Browsing by Author "van Duijn, C.J."

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    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.
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    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.