Implicit scheme for estuarine water-quality models

Explicit integration schemes used in many water-quality models often require small time steps to satisfy stability criteria. In this paper, we demonstrate an implicit scheme; which is unconditionally stable regardless of the time-step size, for a two-dimensional box model configuration. The scheme is used with an alternating direction implicit (ADI) solution technique, which integrates the box-model mass balance equations in the longitudinal direction over the first half time step, and in the vertical direction over the next half time step. It has been successfully applied to the Patuxent Estuary water quality model with significantly reduced computational effort.