Development of An Implicit Numerical Model For Calculation of Sub-And Super-Critical Flows

A two dimensional numerical model of shallow water equations was developedto calculate sub and super-critical open channel flows. utilizing an implicit scheme thesteady state equations were discretized based on a control volume method. collocated gridarrangement was applied with a simplec like algorithm for depth-velocity coupling. apower law scheme was used for discretization of convection and diffusion terms. underrelaxationfactors were introduced in the model to prevent divergence. momentuminterpolation was used in calculating velocities on cell faces to avoid checker board watersurface fluctuation in the collocated grid. the model was verified in different casesincluding complex water surface profiles and hydraulic jumps. the results are comparedwith experimental and analytical data and the necessary values of under relaxation factorsfor a converged solution are discussed. no artificial viscosity was required, which is theadvantage of the present model.