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 to calculate sub and super-critical open channel flows. Utilizing an implicit scheme the steady state equations were discretized based on a control volume method. Collocated grid arrangement was applied with a SIMPLEC like algorithm for depth-velocity coupling. A power law scheme was used for discretization of convection and diffusion terms. Underrelaxation factors were introduced in the model to prevent divergence. Momentum interpolation was used in calculating velocities on cell faces to avoid checker board water surface fluctuation in the collocated grid. The model was verified in different cases including complex water surface profiles and hydraulic jumps. The results are compared with experimental and analytical data and the necessary values of under relaxation factors for a converged solution are discussed. No artificial viscosity was required, which is the advantage of the present model.