Unconditional stable numerical techniques for a water-quality model in a non-uniform flow stream

Abstract

Two mathematical models are used to simulate water quality in a non-uniform flow stream. The first model is the hydrodynamic model that provides the velocity field and the water elevation. The second model is an advection-diffusion-reaction model that provides the pollutant concentration field. Both models are formulated as one-dimensional equations. The traditional Crank-Nicolson method is also used in the hydrodynamic model. At each step, the flow velocity fields calculated from the first model are the inputs into the second model. A new fourth-order scheme and a Saulyev scheme are simultaneously employed in the second model. This paper proposes a remarkably simple alteration to the fourth-order method so as to make it more accurate without any significant loss of computational efficiency. The results obtained indicate that the proposed new fourth-order scheme, coupled to the Saulyev method, does improve the prediction accuracy compared to that of the traditional methods.