ALTERNATIVE SPLIT-OPERATOR APPROACH FOR SOLVING CHEMICAL-REACTION GROUNDWATER TRANSPORT MODELS

Various schemes are available to solve coupled transport/reaction math ematical models, one of the most efficient and easy to apply being the two-step split-operator method in which the transport and reaction st eps are performed separately. Operator splitting, however, does not so lve exactly the fully coupled numerical model derived from the governi ng partial differential and algebraic equations describing the transpo rt and reaction processes. An error, proportional to Delta t (the time step used in the numerical solution) is introduced. Thus, small time steps must be used to ensure that accurate solutions result. An altern ative scheme is presented, which iterates to the exact solution of the fully coupled numerical model. The new scheme enables accurate soluti ons to be calculated more efficiently than the two-step method, while maintaining separation of the transport and reaction steps in the calc ulations. As in the two-step method, the reaction calculations are per formed node-wise throughout the computation grid. However, because the scheme relies on LU factorisation of the coefficient matrix in the tr ansport equation solution, the reaction calculations must be performed in sequence, the sequence order being determined by the ordering of t he nodes in the grid. Also, because LU factorisation is used, the sche me is limited to solute transport problems for which LU factorisation is a practical solution method. Copyright (C) 1996 Elsevier Science Li mited