Development of an Implicit Numerical Model for Calculation of Sub and Super Critical Flows

A two dimensional numerical model of shallow water equations was developed tocalculate sub and super-critical open channel flows. Utilizing an implicit scheme the steady stateequations were discretized based on control volume method. Collocated grid arrangement was appliedwith a SIMPLEC like algorithm for depth-velocity coupling. Power law scheme was used fordiscretization of convection and diffusion terms. Under relaxation factors were introduced in themodel to prevent divergence. Momentum interpolation was used in calculating velocities on cell facesto avoid checker board water surface fluctuation in the collocated grid. The model was verified indifferent cases including complex water surface profiles and hydraulic jump. The results arecompared with experimental and analytical data and the necessary values of under relaxation factorsfor a converged solution are discussed. No artificial viscosity was required, which is the advantage ofthe present model.