical solution of the original initial value problem provides convincing confirmation of our analytic solutions. In the final section of the paper, by way of motivation for the work, we give some results concerning the temporal behaviour of certain moments of the two dimensional profiles commonly used to compute physical parameter characteristics for contaminant transport in porous media.Item Modeling of in situ Biorestoration of Organic Compounds in Groundwater(1990-10) Chiang, C.Y.; Dawson, C.N.; Wheeler, M.F.A convergent numerical method for modeling in situ biorestoration of contaminated groundwater is outlined. This method treats systems of transport-biodegradation equations by operator splitting in time. Transport is approximated by a finite element modified method of characteristics. The biodegradation terms are split from the transport terms and treated as a system of ordinary differential equations. Numerical results of vertical cross-sectional flow are presented. The effects of variable hydraulic conductivity and variable linear adsorption are studied.Item Several Procedures for Operator-Based Averaging for Elliptic Equations(1992-08) Dawson, C.N.; Dupont, T.F.Numerical procedures are discussed for constructing averaged coefficients for elliptic differential operators. These procedures are intended for problems where the coefficients vary on a scale finer than can be resolved by a reasonable computational grid. Numerical methods for calculating locally averaged coefficients using mixed and Galerkin finite elements are presented. These methods involve solving local elliptic problems either to determine a pseudo-coefficient or as part of the overall solution procedure. The local problems are independent and can be solved in parallel. The procedures are formulated and numerical results demonstrating their performance are presented.Item Some Improved Error Estimates for the Modified Method of Characteristics(1988-01) Dawson, C.N.; Russell, T.F.; Wheeler, M.F.Item The Rate of Convergence of the Modified Method of Characteristics for Linear Advection Equations in One Dimension(1988-03) Dawson, C.N.; Dupont, T.F.; Wheeler, M.F.Item Time-Splitting for Advection-Dominated Parabolic Problems in One Space Variable(1987-11) Wheeler, M.F.; Dawson, C.N.; Kinton, Wendy A.