Fractional step solution to slack tide oxygen balance equation

A time-stepping split-operator method is developed to obtain the steady-state solution of the slack tide oxygen balance equation, which takes different formulations at the aerobic and the anaerobic regions, while the direct iterative solution of the steady-state equation can lead to an oscillatory behaviour. The method treats the advection step by the minimax characteristics method, the dispersion step by the central difference method, and the decay step by an analytical solution. Using a large time step (1 tidal cycle) to be compatible with the model formulation, the solution obtained is in good agreement with the exact solution and the computational effort is low.