Application of a Coupling Algorithm for the Simulation of Flow and Pollution in Open Channels

A hybrid numerical scheme has been presented in this paper for channel flow simulation by coupling one-dimensional and two-dimensional models. Both 1D and 2D differential equations have been discretized by applying the finite volume cell-centered method in a collocated grid system and solved along channel axis for all sections and elements. Due to truncation, dissipation and round off errors, using numerical methods for domains with great number of elements that require huge computations may lead to some sort of divergence. This problem is highlighted, when a collocated grid system is dealt with. To reduce divergence and instability, 2D results of water level and cross section discharge have been compared with those of the 1D results where needed and adjusted properly. Double simulation provides some other advantages as described in the paper. In order to simulate a 2D flow in a channel network, a new sequential implicit scheme has been also suggested and applied. In addition to the above, 2D advection-diffusion equation has been discretized based on general finite volume method to simulate pollution. Three test cases are discussed for proving the mentioned techniques: (a) 2D flow modeling in a meandering channel with 90° bends by applying 1D-2D hybrid model, (b) 2D flow simulation at a 90° open-channel junction by applying both 1D-2D hybrid model and sequential implicit scheme at the junction and (c) tracer test in the S-curved Channel. The comparisons show the advantages of the proposed hybrid scheme for 2D flow and pollution simulation. Also the results show the ability and accuracy of sequential implicit scheme for channel network simulation.