Application of maccormack scheme to the study of aggradation-degradation in alluvial channels

Abstract

Aggradation and degradation are ubiquitous phenomena that occur in most alluvial channels. The complete Saint Venant equations describe the unsteady open channel /low conditions. The continuity equation for the conservation of sediment mass needs to be solved along with the hydrodynamic equations to determine aggradation and/or degradation of channel bottom. In these viewpoints, a one-dimensional mathematical model has been developed that computes the aggradation-degradation of channel bed. The MacCormack explicit finite difference scheme has been used in the model. This scheme is second-order accurate, handles shocks and discontinuities in the solution without any special treatment, and allows simultaneous solution of the water and sediment equations, thereby obviating the need for iterations. The developed model has been applied to two different case studies. The first case is a laboratory investigation where experimental results were obtained due to imposing extra sediment load. The sediment overloading produces aggradation in the channel. It has been found that the model simulates most of the test runs with a reasonable accuracy. In order to verify the ability of the model to real field situation, it has been applied to simulate Jamuna river reach from Bahadurabad to Sirajgang. A test run for three years has been done using field data for that period. The agreement between the computed results and measured data is quite satisfactory. The successful application of the model strongly demonstrates that the model is valid in solving unsteady open channel flow problems in conjunction with sediment transport. The different problems just require incorporating the appropriate initial and boundary conditions .