The Numerical Method For The Model Of The Mixture Of Water And Silt In R～2

The modelling of the mixture of water and silt is a branch of river simulation and it is an important tool to predict the movement of water and silt and the change of the bottom topography. Recently, its numerical simulation has aroused much attention of the hydrodynamic engineers. Since it can describe the formation and development of the delta and expansion of the sediment. Based on the information provided by the numerical simulation ,the decision can be made on flood control and the construction and the reinforce of the bank.The model of the transportation of mixture of water and silt is governed by the following system, Water continuity equationWater dynamic equationsSilt transport equationThe equation of bottom topography change7^ = ^(5-5,), (le)otIn this paper, we simulate the transportation of the mixture of water and silt in two dimensional space by a characteristics-difference method , prove the existence and uniqueness of the discrete solution .Through a delicate analysis, we obtain L2-error estimates for the unknown functions.