An Implicit Scheme for Shallow Water Flow with Wet Dry Interface

A finite difference implicit scheme is presented in this paper for solution of the shallow water equations in one dimensional (1D) form. The present model has many advantages like, handling of discontinuous and complex bed topography, satisfying C-property (preservation of motionless water surface over a wet or dry bed) and capability of handling large value of temporal step etc. Another very important feature of the present model is that, no special treatment of the source vector of the governing equations is required here to deal with very less water depth. To investigate the performance of the present model in diverse situations, it is used to replicate four different problems of known analytical solution, and the model is found to be quite capable for varied situations.